Grade 2 Teacher's Edition - Chapters 1-6

Using the Book: pages 99-100 Adding to the Next Ten Complete the number line. Write the sum. 36 + 34 = 70 We make two jumps. 1. +12 First we jump the tens. 6 and Then we jump to get to 36 68 + 12 = 68 +2 4 make + 34 78 80 a ten. the next ten. 70 2. +24 +34 +30 +4 46 + 24 = 46 +4 66 70 We have 7 tens in all. 36 66 70 Complete the number line. Fill in the sum. 3. +33 1. 27 + 10 = 37 2. 27 + 13 = 40 37 + 33 = +3 CENTRALE LYON 37 CENTRALE LYON 67 70 +13 Help the number machine add. Fill in the sums. 27 37 27 +3 4. +24 4 CENTRALE LYON 3. 48 + 30 = 78 37 40 46 26CENTRALE LYON 50 48 78 5. 37 + 20 = 57 4. 48 + 32 = 80 5. CENTRALE LYON 37 57 46 4 CCEENNTTRRAALLEE LLYYOONN +32 66 70 +2 6. 76 4 80 48 78 80 56 6. 37 + 23 = 60 LET’S WRITE! +23 +3 Look at the sums that came out of your number machine. How are they 57 60 the same? How are they different? Explain why. 37 All are decade numbers, but the tens are different, because we started with different decade numbers. Chapter 3 Lesson 13 99 100 Now let’s practice adding two-digit numbers on the number Point out that the problems on page 99 are presented in line. First we jump the tens then we jump the ones. When the sets; solving the first problem will help them to solve the sum of the ones is ten, we will need to jump to the next ten. second problem. Have the students draw over the gray loops so that they can For the Let’s Write section, discuss the patterns students see “feel” the jumping on the number line. in the number machine, and encourage them to describe When students are tracing the loops, be sure that they these patterns. trace and solve sequentially.Copyright © by SPOTS Educational Resources. All rights reserved. on the number line. And when we add tens and ones, we DIFFERENTIATED INSTRUCTION make two jumps, one for the tens and one for the ones. If the ones together make another ten, the second jump will reach Struggling learners: Practice adding to a sum of ten. This the next ten. will help students identify, without counting, whether a set of addends will equal the next ten. STUDENT TEACHER On the board write 38 + 40, 37 + 20, 46 + 34, 65 + 10, 55 + 25, CLOSING STATEMENT: and 79 + 11. Ask students to tell in which number sentences they will add only the tens and in which they will add both What did we learn today? Today we added 2 two-digit tens and ones (add only tens: 38 + 40, 37 + 20, 65 + 10; add numbers, adding to the next ten using a number line. tens and ones: 46 + 34, 55 + 25,79 + 11). Have each student choose one of the problems and solve it by drawing and Tomorrow we will practice this more. filling in a number line. Then ask volunteers to come up to the board in turn to show and explain their work. 97

Chapter 3 Lesson 14: Practice: Adding to the Next Ten INTRODUCTORY STATEMENT: II. Adding two-digit numbers by forming Copyright © by SPOTS Educational Resources. All rights reserved. Yesterday we learned to add to the next ten. another ten on the number line Today we will practice this. Write 48 + 32 = ___ on the board. Say: This is almost the same as the number sentence we just solved. Will the sum of this GOAL: number sentence also be in the 70s? [no] How can you know? [I can add the ones in my head, and I know that 8 + 2 = Students will practice adding two-digit numbers using 10, so the sum will be in the next ten.] Let’s show this on the the number line and mental math. number line. [Have students guide you through the steps as Materials needed: blank poster paper; two-digit addi- you model it on the number line, as above.] tion equation cards (see Student Teacher section) III. Deciding whether we will get to the nextCommon Core Standard: CCSS2.NBT.5; CCSS2.NBT.7; ten when we addCCSS2.MD.6 On the board write 57 + 22 = ___ and 57 + 23 = ___. Say: In LESSON WARM-UP both of these number sentences we are adding tens and ones. In one of them, when we add the ones we will make a new ten. Add Review facts for fluency using the My Math Facts the ones in your head, and tell me in which number sentence we practice sheets. will make a new ten. [57 + 23] How do you know? [I added the ones: 7 + 3 = 10.] [Together with the class, find the sums of THINKING TRIGGER both of the equations on a number line. Have students tell you the starting number, the landing numbers, and the sum Write 38 + 21 and 38 + 22 on the board. Ask the stu- of each. Complete the number sentences to show 57 + 22 = dents how they would solve each of these equations. 79 and 57 + 23 = 80.]CONCEPT DEVELOPMENT Repeat this with 44 + 32 and 44 + 36. Lead students to determine in advance whether they will or will not get to theI. Adding two-digit numbers using next ten when adding the ones in each equation. the number line STUDENT TEACHEROn the board, write 48 + 31 = ___, and draw an open numberline that you can fill in as you go along. Discuss what is Divide the class into groups of four. Give each group twobeing added (both tens and ones). As you go through the sheets of poster paper and 2 two-digit addition equationsteps, have the students guide you in how to show this on a cards – one whose ones make a new ten and one whosenumber line. Have them tell you what the starting number ones do not make a new ten, such as 27 + 22 = ___ and 27is (48), how many tens we need to jump (3), where we get + 23 = ___; or 54 + 12 = ___ and 54 + 16 = ___. Instruct theto when we add the tens (78), how many ones we need to groups to write one equation on one sheet of poster paperjump (1), and what the sum is (79). Fill in the sum in both the and the other equation on the other sheet, and to use anumber line and the number sentence. number line to solve each equation. Have groups present their work to the class, comparing the solutions of the two equations. You might choose to display some posters on your math bulletin board.98

Using the Book: pages 101-102 Practice: Adding to the Next Ten CENTRALE LYON CENTRALE LYON CENTRALE LYON Complete the number line. Write the sum. Help the number machines add. Fill in the sums. 1. 47 + 21 = 68 +21 1. +14 35 4 +1 25CENTRALE LYON 39 49 47 67 68 89 2. 47 + 23 = 70 +23 2. +4 CCEENNTTRRAALLEE LLYYOONN 69 47 CENTRALE LYON 79 +3 35 45 99 67 70 3. 3. 68 + 21 = 89 +21 85 +4 CENTRALE LYON 68 75CENTRALE LYON +23 +1 66 88 89 Error! Student book shows 7, should be 75. 76 CENTRALE LYON 4. 4. 68 + 22 = 90 +22 3 68 CENTRALE LYON +2 3 CCEENNTTRRAALLEE LLYYOONN 88 90 46 5. 36 + 32 = 68 +32 5. CENTRALE LYON +2 56 36 66 68 6. 76 96 3 6. 36 + 34 = 70 +34 Let’s Review! 36 +4 Identify the missing addend. 7. 45 + 35 = 80 66 70 7.37 + 3 = 40 8. 52 + 8 = 60 9. 86 + 4 = 90 Chapter 3 45 +35 107. 4 + 6 = 80 11. 15 + 5 = 20 12. 68 + 2 = 70 Lesson 14 +5 102 75 80 101 Now let’s practice adding two-digit numbers on the number Remind the class that the number machine works in a way line. First we jump the tens, then we jump the ones. When the that is very similar to number lines. Make sure the students sum of the ones is a ten, we will need to jump to the next ten. understand which numbers are the addends. Have the students draw over the loops, so that they can On page 102, problems 7-12, the students will review find- “feel” the jumping. When students are tracing the loops, ing the missing addend. The ability to find missing addends be sure that they trace and solve sequentially. that form the next ten will help prepare them for solving addition problems that require three jumps. Point out that the problems on page 101 are arranged in sets. Solving the first problem will help them solve the second problem.Copyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Some students may find it hard to Today we practiced adding with two-digit make one jump to add all the tens at once. Suggest that numbers by making two jumps on a number line. they can underline the tens in each of the addends and count on for that number of tens as they make the jump. Tomorrow we will add two-digit numbers Also practice adding with addends that have a sum of by making three jumps on a number line. ten. This will help students identify, without counting, whether a set of addends will equal the next ten. 99

Chapter 3 Lesson 15: Adding with Three Jumps INTRODUCTORY STATEMENT: II. Adding with Dot Cards We’ve already learned how to add 2 two-digit numbers by making two jumps on the number line. Remind students that they can use Dot Cards to add two- Today we will add 2 two-digit numbers by making digit numbers. Write 37 + 25 = ___ on the board. Say: Let’s add 37 + 25 using Dot Cards. [Show 37 using Dot Cards with black three jumps on the number line. dots.] Here we have 3 tens and 7 ones. [Now show 25 using Dot Cards with white dots and counters, aligning the tens and the GOAL: ones.] Here we have 2 tens and 5 ones. How many tens in all? [5 tens] We need to add 7 ones and 5 ones. Let’s make another ten Students will add with three jumps on the number line – with 7 ones and…how many more ones? [3] [Move three of using mental math. the white counters onto the Dot Card-7.] How many ones do Materials needed: Dot Cards and counters; blank we have left over? [2] So, how many tens and ones do we have sheets of paper or dry-erase boards now? [6 tens and 2 ones] What is the sum of 37 and 25? [62] [Complete the number sentence:] 37 + 25 = 62.Common Core Standard: CCSS2.NBT.5; CCSS2.NBT.7;CCSS2.MD.6 III. Adding by making three jumps LESSON WARM-UP Refer to the completed number sentence that is already on Copyright © by SPOTS Educational Resources. All rights reserved. the board – 37 + 25 = 62. Say: We can find the sum using a Review facts for fluency using the My Math Facts number line as well. [Draw an open number line, and fill it practice sheets. in as you go along.] What is our starting number? [37] What jump do we make first? [the tens] How many tens are there in THINKING TRIGGER 25? [2 tens, or 20] [Draw a long jump and label it +20.] What number did we get to? [57] [Write 57 on the number line.] What can we use to help us find the sum of 58 + 25? What do we need to do next? [jump the ones] How many ones are there in 25? [5] In 57 there are 7 ones, and we need toCONCEPT DEVELOPMENT add 5 ones to that. The sum of 7 + 5 is more than ten, so our sum will be in the next ten. So, let’s make a jump to get to theI. Review adding with two jumps on the next ten. How much do we need to jump from 57 to get to the number line next ten? 7 plus what equals 10? [3] We need to jump 3 to get to the next ten. [Draw a jump and label it +3.] What is the nextOn the board draw an open number line, and write 37 + 23 ten? [60] [Fill in 60.] We added 3, but we’re not done yet. What= ___. Ask: Will we make one jump or two jumps when we add is left for us to do? [We need to make one more jump to add37 and 23? [two jumps] How do we know? [We are adding the rest of the ones.] We needed to add 5 ones, and we’veboth tens and ones.] Will the sum have tens and ones or only already added 3 ones to get to 60. How many more ones do wetens? [only tens] How do we know? [We know that 7 + 3 = need to add? [2] So what is our next jump? [2] [Draw the third10.] What is our starting number? [37] [Write 37 at the start of jump and label it +2.] What is our sum? [62] [Fill in 62 as thethe number line.] Let’s jump the tens first. How many tens are sum on the number line and in the equation.]in 23? [2] [Draw one long jump and label it +20.] Where didwe get to on the number line? [57] We’ve landed on 57, but are In the same way, solve 46 + 26.we done? [no] What do we need to do next? [We need to makeanother jump for the ones.] How many ones are there in 23? STUDENT TEACHER[3] [Draw the jump and label it +3.] We are at 57 now, and weneed to jump 3 ones. Where do we land? What is the sum? [60] Give each pair of students a card with sets of 2 two-digit[Fill in 60 as the sum on the number line and as the sum in addition equations – one that can be solved making twothe equation.] Now we see that 37 + 23 = 60. jumps on a number line and one that can be added using three jumps on a number line; (e.g., 36 + 44 and 36 + 47 3 jumps). Have the students solve each set using number lines. Review their work. Ask: When did you use two jumps to solve? When did you use three jumps?100

Using the Book: pages 103-104 Adding with Three Jumps 28 + 26 = 5 4 We make three jumps. Complete the number line. Fill in the sum. First we jump the tens. Then we jump to get 1. 59 + 21 = 80 +21 59 8 and to the next ten. +1 2 form Then we jump again for 79 80 a ten. the rest of the ones. 2. 59 + 28 = 87 +28 +26 +2 +4 59 79 80 +7 +20 48 50 54 87 We have 5 tens 28 3. 48 + 32 = 80 +32 and 4 ones in all. 48 +36 Complete the number line. Fill in the sum. 4. 48 + 36 = 84 +2 48 78 80 1. 39 + 21 = 60 +21 +4 39 59 60 78 80 84 2. 39 + 26 = 65 +26 5. 68 + 22 = 90 +22 +25 39 59 60 65 68 +2 3. 58 + 12 = 70 +12 6. 68 + 25 = 93 +30 88 90 58 68 70 68 +3 4. 58 + 14 = 72 +14 88 90 93 7. ON YOUR OWN! 58 68 70 72 57 + 35 = 92 +3 +2 57 87 90 92 Chapter 3 Lesson 15 103 104 Now let’s practice adding two-digit numbers on the Point out that the problems on both pages are arranged in number line. When the sum of the ones will be more than sets. Solving the first problem will help to solve the second ten, we will need to make three jumps: first a jump for the problem. Tell the students that on page 103 they need to tens, next a jump to get to the next ten, and last, a jump fill in only the landing numbers, since the number for each for the rest of the ones. jump is labeled on every number line. On page 104 students Have the students draw over the loops so that they will need to determine the number for the final jump. can “feel” the jumping. When students are tracing the loops, be sure that they trace and solve sequentially: (Adding with three jumps might be too challenging for some 1) Trace the first loop and write in the first jump, and students. When working with the Student Edition, guide solve. 2) Trace the second loop, write in the second them step-by-step. Explain that they will soon learn anoth- jump, and solve. 3) Trace the third loop, write in the er strategy [column addition with regrouping], which they third jump, and solve for the final sum. might find easier.Copyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: What did we learn today? Today we added 2 two-digit Struggling learners: Some students may need to review adding ones to decade numbers to help them easily numbers, making three jumps on the number line. process the final jump to the sum. Practice by modeling Tomorrow we will practice this more. with Dot Cards for the tens in black, and white counters for the ones, and then provide equations on the digit-lev- 101 el as well. You may also create number-line problems for adding ones to decade numbers to solve with one jump for the ones. Also, review reverse facts, such as 83 = 80 + 3, as taught in Chapter 2 Lesson 3 (Expanded Form).

Chapter 3 Lesson 16: Practice: Adding with Three Jumps INTRODUCTORY STATEMENT: for us to do? [We need to make one more jump to add the Yesterday we found the sum of 2 two-digit numbers rest of the ones.] We needed to add 7 ones, and we’ve already added 1 one to get to 70. How much more do we need to jump by making three jumps on the number line. for the rest of the ones? [6] [Draw the third jump and label it Today we will practice this. +6.] What is our sum? [76] [Fill in 76 as the sum on the number line and in the number sentence.] 49 + 27 = 76. GOAL: II. Practice Students will practice adding two-digit numbers with three jumps on the number line using mental math. On the board write 48 + 18 and 66 + 25. Draw a number line Materials needed: blank sheets of paper or dry-erase under each. Ask: Are we adding tens, ones, or both? [both] boards Have students tell you how to use the number line to find the sum for each number sentence. Discuss the three jumpsCommon Core Standard: CCSS2.NBT.5; CCSS2.NBT.7; as you first jump the tens, then jump ones to get to the nextCCSS2. MD.6 ten, and last, jump more for the rest of the ones. LESSON WARM-UP STUDENT TEACHER Review facts for fluency using the My Math Facts Write 48 + 26 on the board. Call up four students, one at a practice sheets. time, to show how to solve the problem using the number line. Have the first student draw the number line and fill in THINKING TRIGGER the starting number. Have the second student draw the first jump to add the tens, label it (+20), and solve (68). Have the Think of a number sentence with 2 two-digit numbers that third student draw the second jump to show getting to the can be solved using three jumps on the number line. next ten, label it (+2), and solve (70). Have the fourth student show the third jump for the rest of the ones, label it (+4), and solve to find the sum (74).CONCEPT DEVELOPMENT Copyright © by SPOTS Educational Resources. All rights reserved.I. Adding with three jumps on the number lineWrite 49 + 27 = ___ on the board. Say: Let’s review using thenumber line to find the sum. [Draw an open number line andfill it in as you go along.]What is our starting number? [49] What jump do we make first?[the tens] How many tens are there in 27? [2 tens, or 20] [Drawa long jump and label it +20.] What number did we get to onthe number line? [69] [Write 69 on the number line.] What dowe need to do next? [jump the ones] How many ones are therein 27? [7] In 69 there are 9 ones, and we need to add 7 to that.Will our sum be in the next 10? [yes] How do you know? [Thesum of 9 + 7 is more than 10.] So, let’s make a jump to get tothe next ten. How much do we need to jump from 69 to reachthe next ten? [1] [Draw a small jump and label it +1.] What isthe next ten? [70] [Fill it in.] Are we done yet? [no] What is left102

