1. Just In Time Math Grade 3 Second Quarter Mathematical Thinking

2. Flow of Thinking (Number of days is only approximate—use your discretion for what your class needs.) Establishing Meaning Conceptual Understanding Continue through problem solving Prepare 4 Stages Prepare 4 StagesLessons 2, 5, 6, 7, 8, and 9

3. Establishing Meaning Building a Rich Conceptual Understanding of Multiplication Things That Come In Groups Amanda Bean Two Types of Multiplication Problems From Navigating Through Number and Operations

4. Multiplication Things That Come In GroupsThings That Come In Groups Engage: Read poems about pairs (next slide). Make a list of things that come in pairs like eyes, ears, etc. Explore 2: Pose a problem with an example from the twos: If I had six children, how many eyes would there be? Let the students model this with blocks. Make sure they know what the blocks represent. Then the students create problems to solve that include using the items from the class book for grouping problems. Explain 2: Share out their created problems with the group and have the group solve them. ELPS: 1F Use the phrase equivalent sets of objects are joined to learn the meaning of multiplication. Explore 1: Assign partners or triads to make a list of things that come in groups of 3, 4, 5, 6, 7, 8, 9, 10, 12 to make a class book with. Explain 1: Share out what they discovered. Elaborate: Mrs. Jones third-grade class has four pairs of students who are going to the science fair. She wants to honor all the partners with ribbons. Mrs. Jones was responsible for making the ribbons. How many does she need to make? What multiplication sentence could you write for this problem? What does each number in the sentence represent (label). Have students make up another story that would fit this same multiplication sentence. Evaluate: What does multiplication mean? Pick one of the word problems you created and explain how it relates to multiplication.

5. Things That Come in Groups Things that come in Pairs Salt and Pepper Peanut butter and Jelly Popcorn and Movies Pictures and Sound Music and Lyrics Books and Heroes Knights and Swords Wounds and Pain Sickness and Cures Chocolate and Heartache You and Her Me and Myself Poem about Pairs Link

6. Amanda Bean’s Amazing Dream (See Navigation Lesson) Link to ARRC Lesson Which has more wheels—5 tricycles or 7 bicycles? Which has more cookies—3 rows with 8 cookies in each row or 4 rows with 6 cookies in each row? Which has more panes—a window with 5 rows and 4 panes in each row or a window with 3 rows and 6 panes in each row?

7. Two Types of Multiplication Problems with Amanda Bean Navigating Through Number and Operations NCTM Grades 3-5 Engage: If we have 6 cans with 3 tennis balls in each can, how many tennis balls do we have in all? Explore/Explain 2: In pairs, give students Blackline Masters “Multiplication Work Mat” and Multiplication Recording Sheet and 70 small counters. See p. 53. Amanda Beans problem 1 with the illustration that shows 8 sheep riding on bicycles. How many wheels is that? Follow directions p. 53 last paragraph. Explain 2: Explore 1: Have students model the problem by placing 3 balls into 6 groups (use manipulatives to represent the balls and the cans—could use blocks and construction paper place mats. Explain 1: Use the words “how many groups” and “how many in a group” to discuss the problem. Explore 2: Continued Use the recording sheet each time to transfer the data from the work mat. See figure 2.1 p. 54 to show labeling of representations. Keep using this same recording page to finish pages 54-56. Part 1 of lesson

8. Two Types of Multiplication Problems with Amanda Bean Navigating Through Number and Operations NCTM Grades 3-5 Explore 3: p. 56-58 Suppose that Amanda Bean made 3 caramel apples yesterday for a party. Then today she and her mom made 5 times as many. How many caramel apples did they make today? Use a new recoding sheet for these activities. Reflect (Explain and Elaborate): p. 59 Students need a copy of Multiplication recording sheet and a copy of “Can You Solve It with Multiplication?”. It is not important that students can name the type of problem but that they can understand it as a multiplication situation. Skip the “Extend” part as it deals with division. We can use it later on when we get to division. Evaluation: Give them a couple of multiplication problems to solve using a recording mat. Have them explain how the problem is a multiplication situation. Part 2

9. Continued Problem Solving With Multiplication On a ppt entitled “Equal Groups Problem Solving Representations”, there are some problems that could be used to conceptually build the idea of representations for multiplication. You could continue to build on this concept during the fluency part of this timeline. The problems range from acting out the problems with real objects to making decisions on what manipulatives or pictorial representations to use to represent the problems.

10. Prerequisites to Multiplication Thinking Strategy of Use Ten Addition Facts Including Doubles Know the 10s facts Familiar with Turnarounds Two-digit Numeration Read a standard clock to the nearest 5 minutes Double Two digit numbers and find half

11. Thinking Strategy: Use Tens “Since 5 is half of 10, the product of a 5s fact will be half of the product of a related 10s fact. Use any of the “prepare” activities for students that you think do not understand the meaning of multiplication (p. 6-8). Prepare: Last activity p. 8. Have the students count by tens as you place ten “tens” blocks, one at a time, using an overhead projector, document camera, or promethean models. Move one block to one side saying, “One ten is ten” repeat until “10 tens is 100”. Arrange the blocks into different arrays and ask students to describe what they see. “3 tens is 30”, “I see three rows (or columns) of 10 so 10, 20, 30.” You want to get them to be able to say 4 tens is 40 instead of counting.

