Teacher Edition 2015(2) with cover

Mixed Practice: Story Problems Fill in the math puzzle. Write the number sentence and solve.Fill in the math puzzle. 1.Write the number sentence and solve. Elisha had a ribbon that measured1. Whole 13 paper clips long. He used some Whole of it for a craft project he made. Part Part There were 7 blocks in Simon’s Part Part Now the ribbon measures 8 paper tower. Simon added some more clips long. How long is the piece = blocks to the tower. Now there are = he used for his project? 12 blocks in the tower. How many ___ paper clips long Whole blocks did Simon add to the tower? Part Part ___ blocks 2. =2. Whole Jeff built a tall tower with blocks. 4 blocks fell off the tower. Whole Zoe used some links to make a Part Part Now there are 9 blocks in the Part Part chain. Then she added 5 more tower. links. Now there are 11 links in the = How many blocks were in Jeff’s = chain. How many links were there tower before some of them fell off? at first? ___ links ___ blocks 3. Laura had a necklace with 15 beads. She gave some beads to her sister. Now she has 10 beads on her necklace. How many beads did she give her sister? ___ beads 1723. Student Workbook pageWhole Copyright © by SPOTS Educational Resources. All rights reserved. Student Workbook page Estee had a long piece of yarn. Part Part She cut off a piece that measuresCopyright © by SPOTS Educational Resources. All rights reserved. 7 paper clips long. Now she has a = piece of yarn that is 6 paper clips long. How many paper clips long 171 171 172 was her yarn at first? ___ paper clips longChapter 9 Lesson 5 CCSS 1.OA.1 Use addition and subtraction to solve word problems.puzzle and exchange it with another pair’s story. Have the other pair write a corresponding number sentence and solve theproblem. Have pairs share their work with the class.CONCLUSION:Today we used math puzzles to help us solve story problems.USING THE BOOK: Pages 171-172Pages 171-172: Read the directions. Read each story problem together with the class. Have the students solve themindependently using the math puzzles. Review the pages together. Closing Statement: Who can tell us what we learned today? [Accept relevant answers.] Today we solved story problems using math puzzles. For some stories we needed to add, and for others we needed to subtract. Tomorrow we will learn about how to solve story problems in which we compare two quantities. 197

9.6 Chapter 9 Lesson 6: Subtracting to CompareCCSS 1.OA.1 Use addition Concept Developmentand subtraction to solve wordproblems. I. Introducing the concept of how many more Build two towers, one with 4 blue blocks and the other with 7 red blocks, counting the blocksGoal: as you build them. Ask: Which tower has more blocks? [red] How many more blocks does theStudents will solve story problems red tower have? [Place the towers next to each other. Point to the bottom four blocks of boththat require them to compare towers and say:] Both these towers have four blocks. Let’s take away the part that is the same,quantities by making simple math and then let’s count on for the part that is more. [Cover the bottom four blocks of both towersdrawings and writing subtraction with your hand, and point to the top blocks of the red tower as you count on.] We take awayproblems. 4, and we count on 5, 6, and 7. We counted 3 more red blocks. There are three more red blocksMaterials needed: red and blue than blue blocks.blocks, counters, bag of pretzels In the same way, compare towers with 8 blue and 5 red blocks to find how many more blueLESSON WARM-UP: blocks there are. Point out that first you match and take away the blocks that have“partners,”Use a lesson warm-up activity and then you count on for the rest of the blocks to see how many more there are. Ask: Howof your choice to practice math many more blue blocks than red blocks are there? [3]facts that still need sharpening forfluency. II. Using counters to compare amounts Distribute counters to each student. Have the students compare the following: 5 black and 9Introductory Statement: white counters; 10 black and 6 white counters; 8 black and 6 white counters. For each, modelToday we will learn about something on the board by lining up the counters next to each other, matching and covering (with yourelse that you can use subtraction for. hands) the ones that have partners, and then count on to see how many more there are.We will compare quantities to seehow many more or how many fewer III. Writing number sentencesthere are. Refer to the setup of 8 black and 6 white counters on the board. Say: Let’s think about what we did. Did we add the two groups together to find how much in all, or did we subtract some to find how many more black counters there are? [we subtracted] Let’s write a number sentence for the counters we just compared. [Draw an equation format on the board under the counters.] Which color counter is there more of? [black] We have 8 black counters. [Write 8.] How many black counters have partners? [6] We subtract the 6 black counters that have white partners. [Cover the 6 black and 6 white counters, and write –6.] We see that the difference is 2. [Write = 2.] 2 black counters don’t have partners. So we know that there are 2 more black counters than white counters. Summarize: To find how much more one number is than another number, we subtract. Compare 5 black and 7 white counters by lining them up and matching the partners. Cover (with your hands) the counters that have partners, and write the equation, as above. Now that we know that there are two more white counters, we also know that there are two tHINKING tRIGGER: fewer black counters than white counters. IV. Applying to story problems; using simple math drawingsWhen you see a minus sign [Draw one Have the students work in pairs for the next activity.on the board.] what do you think of? I was talking to ___ [another teacher]. S/he said, “There are five boxes of chalk in our classroom closet.” I told her, “We have more chalk boxes in our classroom. We have eight chalk boxes.” They have five boxes of chalk and we have eight. What is the difference? How many more do we have? Copyright © by SPOTS Educational Resources. All rights reserved. Work in pairs to show this story using simple math drawings, and figure out the difference. Thinkabout how you will line up the chalk boxes and show partners, and how you will show what the difference is. Then we will discuss what you did.Give the students time to work. Circulate to observe their work. Select partners to share their work, highlighting different methods for solving.Discuss what worked and what didn’t work. If possible, include at least one pair of students who clearly lined up the drawings and connectedthe partners. Use their drawings to model, or model yourself:This is how I showed and solved the problem. I want to know what the difference is; how many more we have. [Draw a row of five squares, labeled“theirs,” and aligned beneath that, draw a row of eight squares, labeled “ours.”] I thought: How will I show partners? I will draw lines to match thepartners. [Match partners on the board. Point to the 3 squares that don’t have partners.] These three boxes show the difference. [Circle the threeboxes.] These are how many more boxes of chalk we have.Point to each row of squares and ask what they show (their boxes of chalk; our boxes of chalk). Do the same with the matched-up squares (the198