Using the Book: pages 105-106 Practice: Adding with Three Jumps Complete the number line. Fill in the sum. Complete the number line. Fill in the sum. 1. 27 + 25 = 52 +25 1. +36 47 + 36 = 83 +3 +3 27 47 77 80 83 2. 38 + 17 = 55 +17 +5 2. +14 55 +2 58 + 14 = 72 +2 +2 38 48 50 58 68 70 72 3. 46 + 35 = 81 +35 3. +25 46 +4 +1 36 + 25 = 61 +4 +1 76 80 81 36 56 60 61 4. 69 + 27 = 96 +27 ON YOUR OWN! +1 +6 4. 67 + 27 = 94 69 89 90 96 67 +20 +3 +4 87 90 94 5. 57 + 34 = 91 +34 57 +3 +1 Fill in the math puzzle and write the number sentence. 87 90 91 Use a for the unknown number. Solve. 6. 36 + 26 = 62 +26 5. The library has 25 children’s books and 45Whole 36 20 adult books on the display shelf. 20 25 +4 +2 56 60 62 How many books are there on the shelf? Part Part 7. 78 + 15 = 93 +15 Number sentence: 25 + 20 = 45 There are __4_5__ books on the shelf. +2 +3 78 88 90 93 Chapter 3 Lesson 16 105 106 Now let’s practice adding two-digit numbers on the number to do even with guidance. This is to be expected; students line. When the sum of the ones will be more than ten, we will should not be pressured. need to make three jumps: first a jump for the tens, next a jump to get to the next ten, and last, a jump for the rest of Read the story problem on page 106 together. Guide stu- the ones. dents to first fill in the puzzle with the numbers they know and to use a box for the unknown number. Next, have them Have the students draw over the loops so that they can write the number sentence, again using a box for the un- “feel” the jumping. When they are tracing the loops, be known number, and solve it. Finally, have them fill in the sure that they trace and solve sequentially. sum in the math puzzle, so that they can see the relation- ship between all the numbers in the problem. On Your Own should be teacher- guided with step-by-step instructions. Some students may find this too challengingCopyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Using flashcards, have students What did we learn today? Today we practiced adding practice solving missing-addend problems so that they 2 two-digit numbers with three jumps on the number review how much is needed to get to the next ten. line. Tomorrow we will add 2 two-digit numbers using either two jumps or three jumps on the number. 103

Chapter 3 Lesson 17: Drawing either Two or Three Jumps INTRODUCTORY STATEMENT: In the same way, solve together 25 + 44. Lead students to Copyright © by SPOTS Educational Resources. All rights reserved. We’ve already learned how to add 2 two-digit understand that for both this number sentence and the numbers by making either two jumps or three previous number sentence, when they add the ones, they do jumps on the number line. Today we will practice not make another ten. So they will make two jumps on the that, and we’ll talk about deciding how many number line – one jump to add the tens, and the other jump to add the ones. jumps we need to make. II. Adding with three jumps GOAL: Write 49 + 48 = ___ on the board. Draw an open number line, Students will add 2 two-digit numbers on the number and fill it in as you go along. Say: Let’s see how many jumps we line using mental math. will make to find this sum. [Elicit answers, and have students Materials needed: No materials needed for this lesson explain their thought processes.] Let’s find out. What is our starting number? [49] First we jump the tens. How many tensCommon Core Standard: CCSS2.NBT.5; CCSS2.NBT.7; are there in 48? [4 tens, or 40] [Draw a long jump and label itCCSS2.MD.6 +40.] Where do we get to? [89] [Write 89 on the number line.] Now, let’s jump to add the ones. How many ones are there in 48? LESSON WARM-UP [8] When we add the 8 ones, will the sum be in this ten or in the next ten? [in the next ten] How much do we need to jump from Review facts for fluency using the My Math Facts 89 to reach the next ten? [1] [Draw the next jump and label it practice sheets. +1.] Where do we get to? [90] We needed to add 8 ones. So far, we’ve added 1 to get to 90. How much more do we need to jump THINKING TRIGGER to add the rest of the ones? [7] [Draw the third jump and label it +7.] Where did we get to? What is our sum? [97] [Fill in 97 in Think of two number sentences with 2 two-digit num- the number line and as the sum in the number sentence.] bers, one that can be solved by making two jumps on the number line and the other by making three jumps. In the same way, solve together 57 + 27. Lead students to understand that for both this number sentence and theCONCEPT DEVELOPMENT previous number sentence, we make three jumps to find the sum: First we jump the tens, then we jump as many ones as weI. Adding with two jumps on the number line need to get to the next ten, and last, we make another jump for the rest of the ones.Write 53 + 32 = ___ on the board. Say: Let’s use a number lineto find the sum. [Draw an open number line, and fill it in as III. Adding with two or three jumpsyou go along.] How many jumps do you think we will make to on the number linefind the sum? [Elicit answers, and have students explain theirthought processes.] Let’s find out. What is our starting number? On the board write 57 + 32 = ___ and 57 + 35 = ___, and[53] [Write 53 at the start of the number line.] Let’s jump all draw a number line under each. Ask: What is similar aboutthe tens at once. How many tens are in 32? [three] [Draw a long these two number sentences? [The first addend is the samejump and label it +30.] Where did we get to on the number line? in both number sentences.] What is different? [The number[83] [Write in 83.] We’ve landed on 83, but are we done yet? of ones in the second addend is different.] How many jumps[no] What do we have left to do? [We need to make one more do you think we will make to find each sum? [Elicit responses.]jump to show adding on the 2 ones that are left.] [Draw a Let’s find out. [Together with the class, solve each equation onsmall jump and label it +2.] We are at 83 now, and we need to the number line.]jump 2. Where do we land? What is the sum? [85] [Fill in 85 asthe sum on the number line and in the equation.] Our sum is Draw student’s attention to the two completed number85. 53 + 32 = 85. How many jumps did we make to find the sum? sentences on the board. Ask: How can you tell, just by looking[two – one jump for the tens and one jump for the ones] at each of these number sentences, whether we will need to make two jumps or three jumps to find the sum? [If adding the ones will give us a sum that is more than ten, we will need to make three jumps; if not, we will make only two jumps.]104

Using the Book: pages 107-108 Drawing with Two or Three Jumps Sometimes we make 2 jumps. Complete the number line.Use either two or three jumps. Write the sum. Circle how many jumps. +32 64 + 32 = 96 +30 +2 1. 37 + 26 = 63 37 +26 63 64 94 96 2 jumps 2 jumps +3 +3 3 jumps 3 jumps 57 60 46 + 45 = 91 Sometimes we make 3 jumps. 2. 57 + 36 = 93 57 +36 2 jumps +45 2 jumps +3 +3 3 jumps +40 +4 +1 3 jumps 87 90 93 46 86 90 91 Complete the number line. Use either 2 or 3 jumps. Write the sum. 3. 74 + 24 = 98 74 +24 Circle how many jumps. 2 jumps +4 1. 47 + 21 = 68 +21 3 jumps 94 98 2 jumps +1 4. 45 + 35 = 80 +35 3 jumps 47 67 68 +5 75 80 2. 68 + 25 = 93 +25 2 jumps 45 3 jumps 2 jumps +2 +3 3 jumps 68 88 90 93 5. 59 + 38 = 97 +38 3. 67 + 15 = 82 +15 2 jumps +1 +7 3 jumps 2 jumps 77 +3 +2 59 89 90 97 3 jumps 80 82 67 +24 ON YOUR OWN! +4 6. 53 + 41 = 94 4. 35 + 24 = 59 55 59 +40 +1 93 94 2 jumps 35 2 jumps 53 3 jumps 3 jumps 108 Chapter 3 Lesson 17 107 Now let’s practice adding two-digit numbers using either Refer students to problem 6, On Your Own, on page 108. two jumps or three jumps on the number line. Challenge student to complete it independently without teacher guidance. Some students may not be able to do this modeling without guidance. This is to be expected.Copyright © by SPOTS Educational Resources. All rights reserved. STUDENT TEACHER CLOSING STATEMENT: On the board write a list of addition number sentences with 2 Today we found the sums of 2 two-digit numbers two-digit numbers. Point to each equation and ask students using either two jumps or three jumps on the to clap their hands two times if we will make two jumps on number line. Tomorrow we will add two-digit the number line and three times if we will make three jumps numbers in columns. on the number line. DIFFERENTIATED INSTRUCTION Advanced learners: Write problems with two or three jumps, and have students solve them on number lines on their own. 105

Chapter 3 Lesson 18: Adding in Columns INTRODUCTORY STATEMENT: II. Adding in columns without Dot Cards Copyright © by SPOTS Educational Resources. All rights reserved.Yesterday we added two-digit numbers with number lines; first we jumped the tens, then we jumped the In a place-value chart, write 34 + 42 on the board. Say: Notice how I made sure that the ones digits are lined up and the tens ones. Today we will add two-digit numbers in col- digits are lined up. Now we’re ready to find the sum! First we addumns, first adding the ones and then adding the tens. the ones. How many ones in all? [6] [Write 6 in the ones place of the sum.] Next, let’s add the tens: 3 + 4 = 7. [Write the 7 in the GOAL: tens place of the sum.] The sum of 34 + 42 is 76. Students will use place value to add two-digit numbers In the same way, solve together 41+ 26. in columns. MATERIALS NEEDED: Dot Cards and counters Summarize: When we add in columns, first we add the ones and then we add the tens.Common Core Standard: CCSS2.NBT.5 III. Adding in columns to solve story LESSON WARM-UP problems Review facts for fluency using the My Math Facts Tell an addition story problem: The children counted 15 sunny practice sheets. days in March and 24 sunny days in April. How many sunny days did they count in all? THINKING TRIGGER Let’s solve this problem together. [Elicit what they know and Write 48 + 31 on the board. Ask a volunteer to show what they want to find out.] How do you know what operation how to find the sum using Dot Cards. Say: We can also to use? [Elicit suggestions.] We want to know how many sunny find the sum by adding in columns. days in all, so we will add. [In column form, write the equation 15 + 24.] Now let’s add in columns. What should we add first?CONCEPT DEVELOPMENT [the ones column] How many ones in all? [9] [Write 9 in the ones place in the sum.] Now we can add the tens: 1 + 2 = 3.I. Adding two-digit numbers using Dot Cards [Write the 3 in the tens place in the sum.] What is the sum of 15 and 24? [39] The children counted 39 sunny days in all.Use Dot Cards to add two-digit numbers, and relate this toadding in columns. On the board, write 25 + 23 in a place- Tell another addition story and solve it with the class: Stuart’svalue chart. Alongside the problem, in another place-value younger sister weighs 35 pounds. Stuart weighs 52 pounds. Howchart, represent 25 using Dot Cards (with black dots). Place many pounds do the two children together weigh?Dot Cards showing 23 (with white dots) below these sothat the tens and ones are aligned. Say: Let’s find the sum by What operation should we use to solve the problem? [addition]adding in columns. When we add in columns, we first add the [Draw a blank place-value chart on the board, and fill it inones. What is 5 + 3? [8] There are 8 ones. [Record the 8 in the with students’ input, as above. Guide them through the twoones column of the sum. Point to the 2 in 25.] How many tens steps for adding in columns.] The two children together weighare there in 25? [2] [Point to the 2 in 23.] How many tens are 87 pounds.there in 23? [2] How many tens in all? [4] [Record the 4 in thetens column of the sum.] What is the sum of 25 + 23? [48] STUDENT TEACHERIn the same way, solve together 58 + 21, using Dot Cardsas support. Lead students to understand that to find the On the board write, horizontally, in a number-sum when adding in columns, first add the ones; second, add sentence format, some two-digit addition equations, such asthe tens. 48 + 31, 54 + 32, and 63 + 41. Call on volunteers to come to the board and write the equations in column form. Have the class find the sums and say them aloud while the volunteers record them. Guide the discussion, having students explain the two steps needed to add in column form: 1) add the ones; 2) add the tens.106

Using the Book: pages 109-110 Adding in Columns Add. 2. Tens Ones 3. Tens Ones 4. Tens Ones We can add in columns. 1. Tens Ones 67 72 53 +3 2 +2 4 +3 6 Tens Ones First we add the ones. 46 Then we add the tens. +2 1 99 96 89 36 +2 3 67 59 5. Tens Ones 6. Tens Ones 7. Tens Ones 8. Tens Ones Add. Remember to start with the ones. 45 25 86 53 +2 3 +2 4 +1 2 +2 3 68 49 98 76 1. Tens Ones 2. Tens Ones 3. Tens Ones 9. Tens Ones 10. Tens Ones 11. Tens Ones 12. Tens Ones 34 72 55 52 42 44 31 +3 2 +1 3 +2 4 +2 6 +3 5 +3 1 +2 7 66 85 79 78 77 75 58 6. Tens Ones Solve the story problem. 47 + 32 4. Tens Ones 5. Tens Ones 41 13. The children at the lemonade stand sold 47 small +2 5 cups of lemonade and 32 large cups of lemonade. 79 52 64 +1 7 +3 5 66 How many cups of lemonade did they sell in all? 69 99 9. Tens Ones They sold 79 cups of lemonade in all. 7. Tens Ones 8. Tens Ones 62 LET’S WRITE! +3 2 72 24 Explain how you added to solve the story problem. +2 6 +2 4 94 Sample answer: I added the number of small cups and large cups. 98 48 109 First I added the ones, then I added the tens. Chapter 3 Lesson 18 110 Now let’s practice adding two-digit numbers in columns. Read the story problem together, and guide the students When we add in columns, first we add the ones, then we add as they write and solve the equation. Explain that in the Let’s the tens. Write section they will write in their own words how they solved the problem. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Some students may forget to start Who can tell us what we learned today? with the ones when adding two-digit numbers in col- Today we found the sums of two-digit numbers umns. Before they begin, have them highlight the ones by adding in columns. Tomorrow we will practice column in each problem on the student pages. Then adding two-digit numbers in columns when the sum remind them to start by adding the highlighted column. Most likely, this support will be necessary only at this of the ones will be a teen number. early stage of their learning.Copyright © by SPOTS Educational Resources. All rights reserved. 107

Chapter 3 Lesson 19: Adding in Columns with Regrouping INTRODUCTORY STATEMENT: To remember that we made a new ten, we will write a small Yesterday we added two-digit numbers in columns. number 1 above the tens column. [Fill in the small 1.] Since we have 5 ones left after making the new ten, we will write a 5 in Today we will add two-digit numbers in columns the ones column of the sum. [Fill in the 5.] Now we are finished when the sum of the ones will be more than ten. adding the ones. Let’s add the tens. [Point at the small 1.] How many new tens did we make? [1] How many tens are there in GOAL: 28? [2] How many tens are there in 27? [2] How many tens in all? [Solve together: 1 + 2 + 2 = 5.] [5] [Record the 5 in the tens Students will use place value to add two-digit numbers column of the sum.] What is the sum of 28 + 27? [55] in columns. MATERIALS NEEDED: Dot Cards and counters; blank Introduce the term“regrouping.”Say: What we just did is called sheets of paper or dry-erase boards “regrouping.” Regrouping means that we move over one part of a number and have it join another group. So, when we areCommon Core Standard: CCSS2.NBT.5; CCSS2.NBT.7, adding and we reach ten, we take the new ten that we made,CCSS2.NBT.9 and we regroup – we move it over to join the group of tens in the tens column. The rest of the ones (the counters) from the teen LESSON WARM-UP number are left in the ones column. Review facts for fluency using the My Math Facts When we’re working with Dot Cards, when we complete a ten, practice sheets. we regroup by moving the new Dot Card-10 over to the left, to join the other Dot Cards-10. When we add in columns, we show THINKING TRIGGER this regrouping by writing a small 1 in the tens column. Then we add all the tens together. Write 28 + 53 on the board. Ask a volunteer to show how to find the sum using Dot Cards. Say: We can also Let’s solve another equation with regrouping. [Write 58 + 26 on find the sum by adding in columns. the board in a place-value chart, and solve, using Dot Cards as support to demonstrate the process of regrouping. Review the steps for regrouping when adding in columns: 1) add the ones; 2) when the sum is a teen number, regroup: write the 1 of the teen number in the tens column (to show the new ten) and the ones digit of the teen number in the ones column of the sum; 3) add the tens.]CONCEPT DEVELOPMENT II. Adding in columns without Dot Cards Copyright © by SPOTS Educational Resources. All rights reserved.I. Adding two-digit numbers using Dot Cards Write 34 + 29 in column form on the board. Say: Let’s find the sum. First we add the ones. How many ones in all? [13]Use Dot Cards to add two-digit numbers, and relate this to Remember, when the sum of the ones is a teen number, we needadding in columns. On the board, write 28 + 27 in a place- to regroup: We write the 1 of the teen number in the tens columnvalue chart. Alongside the problem, in another place-value (to show the new ten) and the ones digit of the teen numberchart, represent 28 using Dot Cards (with black dots). Place in the ones column of the sum. [Write 3 in the ones place ofDot Cards showing 27 (with white dots) below these so that the sum. Then write a small 1 above the 3 in the tens place.]the tens and ones are aligned. Finally, let’s add the tens: 1 + 3 + 2 = 6. [Write the 6 in the tens place of the sum.] The sum of 34 + 29 is 63.Say: Let’s find the sum using Dot Cards to help us. First we addthe ones. What is 8 + 7? [15] [Elicit that we need two counters In the same way, solve together 49 + 26. Lead students tofrom the 7 card (of 27) to complete the 8 card (of 28) and understand the three steps they can use to find the sum: 1)make it a full Dot Card-10. Then move these counters.] Let’s add the ones; 2) fill in the new ten; 3) add the tens.move the new ten over to the tens column and leave the cardwith the remaining 5 counters in the ones column. [Point to 8 + Repeat the process with several more addition equations. If7 in the column equation.] When we added, we got 15. possible, give each student an opportunity to come up to the board and take part in solving the equations.108

