p98-205_Gr3ON-NumberUnit2-mulitply-pass2

Materials: • If we know that 6 × 5 = 30, what would 7 × 5 equal? What strategy did you Digital Slide 40: How use? (e.g., We added one more group of 5 to 30.) Many in the Array? • W hat would 4 × 10 equal? What ×5 fact equals the same product? (8 × 5) What is 5 × 10 and what is its related ×5 fact? If we know that 8 × 5 = 40 and 10 × 5 = 50, what would 9 × 5 equal? How did you figure that out? • How can knowing ×5 facts with even numbers help us solve ×5 facts with odd numbers? • Let’s add this strategy to our anchor chart. Further Practice • Independent Problem Solving in Math Journals: Display Digital Slide 40: How Many in the Array? and pose the following problem: – Jodi says that to find the number of items in the array, you can double 4 × 2 and then double it again. Is she right? If so, why? If not, what strategy would you suggest? • Building Social-Emotional Learning Skills: Positive Motivation and Perseverance: Have students discuss how they feel about using various strategies now compared to before they started learning about them. Ask what strategies they find the most effective and why. Explain that it takes time to fully master all of the multiplication and division facts and students have beyond grade three to learn them. Discuss how strategies can help them out more than just memorizing numbers, because they understand how and why the strategies work. However, if they only memorize and then forget the numbers, there is nothing else to try. Reinforce the idea that learning is a process that takes time and practice. Multiplication and Division 197

21Lesson Guided Math Lesson: Division Bakes Math Number Curriculum Expectations • B 2.6 represent multiplication of numbers up to 10 x 10 and division up to Possible 100 ÷ 10, using a variety of tools and drawings, including arrays Teacher Look-Fors • B 2.7 represent problems involving multiplication and division, including Previous Experience problems that involve groups of one half, one fourth, and one third, using with Concepts: tools and drawings Students have had experience solving • B 2.9 use the ratios of 1 to 2, 1 to 5, and 1 to 10 to scale up numbers and to division problems and representing them using solve problems concrete materials, visual representations such as • B2.2 recall and demonstrate multiplication facts of 2, 5, and 10, and related arrays, and numerical equations. division facts • B 2.1 use the properties of operations, and the relationships between multiplication and division, to solve problems and check calculations Possible Learning Goals • Applies understanding of division to accurately solve division problems • Uses a variety of tools and strategies to solve division problems and explains their thinking NOTE: Adjust your learning goal to meet the needs of each group. Create a list of Teacher Look-Fors for each group (see the possible Look-Fors below) that reflect their learning goals. • Understands the context of the problem and explains what the various numbers represent (e.g., size of groups, number of groups, total number of items) • Uses various strategies and tools to equally divide a set in more than one way • Represents the problem using concrete materials and/or drawings • Explains their selected strategy and why it works • Creates equations that match their solutions • Solves a problem in more than one way 198 Number and Financial Literacy

PMraotcheesmseast:ical About the Lesson Problem solving, This is an example of a guided math lesson that can be used with the digital reasoning and book, Division Bakes. You can modify the lesson to meet the specific needs representing, proving, of students in each group. For example, you may want all students to solve the problems individually and then discuss, or you may want the group to communicating, solve it together. There are several entry points to the problems so you can sscteorlanetnceetgicniteginstgo,orlesflaencdting, select the questions and suggested prompts that best meet the needs of individual students. Math Vocabulary: It is important to remember that the purpose of the book is to provide egqrouuapl isnhga, rdinivgi,sieoqnu, al context for the math and support understanding about division. The set reading is not supposed to be a barrier to the math, nor is the goal to have students independently read the text, although this would be a welcome Materials: secondary outcome. If students are struggling with the text, read it to them. In this way, they can effectively solve the divisional problems by Division Bakes digital hearing the text and applying their mathematical thinking. book, concrete objects (e.g., counters) Assessment Opportunities Time: 25 minutes per group Observations: Record your observations anecdotally according to the Teacher Look-Fors you have established. Plan next steps based on your observations. • If students are still having difficulty solving equal-sharing problems, provide opportunities for them to directly model the situation by acting it out using concrete materials. • Identify students who can solve division problems with concrete materials, drawings, or arrays, but are unable to record their findings with a matching equation. These students may need explicit instruction about how the numbers in the equation match the representations and how the symbols (e.g., ÷ or ×) match their actions with the tools Reading the Book • Read the text aloud together with students in the small group (or read it to them). • Each spread contains a problem that is part of the storyline, and then a related problem written in yellow type. For each spread, hold off reading the problem in yellow type until students have worked with the storyline problem. Cover: • Show the cover page, and read the title with the group. Ask what the story might be about. Multiplication and Division 199