Subtracting to Compare Write the number sentence and solve. 1. There are 10 red kites and 7 purple kites. When we want to compare two numbers, we subtract — How many more red kites are there than purple kites? we take away the amount that is the same. ___ more red kites.The difference tells us how much more or how much less one = number is than the other. 2. Molly uses 8 paper clips to make a chain.Amanda 7–5=2 Freeda uses 6 paper clips to make a chain. How many fewer paper clips are there in Freeda’s Amanda’s tower has 2 more blocks. chain than in Molly’s chain? ___ fewer paper clips Emily’s tower has 2 fewer blocks. = Emily 3. James has 6 cards. Roberto has 2 cards.Draw lines between the blocks to make partners. How many more cards does James have thanCircle the difference. Write the number sentence and solve. Roberto? ___ more cards =1. How many more blocks are in Lizzy’s tower? 4. There are 5 desks in the first row. There are 4 desks in the second row. = How many fewer desks are there in the second row? ___ fewer desks___ more blocks =How many fewer blocks are 174in Sue’s tower?___ fewer blocks Student Workbook pageLizzySue Student Workbook page2. How many more blocks areCopyright © by SPOTS Educational Resources. All rights reserved.in Bill’s tower? = Copyright © by SPOTS Educational Resources. All rights reserved.___ more blocksHow many fewer blocks are Bill Tom 173 173 174in Tom’s tower?___ fewer blocksChapter 9 Lesson 6 CCSS 1.OA.1 Use addition and subtraction to solve word problems.boxes that have partners) and the circled squares (the difference).Let’s write the number sentence to show what we did. [Draw a number sentence format and fill it in as you go along.] Who has more boxes of chalk?[we do] How many boxes do we have? [8] How many boxes have partners? [5] How many do not have partners? What is the difference? [3] We have 3more boxes than them, and they have 3 fewer boxes than us.Tell the following story: In our closet, we have three large bottles of paint and five small bottles of paint. What is the difference? Together with yourpartner, show this with a simple math drawing.Discuss the drawings, modeling the problem for the class, on the board. Then write a number sentence, as above.Now I will tell you another story. Work with your partner to show it with a simple math drawing and to write the number sentence.Liam and Jake were comparing their rock collections. Liam said, “I have 7 rocks.” Jake said, “Well, I have fewer rocks than you. I have 5 rocks.” Can youfigure out how many fewer rocks Jake has?Student Teacher:Pass around a bag of pretzels and have each student take a small handful. Have the students work in pairs to figure out the difference betweenthe number of pretzels each has. Have each pair show it by making a simple math drawing and writing a number sentence. Then have studentsshare and compare their work.Conclusion: Closing Statement:Now we know how to compare two numbers to find out how many more or how many fewer there are. Who can tell us what we learnedWe subtract those that have partners to find the difference between the two amounts. today? [Accept relevant answers.] Today we learned how to solveUsing the Book: Pages 173-174 another kind of story problem. We learned to subtract to compare twoPage 173: Read and discuss the demonstration at the top of the page. amounts. Tomorrow we will learnRead the directions. Have the students complete the page on their own, and review it together. something new. We will learn how toPage 174: Read the directions. Complete examples 1 and 2 together. Have the students complete use graphs.examples 3 and 4 independently. Review them together. 199

9.7 Chapter 9 Lesson 7: Representing and Interpreting Data CCSS 1.MD.4 Organize, represent, Concept Development Copyright © by SPOTS Educational Resources. All rights reserved. and interpret data. I. Introducing a name graph Goal: Discuss the suggestions the students made in the Thinking Trigger. Explain that Students will learn about a bar you want a way that shows how various students come and how many of them graph. come, and a way that shows the results to others too. Materials needed: large papers; One way to do this is to use a graph. [On a large paper draw a graph with three handout #20; bags with samples of columns and say:] This is a graph. We use it to show and compare amounts. This three kinds of cereal — one bag for graph will show our favorite cereal. There are three columns on this graph. [Point to each student the columns.] I will tape a different kind of cereal at the bottom of each column, and each column will show us the cereal that’s under that column. LESSON WARM-UP: Use a lesson warm-up activity Under each column, tape a sample of a different kind of cereal. Distribute small of your choice to practice math bags with three kinds of cereal in each bag. Tell the students to taste each one facts that still need sharpening for and decide which of them is their favorite. Have each student write his/her name fluency. in the column that shows his/her favorite cereal. Introductory Statement: At the end, compare the columns: Count how many students like each cereal Today we will learn about a graph. best. Discuss which one is the most liked and which is the least liked. Check if any are equal amounts. Say: This kind of graph is called a name graph. It shows the tHINKING tRIGGER: names of the children who like each cereal best. A name graph is a graph that shows We get to school in different ways. the names of the people who are being surveyed (counted). Some children walk, some go by bus, some get there in other ways. I’m II. Practice wondering which way our students Draw a name graph to show how the children get to school. Make columns for come to school and how many come walking, bus, car, and any other kind of transportation. Have each student write each way. How can we find that out his/her name in the column that shows how he/she gets to school. Count and and show it in a way that will let other discuss the results. Write a number sentence to compare how many more/less people see it too? [List the students’ walk vs. how many go by bus. Write a number sentence to compare how many suggestions.] more/less walk vs. how many go by car.200 III. More Practice Label areas around the classroom with the months of the year. Have each student stand in the area that shows his/her birthday month. On a large paper, draw a graph with 12 columns labeled with the months of the year. Have each student write his/her name in a square in the column that shows his/her birthday month. Discuss the information the graph shows. You can include which month has the most/least birthdays, how many birthdays are in the summer, which month has more birthdays – January or March? Compare how many more or less birthdays there are in various months. Add up all the birthdays that are shown on the chart to see that you get the same number of birthdays as there are children in the class. Student Teacher: Divide the class into small groups. Give each group handout #20 with instructions to make a specific type of graph, for example, students’ eye colors, hairstyles,