Using the Book: pages 111−112 Adding in Columns with Regrouping Add. Remember to start with the ones. We can add in columns. 1. 2. 3. 4. Tens Ones 2 1 Tens Ones Tens Ones Tens Ones Tens Ones 1 Then, we fill in First we add the ones. 1 Sum is 1 1 the new ten. abDso+oovlnv963eeo9.549t9. 39 3 Last we add the tens. 39 47 25 +2 5 +2 6 +3 5 +2 5 64 65 82 50 5. 6. 7. 8. Add. Remember to start with the ones. Tens Ones Tens Ones Tens Ones Tens Ones 1. Tens Ones 2. Tens Ones 3. Tens Ones 1 1 1 1 11 1 1 57 76 38 48 37 +1 6 +1 5 +2 8 +3 7 46 38 +3 4 +3 5 +2 5 73 91 66 85 71 81 63 9. 10. 11. 12. 4. Tens Ones Add5. .RememTebnes rOtnoesstart with6.the oneTsen. s Ones Tens Ones Tens Ones Tens Ones Tens Ones 1 11 1 1 1 1 49 27 39 46 47 19 26 +2 9 +2 7 +2 5 +2 6 +3 7 +1 8 +1 9 78 54 64 72 84 37 45 7. Tens Ones 8. Tens Ones 9. Tens Ones Add to find the value of 2 quarters. 1 13. 1 1 1 25¢ 25¢ + 25¢ 58 67 39 + 25¢ +2 3 +2 5 +1 4 112 50¢ 81 92 53 Chapter 3 Lesson 19 111 Now let’s practice adding two-digit numbers in columns Also remind them that when they’re writing the amount of a with regrouping. number of coins (as in problem13 on page 112), they should use the cent symbol (¢). Remind the students to start with the ones and to record the new ten they make above the tens column.Copyright © by SPOTS Educational Resources. All rights reserved. STUDENT TEACHER DIFFERENTIATED INSTRUCTION Write three or four addition equations on the board in column Struggling learners: Remind students that we can add in form. Call on three students to line up at the board in front any order. Therefore, they can feel free to add the small 1 of each equation. Ask the first student to add the ones and in the box to the ten of the first addend, or they can add fill in the new ten. Have the next student add the tens. Invite it after they’ve added the 2 tens in the equation. They can the third student to check their work and circle the answer choose whichever order is easiest for them. to indicate that it is correct. When they are finished, ask each group to show their work and explain the steps they used to CLOSING STATEMENT: solve their equations. Today we found the sums of two-digit numbers by adding in columns with regrouping. Tomorrow we will practice adding two-digit numbers in columns. 109

Chapter 3 Lesson 20: Practice Adding in Columns INTRODUCTORY STATEMENT: II. Deciding whether we will make a new ten Yesterday we added two-digit numbers in columns. Today we will practice adding two-digit numbers Write 65 + 34 on the board in column form. Say: Sometimes we do not form a new ten when adding two-digit numbers. in columns. Let’s add the ones. How many ones in all? [9] How do we know that we do not form a new ten? [When we add 5 + 4, the sum GOAL: is less than ten, so we do not form another ten.] [Write 9 in the ones column of the sum.] Now let’s add the tens. How Students will use place value to add two-digit numbers many tens are there? [9] [Write 9 in the tens column of the in columns. sum.] How many do we have altogether? [99] MATERIALS NEEDED: blank sheets of white and colored poster paper; addition equation cards Write 36 + 46 and 63 + 22 on the board in column form. Say: (see Student Teacher section) In both of these equations we are adding ones and tens. In one of them we will make a new ten before we add the tens that areCommon Core Standard: CCSS2.NBT.5; CCSS2.NBT.7 already there. Add the ones of both equations in your head, and then tell me: In which one will we make a new ten before we add LESSON WARM-UP the tens that are there? [36 + 46] How do you know? [The sum of the ones is 12.] Let’s find the sum for both equations. [Solve Review facts for fluency using the My Math Facts both equations together.] practice sheets. Write the following equations on the board: 55 + 28, 32 + 46, THINKING TRIGGER 77 + 12, and 28 + 39. Before solving each equation together, discuss whether we will form another ten or not and how we know. Then solve. Write 36 + 48 and 26 + 53 on the board. Ask: In which STUDENT TEACHER: equation do we make a new ten? How do you know? Divide the class into four groups. Give each group twoCONCEPT DEVELOPMENT pieces of paper, one white and the other colored, and two addition equation cards – one in which the ones form a newI. Making a new ten when adding ten and one in which they do not. Have the students write two-digit numbers the equation of the first type on the colored paper and the equation of the second type on white paper. Then ask themWrite 54 + 39 in column form on the board. Ask: What should to solve both equations. When they are finished, have eachwe do first to find the sum? [Add the ones.] Add the 4 ones and group exchange papers with another group and check eachthe 9 ones in your head. How many ones are there in all? [13] others’ work. You might want to display their papers on yourWhat happens when you add the ones? [We make a new ten.] math bulletin board, divided by type.So, we have 1 ten and 3 ones. Let’s record the ones in the sum.[Write 3 in the ones place of the sum of the equation.] How Copyright © by SPOTS Educational Resources. All rights reserved.can we show the new ten in our equation? [We write a small 1above the 5 in the tens column.] [Write a small 1 above the 5in the tens place.] This helps us keep track of the new ten. Nowlet’s add the tens: 1 + 5 + 3 = 9. [Write 9 in the tens place underthe column-form equation.] The sum of 54 + 39 is 93.Repeat this with 37 + 28. Lead students to follow the threesteps needed to find the sum: 1) add the ones; 2) fill in thenew ten; 3) add the tens.110

Using the Book: pages 113-114 Practice: Adding in Columns Tens Ones Tens Ones Will we fill in a new ten? Circle the correct sign. Add. Remember to start with the ones. P 46 P 74 1. 2. 1 3. 1 4. O +3 5 O +1 4 P 56 P 69 P 38 P 55 8 88 O +23 O +17 O +25 O +34 Sometimes we do Sometimes 79 86 63 89 fill in a new ten. we do not. 5. 6. 7. 1 8. 1 Will we fill in a new ten? Circle the correct sign. Add. Remember to start with the ones. P 45 P 57 P 46 P 62 O +44 O +12 O +4 6 O +28 1. 2. 3. Tens Ones Tens Ones Tens Ones 89 69 92 90 1 9. 10. 1 11. 12. 1 P 35 P 61 P 36 P 43 P 28 P 53 P 37 +6 4 +2 8 +2 6 O +25 O +27 O +3 4 O +14 O 99 O 89 O 62 68 55 87 51 4. 5. 6. 1 1 Fill in the math puzzle and write a number sentence. P 49 P 53 P 47 Use a for the unknown number. Solve. +3 9 + 4 6 + 2 5 O 8 8 O 9 9 O 7 2 10. Mrs. Kramer baked 22 chocolate chip cookies and 14 oatmeal cookies. 7. 8. 9. 36Whole How many cookies did she bake altogether? 22 14 1 1 P 38 P 42 P 67 Number sentence: 22 + 14 = 36 Part Part She baked __3_6__ cookies altogether. O +3 5 O +3 6 O + 2 5 7 3 7 8 9 2 Chapter 3 Lesson 20 113 114 Now let’s practice adding two-digit numbers in columns. Read the story problem on page 114 together. Guide stu- dents to first fill in the puzzle with the numbers they know, Remind the students to decide whether they will fill in a and use a box for the unknown number. Next, have them new ten and then to circle the correct sign – the check write the number sentence, again using a box for the un- mark if they will make a new ten, and the X if they will not known number, and then solve it. Finally, have them fill in make a new ten. Point out that every problem has a box the sum in the math puzzle, so that they can see the rela- above the tens column, but they will not need to fill it in if tionship between all the numbers in the problem. they do not make a new ten.Copyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Remind students that we can add in Who can tell us what we learned today? any order, and therefore they can feel free to add the 1 in Today we practiced finding the sums of two-digit the box to the ten of the first addend or ten of the second numbers by adding in columns. Tomorrow we will addend, whichever is easiest for them. choose a strategy to add two-digit numbers. 111

Chapter 3 Lesson 21: Choosing a Strategy INTRODUCTORY STATEMENT: board.] Jerod thought for a moment, and then he said: I know! Copyright © by SPOTS Educational Resources. All rights reserved. We’ve learned two strategies for adding two-digit It’s 84! numbers: the number line and in columns. Today we will choose which strategy to use for each problem. Michael asked: How did you figure it out so quickly? GOAL: Jerod said: I thought about a number line. I started with 78, jumped 2 to the next ten – 80, and jumped 4 more to 84. [Draw Students will choose a strategy to add two-digit a number line on the board and fill it in accordingly.] numbers. MATERIALS NEEDED: blank sheet of paper or Michael said: I wouldn’t do it that way. I can add in columns to dry-erase boards find the sum. First I’ll add the ones: 8 ones plus 6 ones equals 14 ones. I need to make a new ten. So I have 1 ten and 4 ones. I’llCommon Core Standard: CCSS2.NBT.5; CCSS2.NBT.9; write the 4 ones in the sum, and I’ll write a small 1 above the 7CCSS2.MD.6 in the tens column. Then I’ll add the tens: 1 plus 7 equals 8 tens. I also get the sum of 84. [Show the column addition on the LESSON WARM-UP board.] Review facts for fluency using the My Math Facts Point out that Michael and Jerod each used a different way practice sheets. to find the sum and that each one is correct. Everyone finds a way that works best for him or her. THINKING TRIGGER Write 25 + 5 on the board. Have students draw an open Write 26 + 57 on the board. Ask: How can we find the number line on a sheet of paper and find the sum using the sum using a number line? How can we find the sum by number line. adding in columns? Then write 39 + 17 on the board. Have the students find theCONCEPT DEVELOPMENT sum using column addition on the second sheet of paper.I. Reviewing adding two-digit numbers on a Discuss how they solved each addition problem. Ask them to number line think about which way worked best for them. Point out that the easiest way for one student may not be the easiest way forWrite 67 + 28 = ___ on the board. Have the class tell you how another student, and that both the methods are good ones.to find the sum using a number line. Show the work on the Also mention that each problem may be solved differently.board as students describe the steps. Even if I prefer column addition for 39 +17, I might prefer the number line for easier problems.II. R eviewing adding two-digit numbers in columns STUDENT TEACHER:Write 45 + 37 = ___ on the board. Discuss with the class how Write 59 + 24 = ___ on the board. Have students choose ato add the numbers in columns. Show the work on the board strategy and find the sum. Then call two students to come upas students describe the steps. to the board to show their work, one using a number line and one adding in columns. Ask for a show of hands to see which strategy each student in the class used to find the sum.III. Choosing a strategy to add two-digit numbersTell a story: Michael and Jerod are friends. Michael said to Jerod:I have a challenge for you. Let’s see if you can tell me the answer!The question is: How much is 78 + 6? [Write 78 + 6 on the112

Using the Book: pages 115-116 Add: 78 + 6 = Choosing a Strategy to Add Choose the way that works best for you. Which way works best for you? Add. I like to use I like to use columns. 1. 1 a number line. 29 + 7 = 36 29 +7 1 +1 +6 29 30 36 36 78 +6 +6 2. 1 +2 +4 84 +3 57 78 80 84 57 60 57 + 3 = 60 +3 46 Choose the way that works best for you. Add. + 30 60 1. 76 46 + 30 = 76 1 +30 76 86 3. 75 + 23 = 98 75 46 +4 + 23 +20 +3 2. 90 75 95 3 98 86 + 4 = 90 1 4. 45 + 38 = 83 1 +4 69 45 86 90 + 26 3. 69 + 26 = 95 95 +30 +5 +3 + 38 +20 +1 +5 115 45 75 80 83 83 89 90 95 69 Lesson 21 116 Chapter 3 Now let’s practice adding two-digit numbers using a number ently, and that both ways are correct. line or adding in columns. For each problem, you will choose the strategy that works best for you. Tell students that for each problem they can decide which strategy they will use to find each sum. Review the page Read and discuss the demonstration at the top of the together, calling on different students to share their work, page. Point out that each boy solved the problem differ- and discussing which strategy each used. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Write 59 + 24 = ___ on the board. Today we practiced different ways of adding, Have students choose a strategy and find the sum. Then and for each problem we thought about call two students to come up to the board to show their which way works best. work, one using a number line and one adding in col-Copyright © by SPOTS Educational Resources. All rights reserved. umns. Ask for a show of hands to see which strategy each student in the class used to find the sum. 113

Chapter 3 Lesson 22: Adding with Three Addends INTRODUCTORY STATEMENT: two addends combine to form a new ten? [19 and 1] So let’s We’ve already learned how to add three single digits reorder the addends. [Write 19 + 1 + 15 on the board.] Now we can add the first two addends. [Write and solve 19 + 1 = 20 in together. Today we will add 3 two-digit addends. column form on the board.] Now let’s add the third addend to the sum. [Write 20 + 15 on the board, and elicit the sum – 35.] GOAL: Remember, we can add in any order to find the sum. Students will find the sum of three addends. II. Adding 3 two-digit numbers in any order MATERIALS NEEDED: blank sheets of paper or dry-erase boards Write 37 + 45 + 13 = ___ on the board. Say: Let’s see if we can reorder the addends to make it easier to find the sum. WhichCommon Core Standard: CCSS2.NBT.6; CCSS2.NBT.9 digits in the ones place of these numbers add up to ten? [7 and 3] So let’s reorder the addends: 37 + 13 + 45. Now we can LESSON WARM-UP add together the first two addends. [Write 37 + 13 in column form, and add to find the sum – 50.] Then we can add the third Review facts for fluency using the My Math Facts addend to the sum. [Write 50 + 45 in column form, and solve practice sheets. together with the class. Complete the equation: 37 + 45 + 13 = 37 + 13 + 45 = 95.] THINKING TRIGGER Repeat the process with 32 + 16 + 28 and 54 + 13 + 16. Guide Tell a story: Sharna collects animal stickers. She has 34 the students as together you reorder the addends, add the cat stickers, 19 dog stickers, and 26 wild animal stickers. two addends that make another ten, then add the third How do you think we can find how many animal stickers addend to that sum to find the sum of all three addends. Sharna has in all? STUDENT TEACHER:CONCEPT DEVELOPMENT Write two equations with three addends, two of which haveI. Reviewing adding three addends digits in the ones place that together add to 10, such as 18 + 16 + 42 and 46 + 29 + 14. Have students work in pairs to solveWrite 27 + 9 + 3 = ___ on the board. Have the class tell you the problems. Elicit that it is easier to solve problems whenin what order to add these three numbers. Elicit that it might we can find two addends whose ones add up to ten, and thatbe easiest to add together the two addends that form a new because we can add in any order, we can choose the orderten and then to add the third addend to the sum. Remind the that makes adding simplest (e.g., add 18 and 42 to get 60,students that we can always add in any order, so they should and then add 16 to get 76).choose the order that is easiest for them. Ask: Which twonumbers combine to form a new ten? [27 and 3] [Reorder the Copyright © by SPOTS Educational Resources. All rights reserved.addends and write them on the board: 27 + 3 + 9.] Now let’sfind the sum of the first two addends. [Write 27 + 3 in columnform, solve together with the class, and fill in the sum – 30.]Now let’s add the third addend to the sum. [Write 30 + 9 incolumn form, and solve together.] So, 27 + 9 + 3 = 39. Whenyou add three numbers, first look for numbers that make a ten,add them together, and then add the third addend. [Elicit thatsince 30 has a zero in the ones place, it is easy to add 9 to it.]Repeat with three more addends: 19 + 15 + 1. Ask: How canwe change the order of the addends to make it easier to findthe sum? [Find the two addends that combine to form anew ten, and write them as the first two addends.] Which114

Using the Book: pages 117−118 Adding with Three Addends We can add in any order. Reorder and add to find the sum. We can reorder the addends to add 36 + 28 + 14. 1. 16 + 33 + 34 2. 32 + 24 + 36 Look for digits in Reorder the Now add the first Add the third Reorder: Reorder: the ones place addends. two addends. addend to the that add to 10. 16 + 34 + 33 24 + 36 + 32 sum. 36 + 28 + 14 36 + 14 + 28 1 50 1 50 1 60 + 28 + 33 + 32 6 and 4 make 36 16 24 a ten. 83 92 + 14 + 34 + 36 50 78 50 60 So, 36 + 28 + 14 = 36 + 14 + 28 = 78. Reorder and add to find the sum. 2. 3. 52 + 17 + 23 4. 43 + 16 + 27 1. 19 + 27 + 23 Reorder: Reorder: 17 + 18 + 22 17 + 23 + 52 43 + 27 + 16 Reorder: Reorder: 1 40 1 70 + 52 + 16 + 18 + 17 + 23 + 19 17 43 + 23 92 + 27 86 Add the first Add the third Add the first Add the third two addends. addend to the two addends. addend to the 40 70 50¢ sum. sum. + 25¢ 1 1 Add to find the value of 3 quarters. 1 40 50 5. 75¢ 22 + 17 27 + 19 25¢ + 18 + 23 25¢ + 25¢ + 25¢ + 25¢ 57 69 40 50 118 50¢ Chapter 3 Lesson 22 117 Now let’s practice adding 3 two-digit numbers by reordering Read and discuss the example at the top of the page. Point the addends and then adding to find the sum. out that the sum in the first column-addition setup needs to be rewritten in the next step, and that the arrow shows us where to copy that first sum. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Some students may get confused Today we added 3 two-digit numbers. Tomorrow we when trying to find the sum of three addends. Have them will solve story problems with 3 two-digit numbers. first circle the ones digit of each of the two addends whose sum is a ten.Copyright © by SPOTS Educational Resources. All rights reserved. 115