12. Introduce Use Tens Thinking Strategy for Fives Facts p. 9 (Your choice) #2 Invite ten students to stand at the front of class. The other students count by 10s as each student at the front raises both hands. What number did we end at? Now the other students count by 5s starting at 0 and the students at front raise only 1 hand. What do you notice about the two totals? (Fifty is half of 100). Repeat with other multiplies of ten. Do 40, 60, 80 first then harder ones to halve like 70. The fives total is always half of the tens total. #3 Clock face #4 Use tens strategy cards (teacher set)

13. Reinforce Use Tens Strategy p. 10 # 2, 3, 4

14. There are bags of 5 apples for sale. If you buy 3 bags, how many apples will you have? It takes 5 minutes to fill a wheelbarrow with soil. How long will it take to fill 6 wheelbarrows? There are 5 rows of 8 chairs. How many people can be seated? Nine cats each had 5 kittens. How many kittens are there in total? When Ben places 4 shoes from heel to toe in a line, They measure 1 meter. How many of these shoes will measure 5 meters? Jacob has to sow 7 rows of 5 seeds. How many seeds will he need? students lines up in 2 rows of 9. How many studentthere in total? Reinforce Use Tens Strategy p. 10 #5

15. Practice Use Tens Strategy p. 11-12 Game #2 p. 11. You need spinners BLM 7 numbered 1-9. Note: Using a blank transparent spinner over the copy of the spinner works very well. You can find them at Lakeshore but also online at http://www.educatorsoutlet.com/index.php?main_page=prod uct_info&cPath=39_112&products_id=450 http://www.educatorsoutlet.com/index.php?main_page=prod uct_info&cPath=39_112&products_id=450

16. Extend Use Tens Strategy p. 12 #2

17. Extend Use Tens p. 13 #3 X105 6 7 8 9 X 5 7 11 15 13

18. Prerequisites to Multiplication Thinking Strategy of Doubling (2s and 4s) Addition Facts Including Doubles Familiar with Turnarounds Two-digit Numeration Double Two digit numbers Mentally add one and two- digit numbers

19. Thinking Strategy: Doubling See the other PowerPoint I am sending to you. This 9 weeks covers multiplying by two and four. Next 9 weeks has multiplying by eight.

20. If You Didn’t Know—Using known facts to figure out other facts Lesson from Teaching Student Centered Mathematics John Van de Walle Building up or building down

21. Patterns and Algebraic Thinking Lesson 2 Coins in your Pocket 3 days Thinking Algebraically Student Book p. 9-14 Exemplar Should Jesse Guess? Lesson 6 Building Patterns 2 days Growing Patterns Making Predictions Exemplars L is for Linda Building Towers Lesson 7 Animal Legs 2 days Book; One is a snail, Ten is a Crab Thinking Algebraically p. 27-35 Lesson 8: Building Tables 2 days Exemplars: Meg’s Muffin Machine Popcorn Measuring a Tulip A Broken Gumball Machine Algebra for All p. 35, 37, 39, 41, 43, 63 Lesson 9: New Zoo Sticker Book 2 days Thinking Algebraically Student p. 36-41 Thinking Algebraically Teacher Edition p. 23-28 Lesson 5: What Comes Nex_? 2 days Name- Silent Teach Animal Parade Corrals Lesson 5: What Comes Nex_? 2 days Name- Silent Teach Animal Parade Corrals

22. Lesson 2 Coins in Your Pocket Engage: Review value of penny, nickel, dime and quarter. Tell students, “I have 2 coins in my pocket. What could they be? Suppose each of the coins is a nickel or dime, what are the possible combinations now? Record on chart. Thinking Algebraically p. 9 TE Exploration: 1.Three Coins in your pocket pages 9-10 Thinking Algebraically Whole class #1, partners #2-4. 2. Thinking Algebraically p. 11 Discussion Questions 3. Thinking Algebraically p. 12-13 4. Thinking Algebraically p. 14. Explain: Discussion questions for each section are listed under Explore in each section. Elaborate: Exemplar: “Should Jesse Guess” Informal: Are students able to organize data systematically in a table? Are students able to communicate choices and justify answers? Can students describe patterns and make predictions based on patterns in the table? Do students use a variety of strategies? Formal: Page 16 of Thinking Algebraically Student Activity Book, included in kit.

23. Lesson 2: Coins in Your Pocket Assessment Should Jesse Guess? Seth has 21 cents in his pocket. Seth told Jesse that he would give Jesse the 21 cents if he could correctly guess what coins they were. He would give Jesse 3 guesses. If Jesse did not guess correctly, Jesse would have to give Seth 21 cents. Should Jesse guess? Explain your math thinking.