Representing and Interpreting Data A class took a survey to find out which is their favorite fruit. Fill in the number of students who voted for each fruit.Some neighbors took a survey about their favorite ridingtoys — bike, scooter, or trike. Favorite FruitFill in how many students voted for each riding toy. Favorite Riding Toy Isaac Emma SofiaBike Hilda Tommy Shelly Teddy KittyScooter Emily Sylvia Alejandro Nancy Peggy Phil Frank Peter Lila Adam Abby Charlie Camilla Kristen Audrey Lucia SammyTrike Tomas Brian Lea David Nicolas1. Which riding toy got the most votes? April Howie Shawn Plum2. Which riding toy got the fewest votes? Willy Bruno3. Write the number sentence and solve. Apple Pear How many children took part in the survey? children ++= Student Workbook page1. Student Workbook page Which fruit got the most votes?Copyright © by SPOTS Educational Resources. All rights reserved. 2. Which fruit got the fewest votes? 175 175 3. Write the number sentence and solve. Copyright © by SPOTS Educational Resources. All rights reserved. 176 How many more students voted for apple than forChapter 9 Lesson 7 CSS 1.MD.4 Organize, represent, and interpret data. pear? students = 176favorite lunches, etc. Give the students time to collect the information and make their graphs, while you assist as needed.Have the students of each group present their graph to the class. Hang the graphs on your math bulletin board.Conclusion:Today we used graphs to show information about our class.Using the Book: Pages 175-176Page 175: Read about the neighbors’ survey, and read the directions. Discuss the graph. Have the students count and fill in thenumber of children (at the right side of each row) on their own.Examples 1-3: Read each question, discuss it, and find the answer together.Page 176: Complete the page in the same way as page 175. Closing Statement: Who can tell us what we learned today? [Accept relevant answers.] Today we learned to use name graphs to show information. Tomorrow we will learn about a different kind of graph. 201

9.8 Chapter 9 Lesson 8: Practice: Representing and Interpreting DataCCSS 1.MD.4 Organize, represent, Concept Development Copyright © by SPOTS Educational Resources. All rights reserved.and interpret data. I. Introducing a check graphGoal: Discuss the suggestions the students made in the Thinking Trigger. Explain thatStudents will learn about a graph you are looking for a way to show the number of people in each category. It hasmarked with checks. to be a quick, clear way of showing that.Materials needed:large blank graphs (with columns Display a blank graph with three columns and as many rows as needed forand rows); handout #20; large your class. Say: Here is a different kind of a graph. We can fill it in to show what wecontainer with 3 colors of Lego or want to know, and it’s easy to compare the amounts. Let’s talk about our favoriteother small objects school subject. I will write the names of the subjects under the columns. [Point to the columns, and write the names of three subjects – one subject under eachLESSON WARM-UP: column.] We will see which is the most liked and which is the least liked.Use a lesson warm-up activityof your choice to practice math We don’t need to know who likes which subject, so we don’t need to bother withfacts that still need sharpening for all the students writing their names. What can we do instead? What is a quick wayfluency. to show this? [Accept suggestions.] We can also use check marks. [Have each of the students tell which of the three subjects listed is his/her favorite. For eachIntroductory Statement: answer, mark a check in the correct column.]Yesterday we learned about a graphthat was filled in with names. Today Now it’s easy to see which is the most liked and which is the least liked, even withoutwe will learn about a different kind of counting. We just have to look at the columns to see which has the most squaresgraph. checked and which has the least squares checked. This is called a check graph. [Compare the results to see which has most checks and the least checks, and if tHINKING tRIGGER: any two columns have an equal amount of checks.]On yesterday’s graph we wrote namesthat showed us something about II. Practiceeach person. Sometimes we don’t In the same way, draw or display another graph. Ask: What should we make thisneed to know about each person; we graph about? [Accept suggestions. Graph one suggestion, as above. Comparejust want to compare how many there the results. Include questions about how many checks there are (more, less, andare in each column. Can you think of equal).]a clearer, quicker way to show howmany people are in each column? In the same way, make additional graphs, as per your class’s needs and/or interests. Student Teacher: Divide the class into groups of 3 or 4. Distribute handout #20 to each group. Pass around a container with 3 colors of Lego, colored cubes, or other sets of small, colored pieces. Have each student pull out a handful of whatever is in the container. Have the students in each group sort their pieces according to color, and graph how many of each color the group has using a check graph. (Suggestion: Have each student in the group take all the pieces of one color and graph those pieces.) Have the groups share their work by telling which color has the most and which has the least. Conclusion: Today we used check graphs to show information about our class.202

Practice: Representing and Interpreting DataSome neighbors took a survey asking which activity at the A class took a poll asking which is their favorite place topark they like best — going on the swings, on the slides, or on visit — the zoo, the aquarium, or the museum.the monkey bars. Each child who answered drew a on the Draw a on the chart to organize the votes. Cross off thechart. faces as you fill in the chart.1. How many Favorite Park Activity aquarium zoo museum zoo Favorite Place children chose the to Visit swings as their favorite activity? museum aquarium aquarium museum children2. How many zoo zoo museum aquarium children chose the slides as their zoo aquarium zoo zoo favorite activity? children museum zoo museum museum Swings Slides Monkey Bars Student Workbook pageAquarium Zoo Museum3. Write the number sentence and solve. Student Workbook page Copyright © by SPOTS Educational Resources. All rights reserved. How many more children chose the monkey bars 1. Which place got 7 votes? than the swings? childrenCopyright © by SPOTS Educational Resources. All rights reserved. 2. How many children like the zoo best? children = 3. Which place got the fewest votes? 4. Write the number sentence and solve.4. Which two activities had the same number of votes? How many fewer children like the aquarium than likeChapter 9 Lesson 8 CSS 1.MD.4 Organize, represent, and interpret data. 177 177 the zoo? children 178 = 178Using the Book: Pages 177-178Page 177: Read about the neighbors’ survey, and read the directions. Discuss the graph. Then read each question, discuss it,and find the answer together.Page 178: Read about the class’s poll, and read the directions. Have the students fill in the graph on their own. Review ittogether. Then read, discuss, and answer the questions together. Closing Statement: Who can tell us what we learned today? [Accept relevant answers.] Today we learned to use check graphs to show information. Tomorrow we will review what we learned in this chapter. 203