Chapter 3 Lesson 23: Problem Solving with Two Steps INTRODUCTORY STATEMENT: did Mrs. Larson make? [13] How many tuna sandwiches did Copyright © by SPOTS Educational Resources. All rights reserved. Yesterday we added 3 two-digit numbers. Today we Mrs. Larson make? [24] How many egg salad sandwiches did will solve story problems with 3 two-digit numbers. Mrs. Larson make? [17] How many sandwiches did she make in all? [unknown] Remember that we can use a box to show the GOAL: unknown number. Students will solve two-step story problems with 3 Which number is unknown? [the number of sandwiches two-digit numbers. she made in all – the sum] How can we change the order of MATERIALS NEEDED: blank sheets of paper the addends to make it easier to find the sum? [We can find the two addends that have ones that combine to form aCommon Core Standard: CCSS2.OA.1b new ten, and add them together first.] Which two addends have ones that combine to form a new ten? [13 and 17] Let’s LESSON WARM-UP reorder the three addends. [Write 13 + 17 + 24 = ___ below the original number sentence.] Now we can add the first two Review facts for fluency using the My Math Facts addends. [Write 13 + 17 = ___ in column form on the board.] practice sheets. What is the sum of 13 + 17? [30] [Fill in the sum.] Now let’s add the third addend to the sum. [Write 30 + 24 = ___ in column THINKING TRIGGER form.] What is the sum of 30 + 24? [54] [Fill in the sum.] Now let’s complete our first number sentence. 13 + 24 + 17 = 54. Mrs. Tell a story: Carlos picked 18 carrots, 25 peppers, and 12 Larson made 54 sandwiches. tomatoes from his garden. How many vegetables did Car- los pick from his garden? II. Problem-solving with two steps Ask: How can a number sentence help you solve this story problem? Say: Remember: Whenever we add three addends, we can add in any order. Often we can find two addends have ones thatCONCEPT DEVELOPMENT combine to make a new ten and add them together first. Then we can add the third addend to the sum.I. Reordering addends to solve problems with three addends I will tell another story. Let’s solve it together: Kayla prepared a big fruit salad for a party. She used 28 apples, 15 peaches, andTell a story: Mrs. Larson made 13 cheese sandwiches, 24 tuna 32 pears. How many fruits did Kayla use to make her salad?sandwiches, and 17 egg salad sandwiches for the school picnic.How many sandwiches did Mrs. Larson make in all? Ask: What do we know? [the number of each kind of fruit inLet’s think about how to solve the problem. [Ask students to Kayla’s salad] What do we need to find out? [the number ofrepeat the main details of the story – what they know and fruits in all]what they need to find out. (We know how many of eachkind of sandwich Mrs. Larson made. We need to find out how Step 1. Let’s write a number sentence to help us solve themany sandwiches she made in all.)] problem. [Lead students to understand that they will add,Let’s write a number sentence to help us solve the problem. because they know all the parts but not the whole. Draw aWill we add or subtract to find the answer? [add] How do you blank addition number-sentence format for three addends,know? [We know how many of each kind of sandwich Mrs. and fill it in as you go along.] How many apples did Kayla useLarson made, so we add to find the total.] [Draw a blank in her salad? [28] How many peaches did Kayla use in her salad?addition number-sentence format for three addends, and [15] How many pears did Kayla use in her salad? [32] Howfill it in as you ask questions:] How many cheese sandwiches many fruits did she use in all? [unknown] How can we change the order of the addends to make it easier to find the sum? [We can first add together 28 and 32, because they have ones that combine to form a new ten.] Step 2. Let’s add 28 and 32. [Write 28 + 32 = ___ on the board in column format.] What is the sum? [60] [Fill in the sum.] Let’s add the third addend to the sum. [Write 60 + 15 = ___ in column form.] What is the sum? [75] [Fill in the sum.] Let’s complete our original number sentence. [Fill in the sum – 75.]116

Using the Book: pages 119-120 TwoStep Story Problems Write a number sentence and solve. Use a for the unknown number. Write a number sentence and solve. Use a for the unknown number. 1. Julia put 25 roses, 12 tulips, and Step 1: 1. There are 15 spoons, 10 forks, Step 1: 5 daises in a vase. Write a number sentence. and 5 glasses on a table. Write a number sentence. How many flowers did Julia put How many objects are on the 15 + 10 + 5 = in the vase? table? Step 2: Step 2: 1 20 Julia put 42 flowers in the Solve. There are 30 objects are on Solve. 15 vase. + the table. + +5 + 10 20 30 2. Ken read 32 pages on Monday. Step 1: 2. There are 24 books on the top Step 1: He read 8 pages on Tuesday and Write a number sentence. shelf. There are 22 books on the Write a number sentence. 15 pages on Wednesday. 32 + 8 + 15 = middle shelf and 30 books on the bottom shelf. 24 + 22 + 30 = How many pages did Ken read Step 2: 1 40 How many books are on the Step 2: 46 in all? + 15 bookshelf? Solve. 32 Solve. 24 Ken read 55 pages in all. +8 There are 76 books on the + 22 + 30 bookshelf. 40 55 46 76 3. Talia drew 13 pictures in May. Step 1: 3. Elroy has 22 toy cars, 23 toy Step 1: She drew 15 pictures in June Write a number sentence. trucks, and 14 toy trains. Write a number sentence. and 7 pictures in July. How many pictures did Talia 13 + 15 + 7 = How many toys does Elroy have? 22 + 23 + 14 = draw in all? Step 2: 1 20 Elroy has 59 toys. Step 2: 45 Talia drew 35 pictures in all. Solve. 13 Solve. 22 Chapter 3 Lesson 23 +7 + 15 + 23 + 14 20 35 45 59 119 120 Now let’s practice solving story problems with three Read each story problem together with the class. Then have addends. the students solve the problems independently using the two steps. Kayla used 75 fruits to make her fruit salad. DIFFERENTIATED INSTRUCTION Tell another story: For his math homework, Mario completed 22 addition problems, 15 subtraction problems, and 8 story English-language learners: Discuss key words, such as problems. How many problems did Mario complete for his “and,”“in all,” and “altogether,” that indicate addition. Have math homework? students try using these terms in scenarios that they Guide students as you solve this problem together, using themselves create. the two steps of writing a number sentence and then add-Copyright © by SPOTS Educational Resources. All rights reserved. ing the reordered addends. STUDENT TEACHER: CLOSING STATEMENT: What did we learn today? Today we used two steps Tell a story problem such as: Rachel counted 25 steps from her to solve addition story problems with three addends. classroom to the library, 22 steps from the library to the gym, and 45 steps from the gym to the playground. How many steps Tomorrow we will review what we have learned did Rachel count in all? [Have students solve it on their own. in this chapter. Then, call up four students, one at a time, to demonstrate each step: write a number sentence, reorder, add to form a 117 new ten, add the rest to get the final sum.]

Chapter 3 Lesson 24: End-of-Chapter Review INTRODUCTORY STATEMENT: adding 5 ones to 5 ones make another ten, so now we have We’ve reached the last lesson in this chapter! 3 tens, or 30 in all.) Have students tell how to find the rest of Today we will review all the skills that we’ve the missing addends. learned in this chapter. III. Adding three addends by making a ten GOAL: Write 26 + 3 + 4 = ___ on the board. Ask students to tell which two numbers they would add first, and circle them (26 and 4). Students will review concepts and skills learned in Discuss the reasons for choosing those two numbers (they Chapter 3. equal ten; we can add in any order). Reorder the addends and write the equation: 26 + 4 + 3 = ___. Solve the equation.Common Core Standard: CCSS2.NBT.5; CCSS2.NBT.6; Fill in the sum – 33.CCSS2.NBT.7; CCSS2.NBT.9; CCSS2.MD.6 Do the same for 41 + 6 + 9 = ___. LESSON WARM-UP IV. Adding 2 two-digit numbers Review facts for fluency using the My Math Facts practice sheets. Write two equations on the board: 24 + 30 and 24 + 32. Below each equation, draw an open number line. Have the students THINKING TRIGGER tell you how to show the equations on the number lines: with what number to begin (24), and how many to jump (one Say: Look through your book. Tell us some of the skills that jump of 30 for the first equation; two jumps, one of 30 and we’ve learned and reviewed in this chapter. [List them on one of 2, for the second equation). the board as students say them. Add to the list other skills that were not mentioned.] Write 48 + 27 on the board. Draw an open number line under it. Have students tell how to show the equation on the number line. Discuss making three jumps: first a jump of the tens: 48 + 20 = 68; then a jump of 2 to get to the next ten: 68 + 2 = 70; then a jump of 5 more, to get to the sum – 75.CONCEPT DEVELOPMENT V. Adding two-digit numbers in columns Copyright © by SPOTS Educational Resources. All rights reserved.I. Adding ones to two-digit numbers Write 57 + 36 on the board in column form. Ask students to tell how to solve the equation. Discuss adding the onesOn the board write 6 + 3 and 56 + 3 in column form. Have first, making a new ten and recording the new ten in the boxstudents tell how to solve the first equation (add the ones). above the tens column, and lastly, adding the tens.Fill in the sum (9). Say: Now let’s add 56 + 3. What should wedo first? [Add the ones.] How many ones in all? [9] How many Do the same to find the sum of 31 + 29.tens? [5] [Fill in the sum of 56 + 3 (59).] VI. Reordering to find the sum of 3 two-digitII. Finding the missing addend addends using patterns Write 18 + 29 + 32 on the board. Ask the students to tellWrite these four equations on the board, one below you how to reorder the addends to make it easier to addthe other: (18 + 32 + 29). Discuss the process. (Look for digits in the ones place in two of the addends that add up to ten; reorder 5 + ___ = 10 the addends; add the first two addends; then add the third addend to find the sum.)25 + ___ = 30 In the same way, add 46 + 22 + 14.45 + ___ = 50 STUDENT TEACHER:75 + ___ = 80 Choose skills that need extra review. Write some examples of these skills on the board, and for each example have aAsk how much is needed to form a ten in the first equation student solve and explain his/her thinking to the class.(5). Discuss how knowing that 5 and 5 forms a ten helps usfind the missing addend in the next equation. (We know that118

Using the Book: pages 121-122 End-of-Chapter Review Add. Complete the number line. Fill in the sum. 1. 6 46 2. 4 54 3. 5 85 1. +6 53 +3 +3 +3 +3 +4 +4 9 7 9 47 + 6 = 53 47 50 49 57 89 4. 8 68 5. 5 75 6. 7 37 2. 3. +2 +2 +5 +5 +3 +3 10 10 10 49 + 21 = 70 49 + 24 = 73 70 80 40 +21 +24 Fill in the missing addend to complete the number sentence. +1 +1 +3 7. 6 + 4 = 10 8. 3 + 7 = 10 49 69 70 49 69 70 73 16 + 4 = 20 13 + 7 = 20 26 + 4 = 30 23 + 7 = 30 Add. Remember to start with the ones. = 80 = 60 76 + 4 53 + 7 4. 1 5. 1 6. 1 Circle the addends that combine to form a new ten. 56 48 67 Add. Then add the rest. +35 +26 +15 91 74 82 9. 67 + 5 + 3 10. 56 + 4 + 8 Reorder and add to find the sum. 70 + 5 = 75 60 + 8 = 68 7. 27 + 18 + 23 8. 21 + 36 + 34 Add. Reorder: Reorder: 27 + 23 + 18 36 + 34 + 21 11. 46 + 30 = 76 14. 55 + 10 = 65 17. 37 + 40 = 77 1 50 1 70 + 18 + 21 12. 46 + 32 = 78 15. 55 + 13 = 68 18. 37 + 41 = 78 27 36 68 91 13. 46 + 34 = 80 16. 55 + 15 = 70 19. 37 + 43 = 80 + 23 + 34 50 70 Chapter 3 Lesson 24 121 122 Tell the students that these pages are a review of what they together, and have the students complete the sections on have learned in this chapter. Read each set of directions their own. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Some students may still have diffi- Today we reviewed the skills we learned in this culty with a skill or skills taught in this chapter. Have them chapter. Tomorrow we will begin Chapter 4! work with a partner who understands the skill/skills and go through a few exercises together.Copyright © by SPOTS Educational Resources. All rights reserved. 119



Chapter 4 IntroductionIn Chapter 4, the students will continue to expand their math skills as they explore subtractingwith two-digit numbers, both with and without regrouping.Similar to the scaffolded skill-building work they did when they learned addition, in this chapterstudents are introduced to subtracting with two-digit numbers using the concrete model of theDot Cards. When modeling with Dot Cards, as with the other strategies they will learn in Chapter4, students will be reinforcing their understanding of place value and its importance in workingwith two-digit numbers. Dot Cards offer a clear visualization of what is taking place, both inproblems where there are enough ones in the minuend to subtract from, and in problems wherethey will need to regroup. Students learn to regroup by moving a Dot Card-10 over to the right,next to the Dot Card showing the ones, to form a teen number.With this foundation, students have a conceptual basis for each step in the procedure. As theyunderstand the basic concept of subtracting with two-digit numbers, they will move on withconfidence to the algorithm for column subtraction.Once they understand the algorithm of column subtraction, the students will develop mentalmath strategies for subtraction, using the number line as a visual recording tool. The number linefurther reinforces the steps for solving specific types of subtraction problems, as students makea jump or a set of jumps across the number line. When subtracting from a decade number, theyare taught to make one jump, which will bring them into the previous ten. When subtractingfrom a two-digit number, they will make two jumps – the first jump encompassing all the ones inthe minuend, bringing them back to the ten, and the second jump for the rest of the ones in thesubtrahend, bringing them to the difference.Also in this chapter, students will learn to solve two-step story problems that involve bothaddition and subtraction. They will need to think through questions such as whether we willneed to add or subtract, and why. This important exercise will strengthen their skills and will givethem a deeper understanding of addition and subtraction.The last part of the chapter offers a series of problem-solving lessons. Algebraic reasoning iscarefully honed, through a four-step solving method in which students use a to representan unknown quantity in a problem. They also work with a puzzle-piece model, to help themvisualize and describe the problem, and to guide them in how to solve the problem. In the finaltwo steps of the four-step method, they will solve the problem and then check their answer bytesting their solution in context. In subsequent chapters they will continue to practice this four-step method, which will set the stage for a lifetime of problem-solving with confidence!By the time the students complete Chapter 4, they will understand how to solve many complexsubtraction problems.

Chapter 4 Lesson 1: Subtracting Ones from Two-Digit Numbers INTRODUCTORY STATEMENT: the same. Only the number of ones changed. We’ve learned to subtract one-digit numbers from teen numbers. Today we will subtract ones II. Subtracting ones from two-digit numbers using Dot-Cards from two-digit numbers – from numbers between 20 and 99! Write 48 – 3 on the board. Say: Here we are subtracting ones from a two-digit number. We can show this with Dot Cards. GOAL: [On the board, place Dot Cards showing 48.] How many tens are there? [4 tens] How many ones are there? [8 ones] Are Students will subtract ones from two-digit numbers. we subtracting tens or ones? [ones] Will the number of tens MATERIALS NEEDED: Dot Cards change? [no] Let’s subtract the ones. [Cross off the upper three dots.] How many ones are left? [5 ones] How many tens do weCommon Core Standard: CCSS2.NBT.5 have? [4 tens] What is the difference? [45] [Fill in 45.] When we subtract ones, the number of ones changes. LESSON WARM-UP Say: Let’s use Dot Cards to help us write and solve a number Review facts for fluency using the My Math Facts sentence. [Draw a blank subtraction number-sentence format practice sheets. on the board. Show six Dot Cards-10 and one Dot Card-7 with the five lower dots crossed off.] What number do we start THINKING TRIGGER with? [67] Let’s write this in our number sentence. [Fill in 67.] How many ones do we subtract? [Point to the five crossed-off Write 5 – 4 and 25 – 4 on the board. Ask: How is 5 – 4 dots.] [5] [Fill in 5 after the minus sign.] How many ones are different from 25 – 4? How is it similar? left? [2 ones] How many tens do we have? [6 tens] Does the number of tens change? [no] What is our difference? [62] [Fill in the difference: 62.] So, our number sentence is 67 – 5 = 62. Repeat the process, using Dot Cards to write and solve the number sentence for 58 – 5.CONCEPT DEVELOPMENT III. Subtracting ones in column form, without Copyright © by SPOTS Educational Resources. All rights reserved. using Dot-CardsI. Reviewing subtracting ones from teen numbers Write 95 – 4 on the board in column form. Say: Now let’s subtract without using Dot Cards to help us. Are we subtractingWrite 16 – 4 = ___ on the board. Say: We’ve already learned ones or tens from 95? [ones] So, the number of ones will becometo subtract ones from teen numbers. Let’s review. How can we less. Will the number of tens change? [no] Let’s subtract thefind the difference? [Allow time for suggestions. Then place ones. [Point to the ones column and ask:] What is 5 – 4? HowDot Card-16 on the board and ask:] How many tens are there? many ones are left? [1] How many tens are there? [9 tens] How[1 ten] How many ones are there? [6 ones] How do we show much is 95 − 4? [91] [Fill in 91.]subtracting 6 – 4 on the Dot Card? [Cross off the lower fourdots on the Dot Card-6.] [Draw an X over the bottom four Repeat this with 87 – 5 and 56 – 3.dots.] How many are left? [12; 1 ten and 2 ones] What is thedifference? [12] [Fill in the difference in the number sentence.] STUDENT TEACHER:We subtracted 4 ones, so only the ones changed. The tens stayedthe same. Write some equations on the board similar to those in the lesson. Select students to come up to the board and solveWrite 19 – 6 = ___ on the board. Say: Now let’s subtract without the equations. Help them explain the process. Elicit thatusing Dot Cards. What should we do first? [subtract the ones] when we subtract ones, the ones digit will change.Subtract the ones in your head. Think of 9 – 6. How many onesare left? [3 ones] How many tens are there? [1 ten] What is thedifference of 19 – 6? [13] [Fill in 13.] The number of tens stayed122