• Ask students whether they have baked before. Ask what division may have to do with baking Read pages 2 and 3: • Have students work individually or in pairs to find whether the 8 people in Kayla’s family can share the cookies equally. They can use the array in the illustration or concrete objects to help them. When they are done, discuss how they divided the cookies and how the arrangement of the cookies helped. Ask for a division equation that represents the sharing. Ask what the numbers means and how each number is connected to the illustration. • Have students predict whether 4 people can equally share the cookies just by looking at the illustration. Ask whether each person will get more or less cookies than in the first problem. Discuss how the array helped them with this problem. • Read the problem in yellow type. Have students turn and talk to a partner and solve the problem. Ask how the array helped them solve the problem. Ask what is the greatest number of cookies each of the 5 people equally sharing could get. Ask how many cookies would be left over. Ask how they can describe the cookies that could be equally shared using a division equation (e.g., 15 ÷ 5 = 3). Ask what each number represents. Read pages 4 and 5: • Ask what the problem in the story is and what information they know. Ask whether they know the parts or the whole and what they are trying to find out. Have students solve the storyline problem and prove their thinking using concrete materials. • While students solve the problem, observe their actions with the concrete objects. Do they start with 24 objects and deal them out one by one into 6 groups, or do they try giving an equal amount to each group and then adjust when they see how many are still left to share? Do they count the amount in a group by 1s or 2s, or do they subitize the amount? Ask how they could arrange their objects to prove their solution (e.g., in an array). • Ask what equation represents their strategy and actions with the materials. Ask what the numbers mean and how they connect to the illustration. • Ask whether 4 people could equally share the cupcakes and why they think so. • Read the problem in yellow type. Ask whether there is one possible answer or more. Have students solve the problem, selecting their own tools and strategies. • Once some possibilities have been found, have each student share one of their solutions and explain how they solved it. Ask how they knew what numbers might work and what numbers definitely would not work before even solving the problem. Ask how knowing that some equal shares work helped them to find other equal shares (e.g., when you know four people can share, you also know two people can share by putting two people’s shares together). 200 Number and Financial Literacy

Read pages 6 and 7: • Ask what the problem is in the story that they are solving. Ask whether the information they know is about the whole or the parts. • Ask how this problem is different from the one on the previous page. (e.g., In the previous problem, you knew how many people [groups] were sharing and you had to find how many cupcakes were in each group. In this problem, you know how many doughnuts are in each container [group] and need to find out how many groups there are.) • Have students solve the problem. Ask them to demonstrate and explain their solution. (e.g., I took 18 counters and repeatedly subtracted groups of 3 counters to make 6 groups, and then I counted the number of groups.) Ask what equation describes what they did. • Ask how they could use repeated addition or multiplication to solve the same problem. • Read the problem in yellow type. Have students predict the number of containers that might work to solve this problem. Have them explain their reasoning. Ask which number of containers will not work and why they think so. • Have students solve the problem. Observe whether students are adjusting their strategies after discussing the previous problems. Pay attention to how they arrange their materials. • Discuss their solutions. Have them create matching equations for each possible solution. Ask which solution they think makes the most sense. Read pages 8 and 9: • Discuss the storyline problem. Have students solve the problem, choosing their own strategy and materials. • If students were using concrete objects adeptly to solve previous problems, you may want to encourage them to solve it using the illustration or a drawing. Draw attention to the illustration and ask how they could mentally group the cinnamon rolls to make the problem easier to solve. Ask why groups of five work for this problem. • Have students share their solutions. As they share, make connections among the strategies and thinking. Ask what equations can be used to describe their solutions. • Read the problem in yellow type. Have students work with concrete materials and drawings to solve the problem. • Ask why more cousins cannot equally share the 25 cinnamon rolls. Discuss what remainders are and how they frequently happen in real life when sharing items. • Ask how many more cinnamon rolls would need to be added so more people could share. You can narrow this problem down by asking how many more rolls would need to be added so 10 people can share. Multiplication and Division 201

Read pages 10 and 11: • Discuss the storyline problem and have students solve it. Encourage them to try one of the strategies they used for a previous problem. • Have students share their strategies and matching equations. • Draw attention to the illustration. Ask how they might mentally group the buttons. Ask how they might arrange the buttons so the groups are easier to identify (e.g., in an array with five rows). • Read the problem in yellow type. Have students turn and talk to a partner about how to solve it. • Ask how many buttons they would need to add so groups of 10 people could equally share. Ask whether groups of more than 10 people could equally share 40 buttons. Read page 12: • Discuss the highlighted division concepts one at a time, asking for an example of each from the problems that they just solved. Consolidation • Create an anchor chart that includes the ideas on page 12, plus any other significant concepts that arose during the lesson. • Building Social-Emotional Learning Skills: Identify and Manage Emotions; Stress Management and Coping: Ask students how they felt as they solved the various problems. It is important for students to identify their emotions so they can use strategies to cope with their feelings. Ask how they felt when they were uncertain about what to do, and what helped them to move forward (e.g., using concrete materials, drawing a picture, talking to a partner). Discuss what they thought was the most important idea that they learned today. Ask what new strategy interests them and that they would want to try at another time. Reinforce the idea that learning is an ongoing process. The more they explore, the more they learn. Tell them they will learn much more about division in the years to come. 202 Number and Financial Literacy