9.9 Chapter 9 Lesson 9: End-of-Chapter ReviewCCSS 1.MD.1 Order three objects Concept Introduction: Copyright © by SPOTS Educational Resources. All rights reserved.by length.CCSS 1.MD.2 Express the length I. Measuring and comparing lengthsof an object as a whole number of Distribute centimeter cubes. Have the students measure three of their ownlength units. fingers using centimeter cubes. Remind the class that the cubes need to be inCCSS 1.MD.4 Organize, represent, a straight line, touching each other. (Students may need to ask a neighbor forand interpret data. help.) Then have them compare the lengths of their fingers: find the finger that is longest and the one that is shortest.Goal:Students will review the skills and On the board, draw three“fingers”of various lengths. Have the students help youconcepts taught in Chapter 9. order their lengths.Materials needed: centimetercubes; large sheets of paper Talk about fingers: Say: My thumb is shorter than my pointer finger. My middle finger is longer than my pointer finger. Which is the longest? Which is the shortest?LESSON WARM-UP: Which is longer? My thumb or my middle finger? [Repeat the description and askUse a lesson warm-up activity the students to help you draw to find the answer.]of your choice to practice mathfacts that still need sharpening for II. Subtracting to compare for how many more and how manyfluency. fewerIntroductory Statement: Distribute centimeter cubes to the class. Have the students build two towers withWe are almost finished with the last the centimeter cubes: one 8 blocks high and the other 5 blocks high. Say: Let’schapter in our math book! The next write a number sentence to find out how many more blocks are in the taller towerfew lessons are review. Today we will and how many fewer blocks are in the shorter tower. How many blocks does thereview Chapter 9. taller tower have? [8] [Write 8.] How many blocks have partners? [5] Let’s subtract the 5 blocks that have partners. [Write –5.] What is the difference? [3] [Write = 3.] tHINKING tRIGGER: There are 3 more blocks in the taller tower and 3 fewer blocks in the shorter tower.Look through Chapter 9 in your books.Which lesson did you find the most On the board draw a tower with 6 blue squares, and next to it draw a towerinteresting? The most useful? The with 10 red squares. Say: Let’s write a number sentence to find out how manymost exciting? Why did you choose more squares are in the taller tower and how many fewer squares are in the shorterthat lesson? tower. How many squares does the taller tower have? [10] [Write 10.] How many squares have partners? [6] What do we do with the 6 squares that have partners? [We subtract them to find the difference.] [Write – 6.] What is the difference? [4] So how many more squares are in the taller tower? [4] And how many fewer squares are in the shorter tower? [4] III. Graphing Draw a blank check graph with three columns and multiple rows (as needed). Under each write a title: Crayons, Markers, Colored Pencils. Have each student mark a check in a box in the column that shows what s/he most enjoys using to color. Review the graph together. Count how many students prefer each item, and write a number sentence to compare the most and the least popular items. Student Teacher: Choose one or two skills that your class needs to practice. Divide the class into groups. Give each group a large sheet of paper, and have them demonstrate one of those skills. Then have each group present its work to the class.204

End-of-Chapter Review Draw lines between the blocks to make partners. Circle the difference. Write the number sentence and solve.Write the order of the objects from shortest to longest.1. a. 2. a. 1. How many more blocks are in Joseph’s tower? b. b. c. c. =Circle the picture that shows the correct way to measure. ___ more blocks3. A B How many fewer blocks are Joseph Charlie in Charlie’s tower? ___ fewer blocks A class took a survey asking Favorite Subject which subject they like best –Draw to solve the story problem. reading, writing, or math.Circle the correct answer. Each student who answered 4. Craig’s chain is shorter than Maurice’s chain. drew a on the chart. 2. How many students like Brian’s chain is longer than Maurice’s chain. reading best? students Craig Maurice Brian Craig’s chain is shorter/longer than Brian’s chain.Chapter 9 Lesson 9 CSS 1.MD.1, CCSS 1.MD.2, CCSS 1.MD.4 Student Workbook page3. How many students like Student Workbook pagewriting best? studentsCopyright © by SPOTS Educational Resources. All rights reserved.179 179 4. Write the number sentence Reading Writing Math Copyright © by SPOTS Educational Resources. All rights reserved. 180 and solve. How many more students like math than like writing? students = 180Conclusion:Today we reviewed all the different things we’ve learned in this chapter.Using the Book: Pages 179-180Page 179: Examples 1-3: Read each set of directions, and have the class complete the section independently.Example 4: Read the story together. Have the students draw and solve it on their own.Review the page together.Page 180: Example 1: Read the directions, then read the example and have the students solve it on their own.Examples 2-4: Read the text that introduces the examples, then read each example and have the students solve it on theirown.Review the page together. Closing Statement: What did we learn today in math class? [Accept relevant answers.] Today we reviewed Chapter 9. Tomorrow we will review math that we learned all through first grade. 205

9.10 Chapter 9 Lesson 10: Cumulative Review 1 CCSS 1.OA.6 Add and subtract Note: This lesson may take longer than an average lesson. Copyright © by SPOTS Educational Resources. All rights reserved. within 20. CCSS 1.OA.8 Determine the Concept Introduction: unknown number in an equation. CCSS 1.NBT.1 Count to 120, I. Tens and ones starting at any number less than 120. Use Dot Cards to show 69. Ask: How many tens? How many ones? How many altogether? CCSS 1.NBT.2 Understand that the [Draw a place value chart underneath and fill it in.] Do the same with 21. two digits of a two-digit number represent an amount of tens and Write 48¢ on the board. Ask how to show it using dimes and pennies. Draw a dimes- ones. pennies chart and fill it in. Show 12¢, and fill in a similar chart. CCSS 1.NBT.2a 10 can be thought of as a bundle of ten ones – called II. Ten more, ten less a “ten.” CCSS 1.NBT.3 Compare two-digit On the board, write 34, ___. Ask: How can we find the number that is ten more? [add a ten; numbers based on the meanings of think of the next ten] What is ten more than 34? [44] What is ten more than that? [54] [Fill the tens and ones digits. in the numbers.] CCSS 1.NBT. 4 Add within 100. CCSS 1.NBT.5 Given a two-digit Do the same with 32. number, mentally find ten more or ten less than the number. Write ___, 61. Say: Now let’s find ten less. How can we figure that out? [take away a ten; CCSS 1.NBT.6 Subtract multiples think of the ten before] What is ten less than 61? [51] Repeat with ___, 26. of ten. NYS CCLS.1.MD.3 Recognize and III. Solving equations with the sum in the first position identify coins, their names, and their values. Write 60 + 3 = ___. Solve it and write the sum. Write ___ = 60 + 3. Ask: Do you think the sum will be the same? [yes] Solve it and write the sum. Goal: Students will review important skills In the same way solve ___ = 80 + 6 and ___ = 90 + 4. and concepts learned in first-grade math. IV. Forming a new ten Materials needed: index cards Write 34 + 5 on the board. Ask: What are we adding to the 34? [ones] Will the number of Introductory Statement: tens change? [no] How many ones altogether? [9] What’s the sum? [39]. We added ones, We’re almost finished with first- and only the number of ones changed. grade math! Today we will review some of the topics we’ve learned and Write 64 + 6 on the board. Ask: What are we adding to the 64 - tens or ones? [ones] How practiced throughout the year. many ones are there altogether? [ten] We have another ten. How many tens altogether? We had six tens, and we made another ten. Now we have seven tens. We have 70 in all. [Fill in tHINKING tRIGGER: the sum.] Which math topic did you enjoy learning most this year? In the same way, solve 49 + 1 and 58 + 2.206 Write 45 + 5 and 45 + 3. Ask: In which number sentence do you think we will make a new ten? Why do you think that? [45 + 5, because 5 + 5 = 10] [Solve each equation and write the sums.] In the same way, write, discuss, and solve 63 + 5 and 51 + 9. V. Adding tens or ones Write 64 + 20 and 64 + 2 on the board. Point to 64 + 20 and ask: Are we adding tens or ones? [tens] Which number will change? [the number of tens] What is the sum? [84] [Point to 64 + 2 and ask:] Are we adding tens or ones? [ones] Which number will change? [the number of ones] What is the sum? [66] In the same way, compare and solve 54 + 40 and 54 + 4; and 37 + 20 and 37 + 2. VI. Adding to get teen sums Write 7 + 6 = ___ on the board. Ask: How can you solve this equation? [Do the same with 9 + 5 and 6 + 6. Emphasize first adding to get to ten and then adding the rest.] Flash a few relevant equation cards for further practice. VII. Subtracting from teen numbers Write 18 – 5 on the board, and solve it. Say: Here we are subtracting some of the ones we