UUsisnigngthteheBBooko:kp: apgaegses1275-17266 Subtracting Ones from Two-Digit NumbXexrxs Subtract. 67 2. 39 3. 48 1. –5 –6 –4 We can subtract ones 9 8 44 from a two-digit number. 7 62 –6 33 –4 –5 27 – 3 = 24 3 4 2 Write the number sentence. 2. 4. 84 5. 98 6. 58 7. 84 8. 27 1. –2 –3 –6 –4 –1 82 95 52 80 26 36 – 2 = 34 57 – 3 = 54 9. 10. 11. 12. 13. 3. 4. 56 47 38 77 89 –5 –2 –6 –6 –7 51 45 32 71 82 Fill in the math puzzle and write the number sentence. Use a for the unknown number. Solve. 49 – 7 = 42 38 – 5 = 33 14. Paul and Bill went fishing. 46 – 5 = 41 Together they caught 19 fish. Cross off to subtract. Write the difference. Paul caught 8 of them. 5. 6. How many fish did Bill catch? 19 58 – 3 = 55 Number sentence: 19 – 8 = 11 Whole Bill caught 11 fish. 8 11 Part Part Chapter 4 Lesson 1 125 126 Now let’s practice subtracting ones from two digit numbers. Next, have them write the number sentence, again using When we subtract ones, the number of ones changes. a box for the unknown number, and solve it. Finally, have them fill in the sum in the math puzzle, so that they can see Read the story problem on page 126 together. Guide the the relationship between all the numbers in the problem. students to first fill in the math puzzle with the numbers they know and to use a box for the unknown number.Copyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Some students may have difficulty What did we learn today? Today we subtracted subtracting in columns. Suggest that they draw a dividing ones from two-digit numbers. Tomorrow we will line between the tens and the ones and label the col- umns Tens and Ones, respectively (or T for Tens and O for subtract tens from two-digit numbers. Ones). 123

Chapter 4 Lesson 2: Subtracting Tens from Two-Digit Numbers INTRODUCTORY STATEMENT: subtract? [3 tens] How many tens are left? [2 tens] How many We’ve learned to subtract ones from two-digit ones are there? [7 ones] [Elicit what number sentence the Dot Cards show (57 – 30 = 27). Explain:] In this number sentence numbers. Today we will subtract tens from we subtracted tens, so the number of tens changed. We did not two-digit numbers. subtract any ones, so the number of ones stayed the same. GOAL: Write 68 – 20 =___, and next to it place Dot Cards showing 68. Ask: How many tens are in 68? [6 tens] How many tens do Students will subtract tens from two-digit numbers. we need to subtract? [2 tens] [Cross off the two Dot Cards-10 MATERIALS NEEDED: on the left.] How many tens are left? [4 tens] How many ones Dot Cards; blank sheets of paper or dry-erase boards are there? [8 ones] [Write 48 as the difference in the ones place.] What changed in this number sentence? [the tens]Common Core Standard: CCSS2.NBT.5 Why? [because we subtracted tens, so only the number of tens changed] Why did the number of ones stay the same? LESSON WARM-UP [because we did not subtract any ones] Review facts for fluency using the My Math Facts Repeat the process using Dot Cards to solve 76 – 40. practice sheets. Note: Always cross off Dot Cards-10 from the left, so that the tens and ones that remain (i.e., the difference) are next to each other. THINKING TRIGGER III. Subtracting in columns Copyright © by SPOTS Educational Resources. All rights reserved. On the board write 50 – 40 and 56 – 40. Ask: How is 50 – Say: Now let’s subtract in columns. [Write 79 – 20 on the 40 different from 56 – 40? How is it similar? board in column form.] Let’s subtract without using Dot Cards to help us. Are we subtracting ones or tens from 79? [tens] So,CONCEPT DEVELOPMENT the number of tens will decrease (it will become less). Will the number of ones change? [no] How do you know? [There are noI. Subtracting decade numbers ones in 20 to subtract from the 9 ones in 79.] So let’s subtract the tens. How many tens are there in all? [7 tens] How manyWrite 50 – 30 = ___, and place five Dot Cards-10 on the board. tens are we subtracting? [2 tens] What is 7 tens minus 2 tens? [5Ask: How many tens do we have? [5] How many tens are we tens] Will the number of ones change? [no] How do you know?subtracting? [3] [Draw an X over the three Dot Cards on the [There are no ones in 20 to subtract from the 9 ones in 79.]left.] How many tens are left? [2] What is the difference? [20] The difference has 5 tens and 9 ones. What is the difference? [59][Fill in the difference on the board.] [Fill in 59 as the difference.]Write 60 – 40 = ___ on the board, and say: Let’s subtractdecade numbers without Dot Cards. How many tens are there in Repeat this with 86 – 50 and 49 – 20.60? [6 tens] How many tens are we subtracting? [4 tens] Are wesubtracting any ones? [no] So, 6 tens minus 4 tens equals how STUDENT TEACHERmany tens? [2 tens] There are 2 tens left; 2 tens is 20. 60 – 40 =20. [Write in the difference.] Write some two-digit subtraction equations on the board, such as 34 – 20, 48 – 30, 54 – 30, and so on. Divide the classIn the same way, solve 70 – 30. into pairs. Ask the partners to choose two equations, and have each partner solve them in column form. Then haveII. Subtracting tens from two-digit numbers the partners compare their work. Afterward, call on some using Dot Cards sets of partners to come up to the board and solve one of their problems using Dot Cards.Now let’s subtract tens from numbers that have both tens andones. [On the board, place Dot Cards showing 57. Cross offthe three Dot Cards-10 on the left.] How many tens did we124

UUsisnigngthteheBBooko:kp: apgaegses1277-17288 Subtracting Tens from Two-Digit Numbers Subtract. When we subtract 1. 6 8 2. 5 4 3. 7 1 4. 8 7 5. 9 6 tens, the number of –3 0 –2 0 –20 –1 0 –3 0 ones does not change. 38 34 51 77 66 45 – 20 = 25 Write the number sentence. 2. 6. 7 2 7. 6 6 8. 9 1 9. 5 7 10. 8 9 1. –4 0 –50 –4 0 –30 – 60 32 16 51 27 29 54 – 30 = 24 32 – 20 = 12 11. 4 8 12. 9 3 13. 8 4 14. 7 6 15. 7 3 56 – 40 = 16 –30 –7 0 –5 0 –2 0 –5 0 18 23 34 56 23 Cross off to subtract. Write the difference. Fill in the math puzzle and write the number sentence. Use a for the unknown number. Solve. 3. 47 – 20 = 27 4. 5. 45 – 30 = 15 6. 35 – 10 = 25 16. Mark has 18 fish in his fish tank. 18 10 of them are orange and the rest of them are gray. Whole How many gray fish are there in Mark’s 10 8 fish tank? Part Part Number sentence: 18 – 10 = 8 There are 8 gray fish in his tank. Chapter 4 Lesson 2 127 128 Now let’s practice subtracting tens from two-digit numbers. know and to use a box for the unknown number. Next, have Remember, when we solve equations like “54 – 20”, only the them write the number sentence, again using a box for the tens change. The ones stay the same. unknown number, and solve it. Finally, have them fill in the sum in the math puzzle, so that they can see the relation- Read the story problem on page 128 together. Guide ship between all the numbers in the problem. students to first fill in the puzzle with the numbers they DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Some students may have difficulty What did we learn today? Today we subtracted subtracting in columns. Suggest that they draw a dividing tens from two-digit numbers. Tomorrow we will line between the tens and the ones and label the col- umns Tens and Ones, respectively (or T for Tens and O for solve two-step story problems. Ones).Copyright © by SPOTS Educational Resources. All rights reserved. 125

Chapter 4 Lesson 3: Two-Step Story Problems: Subtracting Twice INTRODUCTORY STATEMENT: Step 2. Say: Now let’s rewrite this number sentence in column We’ve learned to solve two-step addition form, so we can subtract the ones and tens more easily. Let’s go story problems. Today we will solve two-step in order. First we subtract 20 from 47. [Write 47 – 20 in column form on the board.] Since the ones will not change, let’s subtract subtraction story problems. the tens. How many tens are there in 47? [4 tens] How many tens do we subtract? [2 tens] What is the difference? [2 tens] GOAL: Do the ones change? [no] [Write 27 as the difference.] So, 47 minus 20 equals 27. After Jenna gave 20 flowers to her mother, Students will use two steps to solve subtraction story she has 27 flowers left. Are we finished? [No; we still need to problems. subtract the 6 flowers she gave to her grandmother.] Let’s MATERIALS NEEDED: blank sheets of paper or write another problem in column form to solve the rest of the dry-erase boards number sentence. How many flowers did Jenna have after she gave some to her mother? [27] [Draw an arrow from theCommon Core Standard: CCSS2.OA.1 difference, 27, diagonally up to the upper right (as shown LESSON WARM-UP on pages 129 and 130 in the Student Edition), and write 27 Review facts for fluency using the My Math Facts as the new minuend.] How many flowers did she give to her practice sheets. grandmother? [6] [Write –6 in column form under the new minuend.] Now let’s solve this. Let’s subtract the ones. What is THINKING TRIGGER 7 – 6? [1] Will the number of tens change here? [no] [Fill in 21 as the difference.] Now we know that 47 – 20 – 6 = 21. [Fill in 21 in the box.] Jenna kept 21 flowers for herself. Tell a story: Gino had 79¢. He bought a stamp for 50¢ II. Practicing the skill Copyright © by SPOTS Educational Resources. All rights reserved. and an envelope for 8¢. How much money does Gino have left? [Ask:] What number sentence can we write to Say: I will tell another story. Let’s solve it together. Hal has 58 solve this problem? books to sell at his garage sale. He sells 30 books in the morning. He sells 5 more books in the afternoon. How many books doesCONCEPT DEVELOPMENT Hal have left?I. Writing and solving two-step Ask students to repeat the main details of the problem, such story problems as what they know (the number of books Hal has to start with, how many he sells in the morning, and how many heTell a story: Jenna picked 47 flowers. She gave 20 flowers to her sells in the afternoon) and what they need to find out.]mother and 6 flowers to her grandmother. How many flowersdid Jenna keep for herself? Step 1. Let’s write a number sentence. How many books did Hal have in his garage at first? [58] [Write 58.] He sold 30 books inLet’s think about how to solve this problem. [Ask students to the morning. Will we add or subtract? [subtract] Why? [Whenrepeat the main details of the problem, such as what they he sold books, the number of books became less, so weknow (the number of flowers she picked, how many she gave subtract.] [Write –30.] He sold 5 books in the afternoon. Whatto her mother, and how many she gave to her grandmother) should we do with the 5? [We should subtract it as well.]and what they need to find out.] [Write –5.] How many books does he have left? [unknown]Step 1. Let’s write a number sentence to help us solve the [Write = .]problem. How many flowers did Jenna pick? [47] [Write 47.]She gave 20 flowers to her mother. Will we add or subtract? Step 2. Let’s rewrite this number sentence in column form to[subtract] Why? [When she gave flowers away, the number solve it. What number do we start with? [the number of booksof flowers became less, so we subtract.] [Write –20.] She also in the garage, which is 58] [Write 58.] What do we do next?gave 6 flowers to her grandmother. What should we do with [subtract the 30 books he sold in the morning] [Write –30the 6? [We should subtract it as well.] [Write –6.] How many (in column form), and solve together with the class.] Howflowers did Jenna keep? [unknown] [Write = .] many books did Hal have after he sold the 30 books? [28] Are we done yet? [no] What do we still need to do? [subtract the 5126 books that he sold in the afternoon] [Draw an arrow, write 28 – 5 in column form, and solve.] How many books does Hal

UUsisninggththeeBBoookk: p: apgaegse1s2799--18300 Two-Step Story Problems, Subtracting Twice Write a number sentence and solve. Write a number sentence and solve. Use a for the unknown number. Use a for the unknown number. 1. Ms. Jensen has $78. She bought Step 1. 1. There are 56 markers in a bin. Step 1. 4 tickets to Adventure World for Write the number sentence. Group A takes 20 markers. Write the number sentence. $50, and she paid another $6 Group B takes 4 markers. for games. $78 – $50 – $6 = 22 How many markers are left in 32 the bin? How much money does Ms. Step 2. Step 2. Jensen have left? Solve. 78 28 Solve. –6 There are markers left in – Ms. Jensen has $ 22 left. – 50 the bin. – 28 22 2. Maddie had 48 stickers. She Step 1. 2. There were 64 water bottles in a Step 1. cooler. The first group of guests Write the number sentence. gave 30 stickers to her sister and Write the number sentence. took 20 water bottles. Jeff then 64 – 20 – 2 = 42 5 stickers to her cousin. took 2 more water bottles. 48 – 30 – 5 = 13 Step 2. How many stickers does Maddie Step 2. How many water bottles are left Solve. have left? Solve. 48 18 in the cooler? 64 44 30 –5 Maddie has 13 stickers left. – There are 42 water bottles left – 20 –2 18 13 in the cooler. 44 42 3. Eduardo had 85¢. He bought Step 1. 3. Olivia has 56 pages to read. She Step 1. a pencil for 30¢, and he Write the number sentence. read 30 pages in the morning. Write the number sentence. paid 4¢ tax. She read 5 more pages in the 85 – 30 – 4 = 51 afternoon. 56 – 30 – 5 = 21 How much money does How many pages does Olivia Eduardo have left? Step 2. 85 55 still have to read? Step 2. 26 Solve. –5 Eduardo has 51 ¢ left. Olivia has 21 pages left Solve. 56 – 30 –4 – 30 to read. 55 51 26 21 130 Chapter 4 Lesson 3 129 Now let’s practice solving two-step story problems by sub- Point out to the students that for Step 2, they will copy the tracting twice. answer from the first column-form subtraction problem (on the left side) into the top box on the right, before they sub- For page 129, read and solve each story problem together tract the second amount. with the class. For page 130, have the students solve the problems independently while you circulate to offer help .Copyright © by SPOTS Educational Resources. All rights reserved. have left in the end? [23] [Complete the first number sentence DIFFERENTIATED INSTRUCTION with the difference: 23.] Hal has 23 books left. Struggling learners: Some students may get confused STUDENT TEACHER when presented with three numbers in a two-step sub- traction problem. Remind students to start each prob- Tell a story, and have students pair up to represent and solve lem with the greatest number. it: There were 59 ducks in the pond. 40 ducks flew into the trees. 4 ducks flew onto a fence. How many ducks are left in the pond? CLOSING STATEMENT: [Circulate and offer help as needed. Then have some pairs What did we learn today? Today we solved share their work with the class. Ask questions such as:] How two-step subtraction story problems. Tomorrow did you decide what operation to use? What number sentence we will subtract two-digit numbers by subtracting did you write? What two subtraction problems did you use to find the answer? How many ducks were left in the pond? [15] both tens and ones. [Note: If a student suggests adding 40 and 4, and then subtracting the results (44) from 59, explain that this is correct, 127 but that today we are solving this problem by subtracting twice, because the class hasn’t yet learned how to subtract two 2-digit numbers.]