24. Lesson 5 What Comes Nex_? Engage: ANN is first in line BRAD is second in line CAROL is third in line DARIUS is fourth in line Can you tell me the name of the next person in line? (Silent Teach Activity) Explore: Part 1: Animal Parade— students use a rule they make up to place animals in positions Part 2: Corral—Sorting cards first by rule; then using horses with numbers to sort by a particular rule they choose. Explanation: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations. Elaboration: Students create list of numbers for someone else to sort. Algebra for All p. 24-27 choose any of the activities. Evaluation: Use the students' responses on the Animal Parade activity sheet to assess their understanding of patterns.

25. Lesson 6 Building Patterns Engagement: Students use transparent counters to build triangular numbers as on next slide. Explore: Patterns to extend—see next slides. Students build patterns shown. Discuss numbering elements of pattern; Make prediction; write reason for prediction in writing; Extend the pattern checking prediction; Explain: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations. Elaborate: Exemplar “L is for Linda” Any of the activities on pages 28-31 from Algebra for All. Evaluate: Provide Student Page “Building Towers” for an assessment tool. See the lesson “Building Towers” from Exemplars (provided with this lesson) for teacher directions.

26. Engagement: Lesson 2 Building Patterns What happens between the second and third triangle? What patterns do you notice in the triangles? How many counters would it take to make the sixth triangle? How do you know? How can you record your information to find patterns or make predictions about how many counters it takes to make bigger triangles?

27. Exploration: Lesson 2 Building Patterns

28. Lesson 7 Animal Legs Engage: Read Book: One is a Snail, Ten is a Crab by Sayre. Discuss some of the solutions suggested and invite students to offer alternative solutions. Explore 1: Thinking Algebraically p. 27- 29. Point out vertical and horizontal relationships if students don’t notice them. Discuss exercise 21 with a partner before writing response. Explore 2: Thinking Algebraically p. 30 Review how many legs 1 grasshopper has, two grasshoppers; do same with turkey. Explore 3: Thinking Algebraically p. 31 Given number of legs, find number of animals. Suggest to make a table. Explore 4: Thinking Algebraically p. 33 Discussion as students find answers differently. Explore 5: Thinking Algebraically p. 34 Open ended—more than one solution Explanation: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations. See Thinking Algebraically Teachers Guide pages 17- 20, included in kit, for more information. Evaluate: Look for Organized tables and lists, understandings of relationship between multiplication and division, concept of equivalence. Thinking Algebraically p. 32 for formal evaluation.

29. Lesson 8 Building Tables Engage: Recipe on next slide; Students develop a chart showing relationship between the number of batches of cookies and the number of eggs needed. Explore: See next couple of slides. Do the bike situation together then read the movie ticket situation to the students and see if they can build a table, extend it, and write a description for finding how much it would cost for 40 people. Explain: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations. Elaborate: Exemplar Meg’s Muffin and Exemplar Popcorn. Use any of the activities on pages 34-43 or 62-63 from Algebra for All. Evaluation: Provide Exemplar “Measuring a Tulip and/or “Broken Gumball Machine.

30. Lesson 8 Building Tables Engage Grandma’s Cookies 3 eggs 1 tsp vanilla 3 c flour 2 c sugar ½ c butter ½ bag chocolate chips How many eggs would you need for 0, 1, 2, and 3 batches of cookies? Batches of Cookies Number of Eggs Needed Can you make a table that will help figure out how many eggs you need? Batches of Cookies Number of Eggs Needed

31. Lesson 8: Building Tables Explore Imagine building a bicycle. How many tires do you need for 1 bike? How many tires for 2 bikes? Write the number of bikes in a row: 1, 2, 3, 4, 5… Write the number of tires in a row: 2, 4, 6, 8, 10… We can organize our list in a table to show the related pairs of numbers. Number of bikes Number of tires If you wanted to build 6 bikes, how can we use the table to figure out how many tires we need to buy? Can we use the table to find out how many tires for 20 bikes? Can we find out without filling the table up to 20? How can we write a description for finding the number of tires for any size bike?

32. Lesson 9 New Zoo Sticker Book Engage: Ask students what they know about zoos. This zoo has sticker books for sale in its gift shop. See next slide for sample page and questions about one particular sticker book. Explore 1: Thinking Algebraically p. 36 in student book. Help students write an equation for #1 and 2. Explore 2: Thinking Mathematically p. 37-39 Multiple equations are possible for #2 p. 38. Explore 3: Thinking Algebraically p. 40 Explain: Students will explain their thinking and justify their solutions in groups and in whole-class discussion, as well as with tables, diagrams, and written explanations. See Thinking Algebraically Teachers Guide pages 23- 26, included in kit, for more information. Elaborate: Use the sticker page pictures (Thinking Algebraically Student Activity Book pages 36-41, included in kit) to create different equations in which the “result” (product or sum) comes first or in which factors (addends) are missing. Evaluation: Is there more than one way to write equation for this problem? Thinking Algebraically student p. 41

33. Lesson 9: Zoo Stickers Engage If we put stickers like these on 2 more pages, what is the total number of stickers for all 3 pages? Is there another way to find the total? How many giraffe stickers would there be on all 3 pages? Explain.