Write how many. Cumulative Review 1 Circle to show if we are adding tens or ones. Add.1. 2. 3. 1. 48 Tens 2. 30 Tens 3. 73 Tens +20 Ones +50 Ones +5 OnesTens Ones Number Tens Ones Number Dimes Pennies Amount ¢ Will we form a new ten? Circle the correct sign. Add.Fill in the numbers that come just before and just after. 4. +455 5. +816 6. +364 7. +5804. 5. 6.     69 36 80 Write the number that is ten more. 10. Add. 9 8 10. 8 11. 9 12. 5 13. 5 +6 +8 +6 +6 +87. 8. 9. 18, 8. 7 +7 53, 76, 34,Write the number that is ten less.11. 12. 13. , 45 , 88 Student Workbook page14., 76Subtract. Student Workbook page , 19 14. 11 15. 18 16. 18 17. 16 18. 12 19. 14Copyright © by SPOTS Educational Resources. All rights reserved. – 5 –10 – 9 – 8 – 6 – 7Solve. 15. 16. 17. = 30 + 6 = 60 + 4 = 90 + 5 Copyright © by SPOTS Educational Resources. All rights reserved.18. 19. 20. 20. 90 21. 80 22. 15 23. 17 24. 58 25. 39 –70 –50 – 3 – 4 – 8 – 9 = 50 + 7 = 40 + 9 = 20 + 3 182Chapter 9 Lesson 10 CCSS 1.OA.6, CCSS 1.OA.8, CCSS 1.NBT.1, CCSS 1.NBT.2, CCSS 1.NBT.2a, CCSS 1.NBT.3, CCSS 1.NBT. 4, 181 181 182 CCSS 1.NBT.5, CCSS 1.NBT.6, NYS CCLS.1.MD.3have in the teen number. How can we solve this? [we can think of 8 – 5] What is the difference? [13]Write 15 – 5 on the board. Say: Here we are taking away all the ones. What is left? [10] [Fill in the difference.] In the same way, solve 18 – 8.Write 13 – 6 on the board. Say: Here we are taking away more than the ones we have. [Display Dot Card-13, and draw spaces for the break-apart numbers. Ask a student to tell you how to show this on the Dot Card and explain his/her thought process as the he/she fills in thebreak-apart numbers.]Write some similar subtraction equations on the board. Have students take turns explaining how to solve them.]Write 18 – 5 on the board, and solve it. Say: Here we are subtracting some of the ones we have in the teen number. How can we solve this? [thinkof 8 – 5] What is the difference? [13]VIII. Subtracting decade numbersWrite 50 – 20 on the board and ask: How can we solve this? [we can think of 5 tens minus 2 tens or of jumping back on the number line.]What is the difference? [30] In the same way, solve 90 – 40.Student Teacher:Divide the class into pairs. Give each pair a set of eight index cards. On each card, have them write an addition or subtraction numbersentence with teen numbers (without writing in the sum or difference). When the partners are done, have them show the cards to eachother, one at a time, and take turns solving the equations.Conclusion: Closing Statement:Today we reviewed so many things we’ve learned about numbers. We discussed tens and ones, and Ask: What did we learn today in mathdifferent kinds of addition and subtraction. class? [Accept relevant answers.] Today we reviewed many things we’veUsing the Book: Pages 181-182 learned this year in math. Tomorrow we will review some more.Pages 181-182: For each section, read the directions and have the students complete thesection independently. Review each page together. 207