Chapter 4 Lesson 4: Subtracting Two-Digit Numbers INTRODUCTORY STATEMENT: [Cross off four dots.] How many ones are left? [2 ones] [Write We’ve already learned how to subtract only ones 2 in the ones place of the difference.] Now let’s subtract tens. and only tens from a two-digit number. Today How many tens are there in 56? [5 tens] How many tens do we subtract? [2 tens] [Cross off the two Dot Cards-10 on the far we will subtract both ones and tens from left, leaving 3 tens.] How many tens are left? [3 tens] [Write 3 two-digit numbers. in the tens place of the difference.] So, 56 – 24 = 32. GOAL: Repeat this process with 65 – 34 and 78 – 51. Students will subtract ones and tens from two-digit III. Subtracting in column form numbers. MATERIALS NEEDED: Write 76 – 23 on the board in column form. Say: Now let’s Dot Cards; blank sheets of paper subtract without using Dot Cards to help us. Are we subtracting ones, tens, or both? [both] Which column do we subtract first?Common Core Standard: CCSS2.NBT.5; CCSS2.OA.1 [the ones column] Subtract the ones, 6 – 3, in your head. How many ones are left? [3 ones] [Write 3 in the ones place LESSON WARM-UP of the difference.] Now subtract the tens, 7 tens – 2 tens. How many tens are left? [5 tens] [Write 5 in the tens place of theReview facts for fluency using the My Math Facts practice difference.] How much is 76 – 23? [53]boRoekvlieetw. facts for fluency using the My Math Facts Repeat this with 37 – 22 and 88 – 84. Point out that when we practice sheets. have no tens in a two-digit number we do not write a zero, because a zero in front of a number has no value. THINKING TRIGGER STUDENT TEACHER Write 45 – 20 and 45 – 22 on the board. Ask: How is 45 – 20 different from 45 – 22? Divide the class into pairs. Give each pair of students a blank sheet of paper, and have them fold their papers in half. TellCONCEPT DEVELOPMENT students to label one half of the paper “tens or ones” and the other half “both.”Write several subtraction equations onI. Reviewing subtracting ones or tens from the board – some in which only tens are subtracted, some two-digit numbers in which only ones are subtracted, and some in which both tens and ones are subtracted. Have each pair choose twoWrite 65 – 4 in column form on the board. Ask: What are equations, write each equation in the correct column, andwe subtracting – tens or ones? [ones] [Discuss that we are solve them. Have the pairs present their work to the class.subtracting only the ones and that only the ones will change.Solve together.] Copyright © by SPOTS Educational Resources. All rights reserved.Write 54 – 30 in column form on the board. Ask: What arewe subtracting – tens or ones? [tens] [Discuss that we aresubtracting only the tens and elicit why the ones will notchange. Solve together.]II. S ubtracting ones and tens from two-digit numbers using Dot CardsWrite 56 – 24 in column form on the board. Ask: What arewe subtracting here – tens, ones, or both? [both] Let’s showthis with Dot Cards. What number do we start with? [56] [PlaceDot Cards showing 56.] When we subtract both tens and ones,we subtract the ones column first. How many ones are there in56? [6 ones] How many ones do we need to subtract? [4 ones]128

UUsisnigngthteheBBooko:kp: apgaegses1381-18322 Subtracting Two-Digit Numbers We can subtract two-digit numbers. Subtract. First subtract the ones. Tens Ones Then subtract the tens. 1. Tens Ones 2. Tens Ones 3. Tens Ones 4. Tens Ones 47 46 67 76 89 –2 3 –2 2 –3 6 –2 4 –4 8 24 24 31 52 41 There are 4 ones left. There are 2 tens left. 5. Tens Ones 6. Tens Ones 7. Tens Ones 8. Tens Ones Cross off to subtract. Write the difference. 58 87 65 97 1. 2. –3 6 –5 3 –2 3 –5 3 22 34 42 44 Tens Ones Tens Ones 9. Tens Ones 10. Tens Ones 11. Tens Ones 12. Tens Ones 36 57 74 96 88 69 –1 5 –2 2 –3 1 –6 6 –3 4 –4 2 21 35 43 30 54 27 3. 4. Write a number sentence and solve. Use a for the unknown number. Tens Ones Tens Ones 13. Mr. Peters has $75. He buys a Step 1. book for $30 and a pen for $4. Write the number sentence. 45 56 $75 – $30 – $4 = 41 –3 1 –3 4 How much money does Mr. Peters have left? Step 2. 14 22 Solve. Mr. Peters has $ 41 left. 75 45 _ 30 _4 45 41 Chapter 4 Lesson 4 131 132 Now let’s practice subtracting ones and tens from two-digit Remind students that when we subtract both tens and ones numbers. in columns, we subtract the ones first. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Review place value by writing a list Who can tell us what we learned today? Today we of numbers in a place-value chart (single- and two-digit subtracted two-digit numbers. Tomorrow we will sub- numbers as well as two-digit numbers that end in 0). Have students take turns naming a number and then tract by regrouping with Dot Cards. identifying which digit is in the tens place and which is inCopyright © by SPOTS Educational Resources. All rights reserved. the ones place. 129

Chapter 4 Lesson 5: Regrouping Using Dot Cards INTRODUCTORY STATEMENT: II. Regrouping in column form Copyright © by SPOTS Educational Resources. All rights reserved. Yesterday we subtracted ones and tens from two-digit numbers. Today we will subtract Let’s show the subtraction we just did with Dot Cards by regrouping in column form. We moved one ten over toward the two-digit numbers by regrouping a ten. ones to form a teen number. Do we still have 5 tens? [no] So let’s cross out the 5 tens in the tens column and write that now there GOAL: are only 4 tens. [Cross out the 5, and write a small 4 above the 5.] Now that we took one of the tens to add to the ones column, Students will regroup a ten to subtract two-digit numbers. what teen number do we have? [13] Let’s cross out the 3 and write the new teen number. [Cross out the 3, and write a small MATERIALS NEEDED: Dot Cards 13 above it.] Now we can subtract. First let’s subtract the ones. What is 13 – 5? [8] [Write 8 in the ones place of the difference.]Common Core Standards: CCSS2.NBT.5; CCSS2.NBT.7; Now let’s subtract the tens. What is 4 tens minus 1 ten? [3 tens]CCSS2.OA.1 [Write 3 in the tens place of the difference.] So, 53 – 15 = 38. LESSON WARM-UP Introduce the term“regrouping.”Say: What we just did is called “regrouping.” Regrouping means that we move over one part of Review facts for fluency using the My Math Facts a number and have it join another group. practice sheets. When we’re working with Dot Cards, and we don’t have enough THINKING TRIGGER ones to subtract from, we regroup by moving one Dot Card-10 over to the right, to join the ones. When we subtract in columns, Write 44 – 23 and 44 – 25 in column form on the board. we show this regrouping by crossing off the number in the tens Ask: How are these two subtraction equations different column and writing in the new number of tens; and then we from each other? cross off the number in the ones column and write in the teen number. Then we subtract: first the ones, then the tens.CONCEPT DEVELOPMENT Ask: Why is it that sometimes we need to regroup when weI. Using Dot Cards to regroup subtract? [because sometimes we don’t have enough ones to subtract from] [Write 42 – 29 in column form in a place-On the board write 53 - 15 in column form, in a place-value value chart labeled Tens and Ones.] Let’s show this with Dotchart labeled Tens and Ones (see page 133 in the Student Cards. [On the board place Dot Cards showing 42.] Let’s findEdition). Place Dot Cards showing 53 on the board. Ask: How the difference using the three steps we just followed.many ones are there in 53? [3 ones] How many ones do we needto subtract? [5 ones] Are there enough ones in 53 to subtract Step 1. We need to subtract 9 ones. Are there enough ones tofrom? [No; there are only 3 ones, and we need to subtract subtract from? [No, there are only 2 ones.] So we will regroup.5 ones.] We need to move 1 ten over to the ones to form a teen We will move 1 ten over to the ones to form a teen number.number, so that we will have enough ones to subtract. [Move [Move the Dot Card-10 on the far right over toward the Dotthe Dot Card-10 on the far right closer to the Dot Card-3.] Card-2, and draw a circle around both cards together.] HowNow I’ll draw a circle around the Dot Card-10 and the ones card, many tens do we have now? [3 tens] [Cross out the 4 in theto make the teen number. [Draw a circle around both cards tens column, and write a small 3 above it.] How many do wetogether.] What teen number do we have now? [13] How many have in the ones column now? [12] That’s right! Now we have atens do we have left? [4 tens] Yes; now there are 4 tens, because teen number in the ones column. [Cross out the 2 in the oneswe took away one of the 5 tens to “regroup” it – we moved it over column and write a small 12 above it.]to the ones to make the teen number. Now let’s subtract 5 onesfrom 13. How do we subtract 13 – 5 using Dot Cards? [We cross Step 2. Now we can subtract the ones. How do we subtract 12 – 9off all three dots from the Dot Card-3 and two more dots using Dot Cards? [Cross off 9 dots from the ten card.] [Use onefrom the top of the Dot Card-10.] [Cross off the dots.] So big X to cross of the 9 dots from the ten card.] What is 12 – 9?what is 13 – 5? [8] Now let’s subtract 1 ten from 4 tens. [Cross off [3] [Write 3 in the ones place of the difference.]one Dot Card-10 at the far left.] What is the difference? [3 tens]We have three Dot Cards-10 and 8 dots left. So, 53 – 15 = 38. Step 3. Now let’s subtract the tens. [Cross off two Dot Cards-10 on the far left] How many tens are left? [1 ten] [Write 1 in the tens130 place of the difference.] What is the difference of 42 – 29? [13]

UUsisninggththeeBBoookk: p: paaggeess1833-81344 Regrouping with Dot Cards Regroup a ten to form a teen number. Write the new numbers. Tens Ones Cross off to subtract the ones. Cross off to subtract the tens. 3 14 Sometimes we do not have enough ones to subtract. Then: Write the difference. 1. Regroup. Move over a ten to the ones place to form a teen number. 44 1. Tens Ones 2. –1 8 Write the new numbers. 2. Subtract the ones. 3 13 26 3. Subtract the tens. 43 Tens Ones Tens Ones –3 5 3 16 3 12 8 46 –2 9 42 3. Tens Ones 4. –1 3 17 2 12 Regroup a ten to form a teen number. Write the new numbers. Tens Ones Cross off to subtract the ones. Cross off to subtract the tens. 32 2 13 Write the difference. –1 7 33 1. 2. Tens Ones 15 –2 9 Tens Ones 5. Tens Ones 6. 4 2 16 1 12 3 11 36 22 –2 8 –1 3 41 –2 7 8 9 14 Write a number sentence and solve. Use a for the unknown number. 3. 4. 7. Rajiv had $48. He buys a pair of Step 1. pants for $20 and a belt for $8. Write the number sentence. How much money does Rajiv $48 – $20 – $8 = 20 have left? Tens Ones Tens Ones Step 2. 28 Rajiv has $ 20 left. 3 15 3 17 Solve. 48 45 47 – 20 –8 –2 7 –1 9 28 20 18 28 Chapter 4 Lesson 5 Regrouping with Dot Cards 133 134 Now let’s practice subtracting with regrouping. traction problem and write the new numbers in the small Remind the students to first regroup with the Dot Cards, boxes above. Afterward, they should cross off the ones on by drawing a circle around the ten card on the far right the Dot Cards and fill in the difference for the ones. Then and the ones card. Then they should cross off each of they should cross off the tens on the Dot Cards and fill in the the numbers of the minuend in the column-form sub- difference for the tens.Copyright © by SPOTS Educational Resources. All rights reserved. III. Practicing the Skill DIFFERENTIATED INSTRUCTION In the same way, solve 63 – 16 and 56 – 7, using Dot Cards Struggling learners: Some students may forget that as support. Help the students understand the three steps when regrouping a ten to make a teen number they are we use to find the difference when subtracting with re- taking away one ten. Be sure that they cross out the tens grouping: 1) regroup - move over a ten to make a teen digit and write a small tens-number, that is one less than number, and write the new numbers; 2) subtract the ones; the original number of tens, at the top of the tens place. 3) subtract the tens. CLOSING STATEMENT: STUDENT TEACHER Who can tell us what we learned today? Today we subtracted two-digit numbers with On the board write some subtraction equations, similar to regrouping. Tomorrow we will practice this more. those in the lesson, in column format, with the tens and ones columns labeled. Have pairs of students come up to 131 the board to demonstrate the subtraction process. Have one student show the regrouping using Dot Cards, while the other student shows the subtraction in the column equation.

Chapter 4 Lesson 6: Practice: Regrouping With Dot Cards INTRODUCTORY STATEMENT: Step 2. Now we can subtract the ones. How do we subtract 14 – Copyright © by SPOTS Educational Resources. All rights reserved. Yesterday we used Dot Cards to show two-digit 8 using Dot Cards? [Cross off 8 dots from the ten card.] [Cross off the dots. Use one big X to cross of the 8 dots from the ten subtraction with regrouping. Today we will card.] What is the difference? [6] [Write 6 in the ones place of practice this more. the difference.] GOAL: Step 3. Now let’s subtract the tens. [Cross off the Dot Card-10 on the far left] How many tens are left? [4 tens] [Write 4 in the Students will practice subtracting two-digit numbers tens place of the difference.] What is the difference of 64 – 18? with regrouping using Dot Cards. [46] MATERIALS NEEDED: Dot Cards; blank sheets of pa- per; or dry-erase boards Leave the problem on the board.Common Core Standards: CCSS2.NBT.5; CCSS2.NBT.7 II. Writing in a 1 to form a teen number LESSON WARM-UP Say: Now I will show you a shorter way to record the new teen number for the ones in the problem. [Erase both the 14 Review facts for fluency using the My Math Facts above the 4 and the crossed-out 4. Rewrite the 4 in the ones practice sheets. column.] 14 is 1 ten and 4 ones, so instead of crossing out the number in the ones column and writing the teen number on top THINKING TRIGGER of it, we can just write in a number 1, for the 1 ten, next to the 4 ones to make it a teen number. [Insert a 1 to the left of the 4.] Write 76 – 38 on the board. Ask: How can we solve this with Dot Cards? How can we solve this in column form? On the board write 43 – 26 in column form, in a labeled place-value chart, and place Dot Cards showing 43. SolveCONCEPT DEVELOPMENT the problem with the Dot Cards and in column form simultaneously, as above, relating the action with the DotI. Reviewing subtracting with regrouping Cards to the regrouping in columns.using Dot Cards Repeat with 50 - 8. Point out that there are no ones in 50, soOn the board write 64 – 18 in column form, in a place-value when we regroup, the new number in the ones column willchart labeled Tens and Ones. Say: Let’s solve this with Dot be 10.Cards. [On the board place Dot Cards showing 64.] Let’s findthe difference using the three steps we learned. Summarize: When we don’t have enough ones to subtract from,Step 1. We need to subtract 8 ones. Are there enough ones in and we need to regroup a ten to form a teen number, we can64 to subtract from? [No; there are only 4 ones.] What will we write in a 1 next to the number of ones in the ones column toneed to do? [We need to regroup – to move 1 ten over to the form the teen number (or ten).ones card to form a teen number.] [Move the Dot Card-10on the far right over toward the Dot Card-4, and draw a circle STUDENT TEACHERaround both cards together.] How many tens do we have left?[5 tens] How do we show this on the subtraction problem? On the board write 73 – 27 in column form. Have a student[We cross out the 6 in the tens column, and write a small 5 show it using Dot Cards. Ask the rest of the class to solve itabove it.] [Cross out the 6, and write in a small 5.] How many using column subtraction. Discuss the steps for regroupingdo we have in the ones column now? [14] How do we show shown by Dot Cards: moving a ten over to form a teenthis on the subtraction problem? [Cross out the 4 in the ones number, crossing off to subtract the ones, and crossing off tocolumn and write a small 14 above it.] [Cross out the 4, and subtract the tens; and with column subtraction: writing thewrite in a small 14.] new numbers, subtracting the ones, and then subtracting the tens.132

Using the Book: pages 135-136 Practice: Regrouping with Dot Cards Regroup a ten to form a teen number. Write the new numbers. Cross off to subtract the ones. Cross off to subtract the tens. Write the difference. When we regroup, we can write in a 1 next to the ones to form a teen number. 1. 2. Tens Ones Tens Ones Tens Ones 3 3 4 4 12 4 15 514 –2 5 –1 8 –3 9 17 27 Regroup a ten to form a teen number. Write the new numbers. 3. Tens Ones 4. Tens Ones Cross off to subtract the ones. Cross off to subtract the tens. 5. 3 Write the difference. 7. 2 4 14 1. 3. 136 3 14 –2 8 –1 5 Tens Ones Tens Ones 16 19 3 2 Tens Ones 6. 2 4 16 3 18 –2 9 –1 9 3 11 –1 6 17 19 15 3. 4. Tens Ones Tens Ones Tens Ones 3 6 3 4 11 7 12 4 12 –1 9 –1 6 –2 4 22 56 18 Tens Ones Chapter 4 Lesson 6 3 4 13 –1 6 27 135 Now let’s practice regrouping to subtract two-digit numbers. Remind the class to record the new number of tens they have above the tens column and to write in a 1 next to the Guide students through the process of regrouping with number in the ones column to form the teen number. the Dot Cards.Copyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Some students may be confused Today we practiced subtracting two-digit numbers about how to write the new teen number in the ones with regrouping using Dot Cards. Tomorrow we column after regrouping. Remind them that they can will subtract two-digit numbers with regrouping write in the 1 ten next to the ones to form the teen num- in column form, without using Dot Cards. ber, or they can cross off the ones and then write the new teen number above the ones column (as was done in the previous lesson). 133

Chapter 4 Lesson 7: Regrouping in Columns II. Subtracting with regrouping without using Dot Cards INTRODUCTORY STATEMENT: Yesterday we practiced subtracting two-digit num- Write 84 – 47 on the board in column form, and solve without bers by regrouping tens using Dot Cards. Today we Dot Cards. Guide the class through the steps , and write on will practice subtracting two-digit numbers with the board as you go along. Ask: Are there enough ones in 84 regrouping in columns, without using Dot Cards. to subtract from? [no] What should we do? [Regroup 1 ten to form a teen number.] [Cross off the 8 tens.] How many tens GOAL: do we have after we regroup? [7] How do we show this? [Write a small 7 above the tens column.] How many do we have Students will subtract two-digit numbers with in the ones column after we regroup? [14] How do we show regrouping in columns. this? [Write a small 1 next to the 4 ones to show the teen Materials needed: Dot Cards number 14.] Now let’s subtract the ones. What is 14 – 7? [7] [Write 7 in the ones column of the difference.] Now subtractCommon Core Standards: CCSS2.NBT.5; CCSS2.NBT.7 the tens. What is 7 tens minus 4 tens? [3 tens] [Write 3 in the tens column of the difference.] What is the difference of 84 – LESSON WARM-UP 47? [37] Review facts for fluency using the My Math Facts Repeat the process with 77 – 59 and 74 – 68. Guide the class practice sheets. to notice that the difference of 74 – 68 has no tens. Discuss why this is so. Point out that when we have no tens in a two- THINKING TRIGGER digit number we do not write a zero, because a zero in front of a number has no value. On the board, write 83 – 28 and 76 – 25. Ask: For which of these do we need to regroup to find the difference? How In conclusion, ask: How do you know when you need to do you know? regroup? [You need to regroup when the number you are subtracting (the subtrahend) has more ones than the number you are subtracting from (the minuend).]CONCEPT DEVELOPMENT STUDENT TEACHERI. Reviewing subtracting with regrouping On the board write 65 – 19 in column form in a place-valueusing Dot Cards chart labeled Tens and Ones. Call on individual students to describe each step needed to subtract: 1) check to see if thereOn the board write 75 – 36 in column form in a place-value are enough ones to subtract from; 2) regroup 1 ten to formchart labeled Tens and Ones. Solve, first with Dot Cards and a teen number, leaving 5 tens; 3) add 1 ten to the 5 ones tothen in column form; or you may want to solve in both ways make 15; 4) subtract the ones; 5) subtract the tens. Togethersimultaneously, relating each action with the Dot Cards to as a class, state the difference: 46.the regrouping in columns. Ask: What number will we show?[75] What will we subtract? [36] [Guide the class through the Copyright © by SPOTS Educational Resources. All rights reserved.steps:] Are there enough ones to subtract? [no] What shouldwe do? [Regroup 1 ten to form a teen number.] How manytens do we have now, after we regroup? [6 tens] How many dowe have in the ones column after we regroup? [15] Subtract 6ones from 15 ones. What is the difference? [9 ones] [Write 9in the ones column of the difference.] Now subtract 3 tensfrom 6 tens. What is the difference? [3 tens] [Write 3 in the tenscolumn of the difference.] What is the difference of 75 – 36?[39]134

