Operations and Algebraic Thinking
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1 Lesson 1 Operations and Algebraic Thinking Use Three Bear Family Counters and a Bucket Balance to model each equation. Find the value of the counter shown in the equation. 1. = Papa 2. = Mama Using Three Bear Family Counters and a Bucket Balance, model the equation. Sketch the model. Find the missing value of the counter in the equation. 3. = = 4. = = Find the missing value of the counter in each equation = = = = 10
2 Challenge! If you use a balance to solve Problem 6, how would you substitute for the Mama and Papa Bears and solve the problem. 11
3 Lesson 2 Operations and Algebraic Thinking Use Cuisenaire Rods to build each number and factor pairs shown. Complete the trains. Write each multiplication sentence = 12 3 = 12 4 = 12 6 = = 18 = 18 = 18 = 18 Build each number and its factor pairs using Cuisenaire Rods. Sketch your models. Write each multiplication sentence Find factor pairs for each number. Write each multiplication sentence
4 Challenge! Why does Problem 4 have an odd number of factor pairs? Are there other problems on the previous page that have an odd number of factor pairs? Explain. 15
5 Lesson 3 Operations and Algebraic Thinking Use Color Tiles to model each number. Write the number. Is the number prime or composite? Using Color Tiles, model each number to determine if the number is prime or composite. Sketch the model List all the factors of each number
6 19
7 Lesson 4 Operations and Algebraic Thinking Use Color Tiles. Build the array. Answer the questions. 1. Is 18 a multiple of 6? Why or why not? 2. Is 21 a multiple of 5? Why or why not? Use Color Tiles. Make as many arrays as possible for the number. Draw your arrays
8 Challenge! A class of 72 students is going on a field trip. There are vans for boys and vans for girls. The boys vans can each take 7 students, and the girls vans can each take 5 students. One group has 30 students, and the other has 42. Each van will be full. Using what you know about multiples, find which group is the boys and which is the girls. Then tell how many vans each group will need. Explain how you know. How many boys: How many boys vans: How many girls: How many girls vans: 23
9 Lesson 5 Operations and Algebraic Thinking Use Attribute Blocks to model each pattern. Describe the repeating part. How many times does it repeat? Using Attribute Blocks, sketch a pattern. The repeating part is given. Repeat it 3 times. How many of each block is used in all? 3. Make a pattern with Attribute Blocks that has the repeating part given. How many of each block is used?
10 Challenge! If you repeat the pattern in Question 1 four times, how many times do you need to repeat the pattern in Question 2 so that both extended patterns will have the same number of shapes? Explain. Include a picture with your explanation. 27
11 Lesson 6 Operations and Algebraic Thinking Use Pattern Blocks to model the pattern. Write the rule for the pattern. What are the next three steps in the pattern? 1. Rule Step 5 Step 6 Step Using Pattern Blocks, model the pattern. Write the rule for the pattern. Sketch the extended pattern. How many shapes are in Steps 7 9? 2. Rule Step Step 8 Step 9 Write the rule for each pattern. Describe the next three steps , 12, 14, 16, 4. 2, 10, 18, 26, 5. 8, 7, 6, 5, Rule Rule Rule Steps 5 7 Steps 5 7 Steps , 8, 13, 18, Rule Steps , 17, 14, 11, Rule Steps , 8, 12, 16, Rule Steps
12 Challenge! Write the first 10 steps of a pattern that begins with 4 and each step increases by 4. Describe the pattern in terms of multiples. Draw a picture to help. 31
13 Lesson 7 Operations and Algebraic Thinking Use Centimeter Cubes to model each table. Find the pattern in the table. Use the pattern to find the missing numbers. 1. Input Output 2. Input Output Missing Output Missing Input Missing Input Missing Output Using Centimeter Cubes, make a table that models each rule. Sketch the models. Then write the output numbers in each row. 3. Input + 5 = Output Input Output 4. Input 3 = Output Input Output 2 4 Find the output values for each set of input values. 5. Input + 4 = Output Input Input 10 = Output Output Input Output 34
14 Challenge! Write the output rules for Problems 1 and 2. 35
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