9.11 Chapter 9 Lesson 11: Cumulative Review 2 CCSS 1.G.1 Distinguish between Concept Introduction: Copyright © by SPOTS Educational Resources. All rights reserved. defining attributes versus non- defining attributes. I. The value of coins CCSS 1.G.2 Compose two- Place a penny, a nickel, a dime, and a quarter on the board. With the class’s help, write dimensional shapes. the value of each coin underneath it. CCSS 1.G.3 Partition circles and Place a dime on the board. Leave some space and place two nickels. Ask the class to tell rectangles into two and four equal the value of the two nickels together (10¢). Ask: Is the dime worth more than, less than, shares. or equal to the two nickels? [equal] Use your fingers to draw the correct sign in the air CCSS 1.MD.3 Tell and write time [Write an equal sign between the sets of coins, and read:] 10¢ is equal to 10¢. in hours using analog and digital Remove the dime. Place three dimes and a nickel together on the board and count and clocks. write their value (35¢). Leave some space and place a quarter next to the group of coins. NYS CCLS.1.MD.3 Recognize and Ask: Is the value of this group of coins greater than, less than, or equal to a quarter? identify coins, their names, and [greater than] To which number will the open mouth be facing? [35] Draw the greater- their values. than sign in the air. [Draw the sign on the board between the group of coins and the CCSS 1.OA.1 Use addition quarter, and read:] 35¢ is greater than 25¢. and subtraction to solve word Do the same with a quarter and a group of a dime, a nickel, and 4 pennies. problems. Continue in this way with other groups of coins, as per your class’s needs. CCSS 1.OA.2 Solve addition II. Plane shapes word problems with three whole Use pattern blocks or shape cutouts for this section. Place a triangle, a rectangle, a numbers. square, a hexagon, and a trapezoid on the board. Name each shape. Ask the students to help in making more shapes: For example, place another triangle on the board, and Goal: use the two triangles to make a square. Use two squares to make a rectangle, and two trapezoids to make a hexagon. Students will review important skills III. Fractions and concepts learned in first-grade Draw  somecirclesontheboard.Divideeachcircleintotwoorfourequalparts  horizontally, math. vertically or diagonally. Shade some circles to show “one-half” and others to show “one- Materials needed: model coins; fourth.” Have students name the part of each circle that is shaded. pattern blocks or shape cutouts; label it with the correct name. Repeat with squares and rectangles. large model clock with moveable IV. Telling time hands Display the model clock. Ask the students to describe what they see. Describe the minute hand, the hour hand, the numbers, and their functions. Remind the class that when the Introductory Statement: minute hand points to the 12, it is exactly on the hour, and we read the time “o’clock.” Wow! This is the last lesson in this Move the hands to show 5:00. Have the class read the time together. On the board write math book. Can you believe how 5:00. In the same way, show, read, and write 2:00 and 9:00. much we’ve learned this year? We Show 9:30, and ask what time the clock shows. Review that when the minute hand finished two math books, and we did points to the 6, it is half past the hour, and we say “thirty”: The clock shows 9:30. Write so much! Today we’re going to review 9:30 on the board. a few of the things we learned this Show, read together, and write 5:30 and 3:30. year. V. Story problems Now we will review different types of story problems. For each one we will think about tHINKING tRIGGER: the number sentence and the answer. [As you tell the stories, draw and write the details Do you remember a math lesson that and the equations on the board, to help the students follow along.] was hard for you? What was it? [Allow In the ice cream shop, there are 20 chocolate ice cream pops and 40 vanilla ice cream time for answers.] There are some pops. How many ice cream pops are there in all? [20 + 40 = 60; there are 60 in all] [Review things we learn that become easier that when adding numbers that have only tens, we can think about how many tens we for us, and some things we learn that are adding. (2 tens and 4 tens equal 6 tens. 60 in all.)] stay hard. Is that lesson still hard for There are 60 in all. Someone bought 30 ice cream pops. Now how many are left in the you? store? [60 – 30 = 30; there are 30 ice cream pops left] [Explain that when subtracting numbers that have only tens, we can think of how many tens we are subtracting: 6 tens208 minus 3 tens equal 3 tens, so there are 30 left.]

Cumulative Review 2 Write the number sentence and solve. Write the value of each group of coins. Compare. 1. There were 60 apples on the tree. Write >, <, or =. 20 apples fell off. 1. 2. How many apples remain on the tree? apples 3. 4. = 2. The store has 43 big balls balls and 10 small balls. Circle the correct shape. How many balls are there? 5. = += 3. There are 9 big butterflies and 5 small butterflies in the garden. Circle how much is shaded. How many more big butterflies are there? 6. one-half ___ more big butterflies = one-fourth Student Workbook page7. one-half Student Workbook page one-fourth Write the time. 9. 4. There are 10 roses and 8 tulips in our garden. Copyright © by SPOTS Educational Resources. All rights reserved.Copyright © by SPOTS Educational Resources. All rights reserved. 8. 10. How many fewer tulips than roses are there? fewer tulips :: : 183 183 = 184 Chapter 9 Lesson 11 CCSS 1.G.1, CCSS 1.G.2, CCSS 1.G.3, CCSS 1.MD.3, CCSS 1.OA.1, NYS CCLS.1.MD.3 184In the store, there are 25 types of fruit drinks and 10 flavors of milk shakes. How many kinds of drinks are there? [25 + 10 = 35] [Explain thatwhen adding ten to a number, we can think of just the tens: 2 tens and 1 ten equal 3 tens; 25 + 10 = 35.]There are 10 packs of salted nuts and 7 packs of unsalted nuts. How many fewer packs of unsalted nuts are there? [10 – 7 = 3; there are 3fewer packs of unsalted nuts] [Review that when comparing amounts we subtract those that have partners.]In the orchard there are 7 lemon trees, 5 orange trees and 3 grapefruit trees. How many trees are there in all?What is different about this story? [it has 3 addends] [Draw an equation format with spaces for 3 addends. Remind students to first find theaddends that equal 10.] There are 15 trees in all.Student Teacher:Choose skills that the class needs to practice. Write an example of each on the board. Have students solve and explain how they solvedthem.Conclusion:Today we reviewed more things in first-grade math.Using the Book: Pages 183-184Page 183: For each section, read the directions and have the students complete the section independently. Review the page together.Page 184: Read each story problem together. Have the students solve the problems on their own. Review the page together.Name: Name: Name: Write the order of the objects from shortest to longest.Circle the shape that shows the fraction. 1. a. 2. a. Draw lines between the blocks to make partners. Circle the difference. Write the number sentence and solve.1. 1 2. 1 b. b. 2 4 c. c. 1. How many more blocks are in Closing Statement: Manny’s tower? Ask: What did we learn today in math Circle the picture that shows the correct way to measure. class? [Accept relevant answers.]Write the time. 4. 5. 3. A B = Today we finished our second math 3. book! Hurray!. ___ more blocks How many fewer blocks are in Manny Adam 209 Adam’s tower? ___ fewer blocks :: : A class took a survey asking which vegetable Favorite Vegetabe 8. they like best – carrots, peppers, or tomatoes.Draw the hands to show the time. Each student who answered drew a on the Assess. 6. 7. chart. Take pride Draw to solve the story problem. Circle the correct answer. 2. How many students like carrot best? in all you’ve 4. Harry’s chain is shorter than Fred’s chain. students accomplished! Kevin’s chain is longer than Fred’s chain. 3. How many students like pepper best? Harry students Fred Kevin Harry’s chain is shorter/longer than Kevin’s chain. Chapter 9 Assessment Form ACopyright © 2012 by SPOTS Educational Resources. All rights reserved.5:30 Permission to duplicate classroom quantities granted to users of SPOTS for M. A. T. H.: Copyright © 2012 by SPOTS Educational Resources. All rights reserved. Permission to duplicate classroom quantities granted to users of SPOTS for M. A. T. H. Copyright © 2012 by SPOTS Educational Resources. All rights reserved. Permission to duplicate classroom quantities granted to users of SPOTS for M. A. T. H. 11:30 8:00 4. Write the number sentence and solve. How many more students like tomato Carrot Pepper TomatoSolve the story problem. than like carrot? students9. I put the muffins into the oven at 3:00. They need to bake for one half hour. = What time should I take the muffins out of the oven?Chapter 8 Assessment Form B 14 15 Chapter 9 Assessment Form B 16



Common Core Mathematics Standards Alignment 211Copyright © by SPOTS Educational Resources. All rights reserved.