Using the Book: pages 137-138 Regrouping in Columns When we subtract more than the ones that there are, Regroup and subtract. we regroup to form a teen number. 1. 2. 3. 4. Regroup and subtract. 2. Tens Ones 3. Tens Ones Tens Ones Tens Ones Tens Ones 1. 5 Tens Ones 3 5 7 6 Tens Ones 6 15 4 4 16 6 12 8 11 –4 8 –2 7 –3 6 –4 3 7 14 6 5 17 –4 8 17 –2 8 19 26 38 73 26 –3 5 29 5. 4 6. 3 7. 5 8. 8 5 13 4 13 6 14 9 15 –1 6 –3 7 –3 5 –5 8 4. 5. 6. 37 37 6 29 Tens Ones Tens Ones Tens Ones 9. 8 10. 6 11. 4 12. 5 5 7 8 9 13 7 17 5 13 6 11 6 11 8 14 9 12 –4 7 –4 9 –2 4 –4 6 –3 4 –5 8 –4 7 28 15 46 29 27 26 45 13. 7 15. 6 7. 8. 9. 14. 8 16. 7 8 15 7 13 Tens Ones Tens Ones Tens Ones –4 9 9 16 –2 4 8 17 –5 7 –7 9 6 4 5 36 49 39 8 7 11 5 13 6 12 –3 8 –1 4 –3 7 LET’S WRITE! 33 39 25 10. 11. Tens Ones 12. Look at exercise number 16. Are there any tens in your answer? Explain why or why not. Tens Ones 8 Tens Ones Sample answer: There are no tens, because I had to take one 6 ten to regroup. That left 7 tens, and I needed to subtract all 7 7 9 18 of those tens. –6 9 7 14 8 12 –2 9 –4 5 29 45 37 137 Chapter 4 Lesson 7 138 Now let’s practice subtracting two-digit numbers with re- students complete the exercises on pages 137 and 138 on grouping. their own. Together with the class, read the text at the top of page Direct the class’ attention to the Let’s Write! section. Read 137. Do the first row of exercises together. Then have the and discuss the question. Then have the students write their explanation.Copyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling learners: Some students may regroup when it Who can tell us what we learned today? Today we is not necessary to do so. Remind them that the top num- subtracted two-digit numbers with regrouping in ber (the minuend) is the number we start with, and that columns. Tomorrow we will solve two-step story prob- they first need to check to see if there are enough ones to subtract from, and that’s how they will know whether they lems using addition and subtraction. need to regroup. For additional help, you may have them draw dots for the number of ones in the minuend. 135

Chapter 4 Lesson 8: Problem Solving: Two-Step Story Problems, Adding and Subtracting INTRODUCTORY STATEMENT: so we can find the answer more easily. Let’s go in order. First we Copyright © by SPOTS Educational Resources. All rights reserved. We’ve learned to solve two-step subtraction story subtract 54 – 20. [Write 54 – 20 in column form.] The ones willproblems. Today we will solve two-step addition and not change, so let’s subtract the tens. How many tens are there in 54? [5 tens] How many tens do we subtract? [2 tens] What is subtraction story problems. the difference? [3 tens] Do the ones change? [no] [Write 34 as the difference.] So, 54 – 20 = 34. After Jon spent $20, he has $34. GOAL: Are we finished? [No; we still need to add the $5 he earned shoveling the snow.] Students will solve two-step addition and subtraction Let’s write another problem in column form to solve the rest of story problems. the number sentence. How much money did Jon have after he MATERIALS NEEDED: blank sheets of paper spent $20? [$34] How much money did he earn? [$5] [Draw an arrow from the difference, 34, up to the upper right side, andCommon Core Standard: CCSS2.OA.1 write 34 + 5 in column form.] Now let’s solve this. Let’s add the ones. What is 4 + 5? [9] Will the number of tens change here? LESSON WARM-UP [no] [Fill in 39 as the sum.] Now we know that 54 – 20 + 5 = 39. [Fill in 39 in the box.] Jon has $39 now. Review facts for fluency using the My Math Facts practice sheets. II. Two-step story problems, adding first THINKING TRIGGER Tell a story: There are 45 cans of red paint and 20 cans of green paint on the shelf. Hanna takes 5 cans of red paint from the shelf. Write a plus sign on the board and ask: What types of How many cans of paint are left on the shelf? [Ask students to problems can we solve by adding? [Accept answers and repeat the main details of the problem, such as what we know discuss. Then write a minus sign on the board and ask:] (how many cans of each color there are and how many cans What types of problems can we solve by subtracting? Hanna takes); and what we need to find out.] [Accept answers and discuss.] What is different about Step 1. Let’s write a number sentence. There are 45 cans of red this story: Lyle has 34 stamps. He gives 10 stamps to his paint and 20 cans of green paint on the shelf. Do we add or brother. Later, he buys 5 more stamps. How many stamps subtract that? [add] Why? [When we have two parts, we add does Lyle have now? them together to find the whole.] [Write 45 + 20.] How many cans of paint did Hanna take from the shelf? [5] Do we add orCONCEPT DEVELOPMENT subtract that? [subtract] Why? [When Hanna takes some cans,I. Two-step story problems, subtracting first the number of cans becomes less.] [Write – 5.] How many cans of paint are on the shelf now? [unknown] [Write = .]Tell a story: Jon has $54. He spends $20 at a school play. He Step 2. Now let’s solve this. Let’s go in order. First we add 45 +earns $5 shoveling the neighbor’s snow. How much money does 20. [Write 45 + 20 in column form on the board, and solveJon have now? [Ask students to repeat the main details of the together.] What’s the sum? [65] [Fill in 65.] Are we done yet?problem, such as what we know (how much money Jon has, [No; we need to subtract the 5 cans Hanna took.] How manyhow much he spends, and how much he earns) and what we cans were on the shelf in all? [65] How many cans did Hannaneed to find out.] take? [5] [Draw an arrow from the sum, 65, to the upper rightStep 1. Let’s write a number sentence for this problem. How side, and write 65 – 5 in column form. Solve together with themuch money does Jon have to start with? [$54] [Write $54.] He class (60).] Now we can complete our original number sentence:spends $20. Will we add or subtract that? [subtract] Why? [When 45 + 20 – 5 = 60. [Fill in 60 in the box.] There are 60 cans of painthe spends, the amount of money he has becomes less, so left on the shelf.we subtract.] [Write –$20.] Then he earns $5 shoveling the I will tell another story. Let’s solve it together: Mrs. Lopez bakedneighbor’s snow. What should we do with the $5? Should we add 24 carrot muffins and 20 blueberry muffins in the morning. Sheor subtract that? [add] Why? [When he earns, the amount of takes 30 muffins to a bake sale in the afternoon. How manymoney he has becomes more.] [Write +$5.] How much money muffins does Mrs. Lopez have left? [Ask students to repeat thedoes Jon have now? [unknown] [Write = .] main details of the problem, such as what we know, and whatStep 2. Now let’s rewrite this number sentence in column form, we need to find out.] Step 1. Mrs. Lopez baked 24 carrot muffins and 20 blueberry muffins. Will we add or subtract that? [add] Why? [When we136

Using the Book: pages 139-140 Two-Step Story Problems, Adding and Subtracting Write a number sentence and solve. Use a for the unknown number. Write a number sentence and solve. Use a for the unknown number. 1. There are 25 thick markers and Step 1. 1. Jill has 10 peas on her plate. Step 1. 20 thin markers in the bin. Billy Write the number sentence. She eats 4 peas. Then she puts 5 Write the number sentence. takes 2 markers from the bin. more peas on her plate. 10 – 4 + 5 = 11 43 How many markers are left in Step 2. How many peas are on Jill’s Step 2. 10 6 the bin? Solve. plate now? Solve. 4 +5 There are markers. There are 11 peas on – 11 Jill’s plate. 6 2. There are 36 eggs in cartons Step 1. 2. Pete has $35. He spends $10. Step 1. and 12 eggs in a bin. Tami takes Write the number sentence. Later, his mother gives him $25. Write the number sentence. 3 eggs. 36 + 12 – 3 = 45 How much money does Pete $35 – $10 + $25 = 50 have now? How many eggs are left? Step 2. 36 48 Step 2. 35 25 Solve. 12 –3 Pete has $ 50 . Solve. 10 + 25 There are 45 eggs left. + – 48 45 25 50 3. Paul has $42. He spends $20. Step 1. 3. There are 36 people on a bus. Step 1. Later, his father gives him $10. Write the number sentence. At the first stop, 10 more people Write the number sentence. How much money does Paul get on the bus. At the second 36 + 10 – 20 = 26 have now? $42 – $20 + $10 = 32 stop, 20 people get off the bus. Paul has $ 32 . Step 2. 42 22 How many people are still on Step 2. 36 46 Solve. 20 + 10 the bus after the second stop? Solve. Chapter 4 Lesson 8 – There are 26 people still on + 10 – 20 22 32 the bus after the second stop. 46 26 139 140 Now let’s practice solving two-step story problems. Read and solve the story problems together with the class. have two parts, we add them together to find the whole.] DIFFERENTIATED INSTRUCTION [Write 24 + 20.] She takes 30 muffins to a bake sale. Will we add or subtract that? [subtract] Why? [When Mrs. Lopez takes Struggling learners: Some students may have difficulty some muffins to the sale, the number of muffins she has deciding what operation to perform first, or which num- becomes less.] [Write – 30.] How many muffins does Mrs. bers to use first when solving two-step story problems. Lopez have left? [unknown] [Write = .] Remind them that two-step problems involve a sequence of events. They need to think of the sequence of events in Step 2. Solve together by writing two problems in column the problem and use that to decide the sequence of the form, as above. Elicit the steps of the process as you solve. steps needed to solve the problem. First find the sum of the muffins Mrs. Lopez baked [44]. Next,Copyright © by SPOTS Educational Resources. All rights reserved. subtract from that sum the number of muffins she took to the sale. Complete the first number sentence: 24 + 20 – 30 = 14]. Say: Mrs. Lopez has 14 muffins left. STUDENT TEACHER CLOSING STATEMENT: Tell a story: Michael has 52 stickers. He puts 42 stickers in his What did we learn today? Today we solved two-step sticker album. His grandma gives him 25 more stickers. How many story problems using addition and subtraction. stickers does Michael have now, that are not in his album? [Have the students work in pairs.] With your partner, discuss what Tomorrow we will practice subtracting in columns. you know and what you need to find out. Then write a number sentence, and solve it. [Circulate to check that students have the correct number sentence before they begin to solve it.] 137

Chapter 4 Lesson 9: Mixed Practice: Subtracting in Columns INTRODUCTORY STATEMENT: How do we show this? [Cross off the 4 tens, and write a small Copyright © by SPOTS Educational Resources. All rights reserved.Today we will practice subtracting two-digit numbers 3 above the tens column.] How many do we have in the ones column after we regroup? [13] How do we show this? [Write in columns, with and without regrouping. a small 1 next to the 3 ones to show 13.] Let’s subtract the ones: 13 – 8. How many ones are left? [5] [Fill in 5 in the ones GOAL: place of the difference.] Now let’s subtract the tens: 3 tens – 1 ten. How many tens are left? [2 tens] [Fill in 2 in the tens place Students will subtract two-digit numbers in columns, of the difference.] What is the difference? [25] 43 – 18 = 25. with and without regrouping. MATERIALS NEEDED: large blank index cards In the same way, solve 71 – 45.Common Core Standards: CCSS2.NBT.5; CCSS2.NBT.7; III. Subtracting with and without regroupingCCSS2.OA.1 On the board, write 55 – 17 and 36 – 23 in column form. LESSON WARM-UP Point to 55 – 17 and ask: Do we need to regroup to subtract? [yes] How do you know? [There are not enough ones in 55 Review facts for fluency using the My Math Facts to subtract from. We can’t subtract 7 ones from 5 ones.] So practice sheets. let’s regroup. How many tens and how many ones do we have after we regroup? [4 tens and 15 ones] [Cross out the 5 tens, THINKING TRIGGER and write a small 4 above the tens. Write a small 1 next to the 5 ones. Solve.] 55 – 17 = 38. Write 54 – 28 and 86 – 24 on the board. Ask: For which of these do we need to regroup to find the difference? Point to 76 – 23 and ask: Do we need to regroup to subtract? Explain. [no] How do you know? [We have enough ones in 76 to subtract 3 ones from 6 ones.] [Solve.] 76 – 23 = 53.CONCEPT DEVELOPMENT: In the same way, compare and solve 84 – 31 and 63 – 34.I. Subtracting without regrouping IV. Solving two-step story problemsWrite 64 – 23 in column form on the board. Ask: What are wesubtracting from 64 − tens, ones, or both? [both] So, both the Now let’s solve a story problem.number of tens and the number of ones will become less. [Guidethe class through the steps to solve the equation.] Are there Zach is writing some words on the board. He writes 25 words.enough ones in 64 to subtract from? [yes] Do we need to regroup Then he erases 10 of the words and writes 20 more words on theto subtract? [no] What should we do first? [subtract the ones] board. How many words are on the board now?How many ones are left? [1 one] [Fill in 1 in the ones place ofthe difference.] Now let’s subtract the tens. How many tens are Ask students to repeat the main details of the problem, suchleft? [4 tens] [Fill in 4 in the tens place of the difference.] What as what we know (how many words he wrote, how many heis the difference? [41] 64 – 23 = 41. erased, and how many more he wrote) and what we need to find out (how many words are on the board now). Say: Let’sII. Subtracting with regrouping write a number sentence to help us solve the problem. [Guide students to help you write the number sentence. ElicitWrite 43 – 18 in column form on the board , and write on the why you need to add or subtract. The completed numberboard as you go along. Say: Let’s find the difference. Are there sentence is: 25 – 10 + 20 = . Then solve together, in columnenough ones in 43 to subtract from? [no] What should we do? form. Elicit what you will solve first (25 – 10). Solve. Elicit what[Regroup: Move 1 ten over to join the ones to form a teen needs to be done next. Draw an arrow to the upper right,number.] How many tens do we have left after we regroup? [3] write the second problem in column form (15 + 20), and solve.] There are 35 words on the board now.138

Using the Book: pages 141-142 Mixed Practice: Subtracting in Columns 54 67 Do we have to regroup? Circle the correct sign. –2 8 –3 4 Subtract. P P 1. 2. 5 3. 8 4. O O P 74 P 6 12 P 9 11 P 68 –3 3 –37 –54 –26 Sometimes we need to Sometimes we have O 41 O 25 O 37 O 42 regroup to have enough enough to subtract without regrouping. 5. 7 6. 7. 6 8. 3 to subtract. Do we have to regroup? Circle the correct sign. P 814 P 43 P 7 12 P 4 13 Subtract. –56 –23 –26 –18 O 28 O 20 O 46 O 25 1. 2. 3. 5 7 P 58 9. 10. 11. 12. P 6 11 P 8 14 –3 6 –4 7 –2 7 5 P 76 P 87 8 O 25 O 37 O 3 1 O –25 O –64 P 615 P 9 11 O –29 51 23 O –56 36 35 4. 5. 6. P 96 6 P 66 Write a number sentence and solve. Use a for the unknown number. P 7 12 –4 6 –2 8 – 4 2 O 50 O 44 O 2 4 10. Sam is putting books in boxes. Step 1. There were 25 books on shelves Write the number sentence. and 14 books on the floor. Sam already put 8 of the books 25 + 14 – 8 = 31 7. 8. 9. in boxes. Step 2. 7 6 Solve. 25 39 P 8 12 P 87 P 7 13 How many books does Sam have left to box? O –5 7 O –5 3 O – 4 5 + 14 –8 25 34 2 8 Sam has 31 books left to box. 39 31 Chapter 4 Lesson 9 141 142 Now let’s practice subtracting two-digit numbers with to circle the checkmark if they need to regroup to subtract, regrouping. and to circle the X if they don’t need to regroup to subtract. Remind students to first check to see if they have enough Read and discuss together the story problem on page 142. ones in the first number to subtract from. Instruct themCopyright © by SPOTS Educational Resources. All rights reserved. STUDENT TEACHER: DIFFERENTIATED INSTRUCTION Have the class work in pairs. Give each student two index Struggling learners: Some students may regroup when cards. Ask them to write on one of the cards, in column it is not necessary to do so. Remind them that the top form, a subtraction equation (without the answer) that number (the minuend) is the number we start with, and needs no regrouping. On the other card ask them to write, that they first need to check to see if there are enough ones in column form, a subtraction equation (without the to subtract from, and that’s how they will know whether answer) that needs regrouping. Have them trade cards and they need to regroup. For additional help, you may have solve each other’s cards. Call on some pairs to share their them draw dots for the number of ones in the minuend. work. Ask questions such as how they knew what problem to write, and how they solved the problems. CLOSING STATEMENT: Who can tell us what we learned today? Today we practiced subtracting two-digit numbers, with and without regrouping. Tomorrow we will learn how to subtract on the number line! 139