22Lesson Reinforcement Activities Math • All of the expectations identified for this unit Curriculum Expectations Possible Learning Goal Teacher • Engages in activities to reinforce the concepts of multiplication and division Look-Fors • Explains what multiplication and division are and how they are evident in real- life problems • Connects multiplication and division to repeated addition and subtraction • Explains that multiplication and division ‘undo’ each other • Carries out activities that reinforce multiplication and division • Has begun to gain automaticity with multiplication facts and related division facts of 2, 5, and 10 PMraotcheesmseast:ical About the Lesson Problem solving, representing, The following activities can be carried out by the whole class in small communicating, groups, or as centres through which students rotate over a few days. They sscrteeoralanestnceoetgnicniitenginsgtgoa,onrledsflapenrcodtviningg, , can also be used throughout the unit any time you decide to offer guided math lessons. For example, you may want to meet with small groups Materials: over a few days and tailor the lesson to meet the needs of the students. coloured tiles, You can do so while the rest of the students solve the same problem in BLM 32: Colour Tile small groups, or you may wish to observe how each group works Challenges, paper, through the same concept. In this case, one group meets with you each markers day, while the other groups rotate through some of the following activities. See the Overview Guide for more information on how to manage guided math lessons. Colour Tile Challenges • Provide students with one of the challenges from BLM 32: Colour Tile Challenges. Have students use coloured tiles to create arrays according to the criteria, and then record the matching multiplication and division equations. Multiplication and Division 203

Materials: Array Game BLM 33: Array Game, Adapted from the nzmaths website (https://nzmaths.co.nz/resource/array- dice, coloured markers game). or pencils • Provide each student with a copy of BLM 33: Array Game and have students play the game in partners. Students take turns rolling two dice to determine the area of the array they will colour in on their blank 15 × 15 grid. For example, if they roll a 2 and a 4, they colour in any 2 × 4 rectangle. If they can’t colour in the array that was rolled, they miss a turn. After colouring in the array, they record the multiplication equation (e.g., 2 × 4 = 8). The first player to colour in all the squares on their grid is the winner. • Variation: Partners can play on the same grid and try to block each other. Once the grid begins to fill up, students will roll products that won’t fit on the grid. Allow students to decompose the products into two factors (e.g., 7 × 4 can be composed of 7 × 2 + 7 × 2). This will reinforce the distributive property of multiplication. Materials: Multiplication Memory BLM 34: Multiplication • Students play in groups of 2 to 4. Provide each group with 24 cards Memory Game Cards (12 matching pairs) from BLM 34: Multiplication Memory Game Cards. (The cards represent multiplication facts of 2, 5, and 10 in different ways. You can make game cards for other multiplication facts using index cards.) • Shuffle the cards and place them face down in a 4 × 6 array. Players take turns flipping over two cards. If the cards match, the player keeps them and takes another turn. If the cards do not match, they are replaced face down in the array, and the next player takes a turn. • T he game is over once all cards have been matched and removed. The player with the most cards wins. Materials: I Have, Who Has? BLM 35: I Have, Who • This is an interactive call-and-response game that involves the whole class Has? Multiplication Cards and requires students’ attentive listening skills. The goal is to have everyone read out their card at the appropriate time without anyone missing their turn. • Give each student one card from BLM 35: I Have, Who Has? Multiplication Cards. One student begins the game by reading aloud the “Who has” statement on the card. The student with the matching “I have” statement reads it aloud, and then reads the “Who has” statement below it. Play continues until it returns to the first person. 204 Number and Financial Literacy

Materials: Connect Four dice, counters in two • Students play in pairs. Provide each student with a number strip from BLM colours (one colour per student in each pair), 36: Connect Four, counters, and two dice. BLM 36: Connect Four • Students take turns rolling two dice (1–6), multiplying the two numbers, and placing one of their counters on the product on his/her number strip. Each product can only be used once, and a player loses a turn if a counter cannot be placed. For example, if a player rolls 24, and 24 is already covered, the player loses that turn. • The first player to get four counters in a row wins. Materials: What’s the Product? red and yellow • Students play in pairs. They need a game board (BLM 37) and counters. The counters, BLM 37: What’s the Product? instructions are available on a separate page (BLM 38). Game Board, BLM 38: What’s the Product? • P layer 1 places a yellow counter on one of the numbers on the strip at the Instructions (optional) bottom of the game board (BLM 37). Player 2 places a red counter on one of the numbers on the strip. Both players can cover the same number. • Player 1 multiplies the two covered numbers, then places a yellow counter over the result on the game board. • Player 2 moves one of the counters on the strip, then multiplies the two numbers that are now covered. Player 2 covers that result on the board with a red counter. • Pairs continue playing in turn. The first player to get four counters in a row on the game board wins. Materials: Division Memory BLM 39: Division • Students play in groups of 2 to 4. Provide each group 24 cards (12 matching Memory Game Cards pairs) from BLM 39: Division Memory Game Cards. • Shuffle the cards and place them face down in a 4 × 6 array. Players take turns flipping over two cards. If the cards match, the player keeps them and takes another turn. If the cards do not match, the cards are returned face down to the array, and the next player takes a turn. • The game is over once all cards have been matched and removed. The player with the most cards wins. Multiplication and Division 205