Common Core Mathematics Standards Lesson AlignmentCritical Area: Operations and Algebraic ThinkingCommon Core Standard Number Lesson NumberCCSS 1.OA.1 2-1, 2-6, 2-13, 2-18Use addition and subtraction within 20 to solve word problems 3-1, 3-9, 3-10, 3-15, 3-16, 3-17involving situations of adding to, putting together, taking apart, 4-17, 4-19, 4-21, 4-24, 4-26and comparing, with unknowns in all positions, e.g., by usingobjects, drawings, and equations with a symbol for the unknown 5-6, 5-8, 5-10, 5-11, 6-14, 6-15,number to represent the problem. 6-16, 6-18, 6-19, 6-23 7-3, 7-4, 7-9, 7-10, 7-15, 7-18, 7-19, 7-20 9-5, 9-6, 9-11CCSS 1.OA.2 4-9Solve word problems that call for addition of three whole numbers 7-20whose sum is less than or equal to 20, e.g., by using objects, 9-11drawings, and equations with a symbol for the unknown numberto represent the problem.CCSS 1.OA.3 2-10, 2-11, 2-12, 2-18Apply properties of operations as strategies to add and subtract. 3-16, 3-17 4-7, 4-10, 4-16, 4-20, 4-23, 4-25, 4-26 7-17CCSS 1.OA.4 3-16,Understand subtraction as an unknown-addend problem. 6-16, 6-23 7-10, 7-19 9-5CCSS 1.OA.5 1-7, 1-8, 1-9, 1-12Relate counting to addition and subtraction (e.g., by counting on 2-2, 2-3, 2-9, 2-182 to add 2). 3-2, 3-7, 3-10, 3-17Volume l covers Chapters 1 - 4. Volume ll covers Chapters 5 - 9.

Common Core Standard Number Lesson NumberCCSS 1.OA.6 2-4, 2-5, 2-8, 2-14, 2-15, 2-16, 2-18Add and subtract within 20, demonstrating fluency for addition 3-3, 3-4, 3-5, 3-6, 3-8, 3-11, 3-12, 3-13, 3-17,and subtraction within 10. Use strategies such as counting on; 4-4, 4-5, 4-6, 4-7, 4-8, 4-11, 4-12, 4-13, 4-14, 4-15, 4-18, 4-19,making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a 4-20, 4-23, 4-24, 4-25, 4-26number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); usingthe relationship between addition and subtraction (e.g., knowing 5-3, 5-6, 5-7, 5-8, 5-9, 5-11that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but 6-4, 6-12, 6-15, 6-16, 6-17, 6-23easier or known sums (e.g., adding 6 + 7 by creating the known 7-1, 7-2, 7-3, 7-4, 7-5, 7-6, 7-7, 7-8, 7-9, 7-10, 7-11, 7-12, 7-13,equivalent 6 + 6 + 1 = 12 = 1 = 13). 7-14, 7-15, 7-16, 7-18, 7-19, 7-20 8-8, 8-11, 8-15CCSS 1.OA.7 9-10 2-2Understand the meaning of the equal sign, and determine ifequations involving addition and subtraction are true or false. 6-13, 6-23 7-20 8-15CCSS 1.OA.8 2-17Determine the unknown whole number in an addition or 3-14subtraction equation relating three whole numbers. 4-8 6-13 7-11, 7-16 9-10Volume l covers Chapters 1 - 4. Volume ll covers Chapters 5 - 9.

Critical Area: Number and Operations in Base TenCommon Core Standard Number Lesson NumberCCSS 1.NBT.1 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-12Count to 120, starting at any number less than 120. In this range, 6-6, 6-7, 6-11, 6-22read and write numerals and represent a number of objects with 7-20a written numeral. 8-15 9-10CCSS 1.NBT.2 5-1, 5-2, 5-3, 5-11Understand that the two digits of a two-digit number represent 6-1, 6-2, 6-3, 6-11, 6-22amount of tens and ones. 7-20 8-15 9-10CCSS 1.NBT.2a 4-1, 4-2, 4-2510 can be thought of as a bundle of ten ones – called a “ten. 6-1 8-15CCSS 1.NBT.2b 9-10 5-3The numbers from 11 to 19 are composed of a ten and one, two, 6-3, 6-11three, four, five, six, seven, eight, or nine ones.CCSS 1.NBT.2c 5-2, 5-3, 5-6, 5-8, 5-11The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, 6-7, 6-11three, four, five, six, seven, eight, or nine tens (and 0 ones).CCSS 1.NBT.3 4-3Compare two two-digit numbers based on meanings of the tens 5-4and ones digits, recording the results of comparisons with the 6-4, 6-5, 6-8, 6-11, 6-22, 6-23symbols >, =, and <. 7-20 8-15 9-10Volume l covers Chapters 1 - 4. Volume ll covers Chapters 5 - 9.