Chapter 4 Lesson 10: Subtracting Ones from a Decade Number INTRODUCTORY STATEMENT: what direction do we jump? [back, toward the beginning of We’ve learned to subtract 2 two-digit numbers the number line] [Write 40 at the end of the number line.] with regrouping. Today we will learn to subtract When we jump back, in which tens will the difference be? [in the 30s] [Draw a small jump back and label the jump –1.] What is single-digit numbers from decade numbers the difference? [39] on the number line. Repeat with 80 – 2. GOAL: Summarize: When we subtract a single-digit number from a Students will subtract single-digit numbers from decade number, the difference will be in the previous ten. decade numbers by making one jump back on the number line. III. Relating subtracting from ten to MATERIALS NEEDED: Dot Cards-10 subtracting from a decade numberCommon Core Standards: CCSS2.NBT.7; CCSS2.MD.6 Write 10 – 4, and draw an open number line next to it. Write 10 at the end of the number line, and draw a jump back LESSON WARM-UP labeled –4. Ask: Where do we get to? [6] Review facts for fluency using the My Math Facts Write 90 – 4, and draw an open number line next to it. Write 90 practice sheets. at the end of the number line, and draw a jump back labeled –4. Ask: In which tens will the difference be? [in the 80s] Since THINKING TRIGGER we know that 10 – 4 = 6, where will we get to for 90 – 4? [86] On the board, write 10 – 4 and 60 – 4. Ask: How are Repeat with 10 – 5 and then with 70 – 5. Point out that 10 – 4 and 60 – 4 alike? [In both problems, we are since we know that 10 – 5 = 5, we can easily figure out the subtracting 4 from a ten – either 1 ten or multiple difference of 70 – 5. tens.] STUDENT TEACHER:CONCEPT DEVELOPMENTI. Subtracting from decade numbers using On the board, write pairs of subtraction number sentences: 10 – 3 and 30 – 3; 10 – 6 and 50 – 6; 10 – 8 and 70 – 8. D raw an Dot Cards open number line next to each number sentence. For each pair of number sentences, call up two students. Have the firstWrite 50 – 1. Place five Dot Cards-10 on the board, and cross student fill in the number line for the first equation and writeoff one dot from the top right of the Dot Card-10 at the far in the answer to that number sentence, and have the secondright. Ask: How many tens are there in 50? [5 tens] How many student fill in the number line for the second equation andtens will there be in the difference? [4 tens] How do you know? write in the answer to that number sentence.[because there are only 4 full Dot Cards-10 left] What is thedifference for the problem 50 – 1? [49] Copyright © by SPOTS Educational Resources. All rights reserved.In the same way, show and solve 60 – 2 and 70 – 3.Summarize: When we subtract a single-digit number from adecade number, the difference will be in the previous ten (theten that is one ten less than the first number in the numbersentence).II. Using the number line to subtractWrite 40 – 1, and draw an open number line next to it. Ask:How do we subtract on the number line? From which side do westart? [from the right side – the end of the number line] In140

Using the Book: pages 143-144 Subtracting Ones from a Decade Number Circle to show in which tens number the difference will be. Complete the number line. Write the difference. We can use a number line to subtract. 40 –2 1. 28 30 –2 38 40 3 0 – 2 = 28 38 10s 20s 30s Cross off the dots you need to subtract. 2. 56 60 Complete the number line. Write the difference. 1. 6 0 – 4 = 56 50s 60s 70s 30 –1 29 30 3. 75 80 29 8 0 – 5 = 75 60s 70s 80s Complete the number line. Write the difference. 2. 37 40 4. 7 0 69 70 5. 6 0 58 60 –1 –2 40 58 –3 69 37 3. 6. 8 0 7. 9 0 85 90 –3 –5 40 –5 77 77 80 8 5 35 35 40 8. 5 0 9. ON YOUR OWN! –4 40 46 –5 –5 46 50 35 35 40 144 Chapter 4 Lesson 10 143 Now let’s practice subtracting single-digit numbers from Have the students draw over the gray loops so that they can decade numbers using a number line. When we subtract “feel” the jumping on the number line. single-digit numbers from decade numbers, the difference When students are tracing the loops, be sure that they trace will be in the previous ten (the tens that is one ten less than and solve sequentially. the first number in the number sentence). On page 144, challenge the students to complete the On Your Own problem independently. Some students may not be able to do so. This is to be expected.Copyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Struggling Learners: Practice subtracting from ten. This What did we learn today? Today we subtracted will help students gain automaticity with the facts need- single-digit numbers from decade numbers on a ed to solve the problems in this lesson. number line. Tomorrow we will subtract a single-digit number from a two-digit number on the number line. 141

Chapter 4 Lesson 11: Subtracting Ones from a Two-Digit Number INTRODUCTORY STATEMENT: When we jump back all the ones in 14, where do we get to? [ten] [Write 10 at the end of the jump.] We need to subtract 5. So far We’ve learned to subtract a single-digit number we’ve jumped back only 4. How much more do we need to jump from a decade number on the number line. back? [1] [Draw a small jump back and label it –1] Where did we get to? What is the difference? [9] [Write 9 at the end of theToday we will subtract a single-digit number from second jump.] We made two jumps – one jump back for all the a two-digit number on the number line. ones in 14, to get to the ten, and another jump back from the ten to the difference.GOAL: Students will subtract single-digit numbers from III. Subtracting from a two-digit number Copyright © by SPOTS Educational Resources. All rights reserved. two-digit numbers by making two jumps back on the number line. Write 74 – 5 on the board, and ask: How is 74 – 5 similar to MATERIALS NEEDED: Dot Cards ; blank sheets of 14 – 5? [In both problems, all the ones are the same.] Let’s paper or dry-rase boards solve this on the number line. [Draw an open number line next to the equation, and write 74 at the far right of the numberCommon Core Standards: CCSS2.NBT.7; CCSS2.MD.6 line.] How many ones are there in 74? [4] We need to subtract 5, so we will need to make two jumps. Let’s first make one jump LESSON WARM-UP back for all the ones in 74. [Draw a jump back and label it –4.] When we subtract all the ones in 74, where do we get to on the Review facts for fluency using the My Math Facts number line? [70] [Write 70 at the end of the jump.] We need practice sheets. to subtract 5. So far we’ve jumped back only 4. How much more do we need to jump back? [1] [Draw a small jump back and THINKING TRIGGER label it –1.] In which tens will the difference be? [in the 60s] On what number do we land? What is the difference? [69] Draw an open number line on the board, and write 65 – 8 = ___. Ask: How do you think we can find the difference Repeat with the teen-number problem 15 – 7 followed by the using a number line? two-digit number problem 35 – 7. Discuss the relationship between the two problems.CONCEPT DEVELOPMENT Summarize: We make two jumps back; one jump back for all theI. Review subtracting from a decade number ones in the first number, to get to a tens number, and another jump from the tens number to the difference.On the board write 80 – 4, and draw an open number linenext to it. Ask: In which tens will the difference be? [in the 70s] IV. Practice.[Solve together with the class: 80 – 4 = 76.] Write 64 – 7, and draw an open number line next to it. Say:II. Subtracting from a teen number Let’s solve this on the number line. [Fill in the number line as you go along.] How much is our first jump back? [4] How do weWrite 14 – 5, and place Dot Card-14 next to it. Ask: Can we know? [because first we jump back all the ones in 64; therecross off all the ones we need to subtract from the ones side? [no] are 4 ones in 64] Where do we get to? [60] We need to subtractWhat do we need to do? [cross off on both sides: the 4 ones 7; we’ve already jumped 4. How much more do we need to jumpon the ones side and one more dot on the ten side.] [Cross back? [3] In which tens will the difference be? [in the 50s] Whereoff the dots.] Now let’s show this on a number line. [Draw an do we get to? [57]open number line next to the Dot Card, and write 14 undera point on the far right of the number line.] We subtracted Repeat with 43 – 6 and 72 – 5.in two steps, by crossing off dots on both sides of the Dot Card,so we will make two jumps back on the number line. What willour first jump back be? [4] [Draw a jump back and label it –4.]142

Using the Book: pages 145-146 Subtracting Ones from a Two-Digit Number Complete the number line. Write the difference. When we subtract more than the ones that there are, 1. 4 3 –2 –5 we make two jumps. –5 38 First we jump back to get to a tens number. 38 43 Then we jump back the rest. 54 –6 40 –6 –2 –4 54 2. 8 5 –1 –6 48 48 50 –6 79 80 79 85 Complete the number line. Write the difference. 3. 7 3 –6 –6 1. –4 67 –3 70 73 67 63 –4 –1 63 4. 9 4 –3 –7 59 60 –7 87 59 87 –4 90 94 2. –7 5. 6 2 –6 –6 34 –3 34 56 –4 –7 27 30 56 60 62 27 3. –8 6. 5 1 –4 –4 96 47 –3 –8 47 50 51 88 –2 96 7. 3 4 –5 88 90 –5 29 –1 29 30 34 Chapter 4 Lesson 11 145 146 Now let’s practice subtracting two-digit numbers on the Have the students draw over the gray loops so that they can number line. First we jump back all the ones in the first “feel” the jumping on the number line. number to get to a tens number; then we jump back again When students are tracing the loops, be sure that they trace for the rest of the ones that we are subtracting, to get to and solve sequentially. the difference.Copyright © by SPOTS Educational Resources. All rights reserved. STUDENT TEACHER DIFFERENTIATED INSTRUCTION Write 94 – 8 = ___ on the board. Have the students solve the Advanced learners: Challenge students to make up equation by using a number line. Have some students show similar subtraction problems and exchange them with a and explain their work to the class. Ask: How did you subtract partner to solve on the number line. with two jumps on the number line? [Elicit that first we need to jump back 4 to get to 90, and then we jump back the rest CLOSING STATEMENT: of the ones that we are subtracting (another 4) to get to the What did we learn today? Today we subtracted a difference, 86.] single-digit number from a two-digit number on the number line. Tomorrow we will practice subtracting single-digit numbers from decade numbers and from two-digit numbers on the number line. 143

Chapter 4 Lesson 12: Practice: Using the Number line to Subtract INTRODUCTORY STATEMENT: digit number (74), and we needed to subtract more ones than We’ve learned to subtract single-digit numbers the ones that there are in 74. So first we needed to jump back to from decade numbers and from two-digit numbers. get to the tens number, and then we jumped back for the rest of the ones that we were subtracting. Today we will practice that. Repeat with 93 – 6 and 37 – 9 . GOAL: STUDENT TEACHER Students will subtract single-digit numbers from decade numbers and from two-digit numbers on On the board write 34 – 6, 30 – 7, 40 – 6, 65 – 8, 54 – 7, and 70 the number line. – 4. Ask students to tell in which number sentences they will MATERIALS NEEDED: blank sheets of paper make one jump and in which they will make two jumps. Elicit how they know, and why they need to make either one jumpCommon Core Standards: CCSS2.NBT.7; CCSS2.MD.6 or two jumps. (When we subtract from a decade number, we make one jump, into the previous ten. When we subtract from LESSON WARM-UP a two-digit number, we make two jumps – the first jump to get to a tens number, and the second jump for the rest of the Review facts for fluency using the My Math Facts ones that we are subtracting.) Have everyone choose one of practice sheets. the problems and solve it by drawing and filling in a number line. Then ask volunteers to come up to the board in turn to show and explain their work. THINKING TRIGGER Copyright © by SPOTS Educational Resources. All rights reserved. Think of a number sentence with a two-digit number and a single-digit number, which can be solved by making two jumps on the number line.CONCEPT DEVELOPMENTI. Review subtracting from a decade numberOn the board write 90 – 5, and draw an open number linenext to it. Ask: In which tens will the difference be? [in the 80s][Solve together with the class on the number line (90 – 5 =85).] How many jumps did we make? [one] We subtracted froma tens number, so we made one jump back, into the previousten.II. Review subtracting from a two-digit numberWrite 74 – 7, and draw an open number line next to it. Fillin the number line as you go along. Ask: How much is ourfirst jump back? [4] How do we know? [because first we jumpback all the ones in 74; there are 4 ones in 74.] Where do weget to? [70] We need to subtract 7; we’ve already jumped back 4.How much more do we need to jump back? [3] In which tens willthe difference be? [in the 60s] Where do we get to? [67] Howmany jumps did we make? [two] We subtracted from a two-144

Using the Book: pages 147-148 Practice: Using the Number Line to Subtract Complete the number line. Write the difference. Complete the number line. Write the difference. 1. 6 0 2. 6 2 1. 8 0 –5 –3 –5 –5 57 –3 57 –5 75 75 80 90 –3 60 62 2. 9 0 –3 74 –3 53 57 60 57 87 87 40 83 3. 9 0 4. 9 3 3. 7 4 –6 –2 –5 –6 34 88 –2 88 –5 68 –2 68 70 88 90 –2 88 90 93 4. 5 3 –5 –5 5. 4 0 6. 4 1 48 –2 –4 –5 48 50 36 36 –4 –5 5. 4 0 –6 –6 –4 34 34 36 40 36 40 41 6. 8 3 –7 –7 7. 7 0 8. 7 3 76 76 –4 –1 –4 80 69 69 –4 ON YOUR OWN! –1 7. 3 4 –1 –5 –1 –4 69 70 69 70 73 29 29 30 Chapter 4 Lesson 12 147 148 Now let’s practice subtracting single-digit numbers from de- Have the students draw over the gray loops so that they can cade numbers and from two-digit numbers using a number “feel” the jumping on the number line. line. When we subtract single-digit numbers from two-digit When students are tracing the loops, be sure that they trace numbers, the difference will be in the previous tens (the and solve sequentially. tens that is one ten less than the first number in the number On page 148, challenge the students to complete the On sentence). Your Own problem independently. Some students may not be able to do so. This is to be expected.Copyright © by SPOTS Educational Resources. All rights reserved. DIFFERENTIATED INSTRUCTION CLOSING STATEMENT: Advanced learners: Challenge students to make up What did we learn today? Today we practiced similar subtraction problems and exchange them with a subtracting single-digit numbers from decade partner to solve on the number line. numbers and from two-digit numbers, using a number line. Tomorrow we will choose which strategy to use. 145

Chapter 4 Lesson 13: Choosing a Strategy INTRODUCTORY STATEMENT: answer: What is 54 – 8?” [Write 54 – 8 on the board.] After a Copyright © by SPOTS Educational Resources. All rights reserved. We’ve learned two strategies for subtracting from moment, Phillip said, “I know! It’s 46!” two-digit numbers: using the number line and sub- tracting in columns. Today we will choose which Mark asked: “How did you figure that out so fast?” strategy we prefer to use. Phillip said, “I thought about a number line. I started with 54, jumped back to get to the ten – 50, and then I jumped back 4 GOAL: more to 46. [Draw a number line on the board and fill it in accordingly.] Students will choose a strategy for subtracting from two-digit numbers. Mark said, “I was thinking about doing it a different way. I would MATERIALS NEEDED: blank sheets of paper subtract in columns. First I’d regroup – I’d change the 5 tens to 4 tens, and I’d change the 4 ones to a teen number – 14 – so I’dCommon Core Standard: CCSS2.NBT.5; CCSS2.NBT.7; have enough to subtract. Then all I’d have to do is subtract 8CCSS2.MD.6 from 14, which is 6, and I’d add on the 4 tens, to get 46 – simple!” [Show the column addition on the board.] LESSON WARM-UP “That may be simple for you,” Phillip said, “but I still like my way Review facts for fluency using the My Math Facts best. My way is easier for me!” practice sheets. Point out that Mark and Phillip each used a different way to THINKING TRIGGER find the sum and that each way is correct. Everyone finds a way that works best for him or her. Write 34 – 7 on the board. Ask: How can we find the differ- ence using a number line? How can we find the difference Write 70 – 5 on the board. Have students find the difference by subtracting in columns? using an open number line. Then have them find the difference by subtracting in column form.CONCEPT DEVELOPMENT Write 45 – 7 on the board. Have students find the difference,I. Reviewing subtracting a single-digit first by using the number line and then by subtracting in number from a decade number column form.Write 50 – 3 = ___ on the board. Have the class tell you how Discuss how they solved each subtraction problem. Askto find the difference using a number line. Show the work them to think about which way they prefer. Point out that, ason the board as students describe the steps. Then solve for Mark and Phillip (in the story above), the easiest way foragain, in column form, together with the class. one student may not be the easiest way for another student, and that both the methods are good ones.II. R eviewing subtracting a single-digit number from a two-digit number Finally, write 53 – 25 on the board, and have the students find the difference by subtracting in columns. Explain that whenWrite 45 – 7 on the board. Have the class tell you how to find they subtract one two-digit number from another, such as inthe difference using a number line. Show the work on the this example, they should subtract only in columns and notboard as students describe the steps. Then solve again, in on the number line, since they haven’t learned how to findcolumn form, together with the class. the difference for this type of problem on the number line (as it’s quite complex for second graders to learn). Have several volunteers come up to the board, each of them showing one step for solving 53 – 25 in column form on the board.III. Choosing a strategy for subtracting two-digit numbersTell a story: One Sunday afternoon, Mark and Phillip wereplaying number games. Mark said, “How fast can you find the146