Common Core Standard Number Lesson NumberCCSS 1.NBT.4 5-6, 5-7, 5-11Add within 100, including adding a two-digit number and a one- 6-8, 6-12, 6-14, 6-15, 6-17, 6-18, 6-19, 6-20, 6-21, 6-22digit number, and adding a two-digit number and a multiple of 10, 7-9, 7-20using concrete models or drawings and strategies based on place 9-10value, properties of operations, and/or the relationship betweenaddition and subtraction; relate the strategy to a written methodand explain the reasoning used. Understand that in addingtwo-digit numbers, one adds tens and tens, ones and ones; andsometimes it is necessary to compose a ten.CCSS 1.NBT.5 5-5, 5-11Given a two-digit number, mentally find 10 more or 10 less than 6-9, 6-10, 6-11, 6-22the number, without having to count; explain the reasoning used. 8-15CCSS 1.NBT.6 9-10 5-8, 5-9Subtract multiples of 10 in the range 10-90 from multiples of 10 6-8, 6-23in the range 10-90 (positive or zero differences), using concrete 7-9, 7-19models or drawings and strategies based on place value, properties 9-10of operations, and/or the relationship between addition andsubtraction; relate the strategy to a written method and explainthe reasoning used.Volume l covers Chapters 1 - 4. Volume ll covers Chapters 5 - 9.

Critical Area: Measurement and DataCommon Core Standard Number Lesson NumberCCSS 1.MD.1 9-1, 9-2, 9-9Order three objects by length; compare the lengths of two objectsindirectly by using a third object.CCSS 1.MD.2 9-3, 9-4, 9-9Express the length of an object as a whole number of length units,by laying multiple copies of a shorter object (the length unit) endto end; understand that the length measurement of an object isthe number of same-size length units that span it with no gaps oroverlaps.CCSS 1.MD.3 8-10, 8-11, 8-12, 8-13, 8-14Tell and write time in hours and half-hours using analog and digital 9-11clocks.NYS CCLS 1.MD.3 1-11Recognize and identify coins, their names, and their values. 2-7, 2-8, 2-10, 2-15, 2-18 3-5, 3-12, 3-17 4-2, 4-7, 4-22, 4-24, 4-25, 4-26This standard applies only to New York State. 5-2, 5-3, 5-4, 5-11 6-2, 6-3, 6-8, 6-11, 6-12, 6-17, 6-22, 6-23 7-1, 7-11, 7-19, 7-20 8-4, 8-15 9-10, 9-11CCSS 1.MD.4 9-7, 9-8, 9-9Organize, represent, and interpret data with up to three categories;ask and answer questions about the total number of data points,how many in each category, and how many more or less are in onecategory than in another.Volume l covers Chapters 1 - 4. Volume ll covers Chapters 5 - 9.

Critical Area: GeometryCommon Core Standard Number Lesson NumberCCSS 1.G.1 8-2, 8-5, 8-6, 8-14Distinguish between defining attributes (e.g., triangles are 9-11closed and three-sided) versus non-defining attributes (e.g., 8-3, 8-6, 8-14color, orientation, overall size); build and draw shapes to possessdefining attributes.CCSS 1.G.2Compose two-dimensional shapes (rectangles, squares, trapezoids, 9-11triangles, half-circles, and quarter-circles) or three-dimensional 8-7, 8-14, 8-8, 8-9shapes (cubes, right rectangular prisms, right circular cones, andright circular cylinders) to create a composite shape, and composenew shapes from the composite shape.CCSS 1.G.3Partition circles and rectangles into two and four equal shares, 9-11describe the shares using the words halves, fourths, and quarters,and use the phrases half of, fourth of, and quarter of. Describethe whole as two of, or four of the shares. Understand for theseexamples that decomposing into more equal shares createssmaller shares.Volume l covers Chapters 1 - 4. Volume ll covers Chapters 5 - 9.

The Spots for Math Program and the CCSS Standards for Mathematical Practice Copyright © by SPOTS Educational Resources. All rights reserved. The Common Core State Standards single out eight practices of importance to develop in students so that they become proficient mathematical thinkers. These are incorporated throughout the Spots for Math program (not specifically cited within each lesson). Following is an overview of how our program develops these strengths within students. MP2 – Reason abstractly and quantitatively In the Spots for Math program, students use unique tools to develop abstract reasoning abilities: Dot Cards to represent numbers and operations, and break-apart number sentences and open number lines to compose and decompose numbers. These tools help bridge the gap between the concrete and the abstract and vice versa. Spots for Math also trains students in the practice of thinking aloud to solve problems. MP4 – Model with mathematics; and MP5 – Use appropriate tools strategically In the Spots for Math program, students are provided with a suite of tools to model mathematical concepts. Throughout each lesson or set of lessons the students progress from more concrete representations (e.g., Dot Cards) to more abstract ones (e.g., open number lines and break-apart number sentences). Embedded throughout the program are opportunities for students to extend the construct of the Dot Cards to understand the value of different coin denominations. In the measurement lessons, students use familiar objects as comparative measurement tools to arrive at the concept of a measurement unit and standardization of measurement. MP7 – Look for and make use of structure The Dot Card model is a representational structure that builds on itself as students become acquainted with the single- and double-digit numbers, number facts, place value, and addition and subtraction through composing and decomposing numbers. Using the same, familiar approach with its progressive layering of concepts allows students to make more sophisticated discoveries about the number system. Puzzle-piece models provide students with a user-friendly structure for analyzing and solving word problems. MP8 – Look for and make use of repeated reasoning In the Spots for Math program, students are habituated to the practice of decomposing numbers long before they need to “make a ten.”Through use of the Dot Cards students learn to represent a number as a composition of two other numbers. They build on these constructs to make a ten, form teen numbers, and represent two-digit numbers using multiple Dot Cards. The lessons on addition and subtraction scaffold student understanding so that they learn to apply similar reasoning patterns to solving equations of increasing complexity. MP1 – Make sense of problems and persevere in solving them; MP3 – Construct viable arguments and critique the reasoning of others; and MP6 – Attend to precision These practice standards are addressed throughout the implementation of the Spots for Math program. The Student Teacher sections in the Teacher’s Edition give specific suggestions to foster peer-to-peer teaching and learning. The scaffolded approach in the program at large as well as the suggested discussion prompts in the Teacher’s Edition enable students to persevere with confidence and to become independent problem solvers who can think critically, construct precise and detailed responses to a math problem or question, and defend their responses using strategic thinking skills.218

ALL THE MATH RESOURCES YOU NEED TO ACHIEVE MAXIMUM RESULTS EFFICIENTLY AND EFFECTIVELY!

TM M A T HFOR ATHEMATICAL BILITIES & HINKING ABITS A UNIQUE SYSTEM THAT CHANGES THE FOCUS FROM ROTE PRACTICE TO REAL MATH WISDOMTeacher’s EditionGrade 1Volume ll ISBN 978-0-98511​29-8-1 (whole set) ISBN 978-0-9893168-0-4