Number and Shape Patterns

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1 Part 1: Introduction Number and Shape Patterns Develop Skills and Strategies CCSS 4.OA.C.5 You have used rules to describe patterns in numbers. In this lesson, you will explore patterns further. Take a look at this problem. What are the next two numbers in the pattern below? 5, 10, 15, 20, 25,, Explore It Use the math you already know to solve the problem. What are two ways to get from 5 to 10? How do you get from 10 to 15? What rule works for all of the numbers in the pattern? How can you find the number that comes after 25? What are the next two numbers in the pattern? 66

2 Part 1: Introduction Find Out More Is add 5 the only relationship between the numbers in the pattern? Look at the numbers, along with the model of the numbers, and try to find a different pattern. 5, 10, 15, 20, 25 If you look only at the ones digits, you see that they alternate between 5 and 0. From the model, you can see that the number of dots alternates between odd and even. The pattern below also follows the rule add 5. 22, 27, 32, 37, 42 Do the other relationships you found in the first pattern apply to this pattern, too? The numbers in this pattern also alternate between odd and even, but the ones digits alternate between 2 and 7 instead of between 5 and 0. So, sets of numbers can share some patterns or rules, but have others that are different. Reflect 1 Describe a pattern that you have noticed in the real world. 67

3 Part 2: Modeled Instruction Read the problem below. Then explore different ways to understand it. Orlando does push-ups every day. Each day, he wants to do 4 more push-ups than the day before. Find out how many push-ups Orlando will do each day this week if he does 20 on Monday. Picture It You can use a table to help understand the problem. Day Monday Tuesday Wednesday Thursday Friday Number of Push-ups Model It You can also use a number line to help understand the problem Monday Tuesday Wednesday Thursday Friday Start at 20, the number of push-ups done on Monday, and then count 4 more for each day. 68

4 Part 2: Guided Instruction Connect It Now you will explore the problem from the previous page further. 2 How many push-ups did Orlando do each day? Monday: Tuesday: Wednesday: Thursday: Friday: 3 What is the rule for the pattern? 4 What does the pattern tell you about what happens when you start with an even number and add an even number? 5 What other pattern(s) do you see in this set of numbers? 6 Explain how you found the additional pattern(s). Try It Use what you just learned to solve these problems. 7 Lori scored 100 points in a game, then doubled her score each of the next 3 times she played. What were Lori s scores the first 4 times she played the game? 8 What is one additional pattern in Lori s scores? 69

5 Part 3: Modeled Instruction Read the problem below. Then explore different ways to understand it. Camille made a shape pattern with pattern blocks that goes back and forth between a triangle and a square. Draw the pattern that Camille made. Picture It You can use models to help understand the problem. Start by describing the pattern with words. Repeat the pattern at least 3 times. triangle square triangle square triangle square Now draw the shapes in the order you named them. Model It You can also use pattern blocks to help understand the problem. Use pattern blocks in the shapes Camille used to create her pattern. 70

6 Part 3: Guided Instruction Connect It Now you will explore the shape pattern from the previous page further. 9 How many sides does a triangle have? 10 How many sides does a square have? 11 How could you describe the pattern using the number of sides the shapes have? 12 What would the 10th shape in the pattern be? 13 Explain how you can figure out what the 85th number in the pattern would be without drawing all 85 shapes. Try It Use what you just learned to solve this problem. 14 Describe any rules you see in the shape pattern below. 71

7 Part 4: Guided Practice Study the model below. Then solve problems The student used the rule add 2 because each sandwich is \$2 more than the one before. Student Model Hungry Heath s sells four different sizes of sandwiches: small, medium, large, and jumbo. The small sandwich costs \$3. Each size after that costs \$2 more than the size before it. How much does each sandwich cost? Look at how you could show your work using a picture. small medium large jumbo Pair/Share Are there any other patterns in this set of numbers? Solution: small: \$3, medium: \$5, large: \$7, jumbo: \$9 There is more than one pattern in these shapes! 15 Draw the next two shapes in the shape pattern shown below. Pair/Share Are your shapes the same as your partner s? Solution: 72

8 Part 4: Guided Practice 16 Eva drew a shape pattern that goes back and forth between rectangles and ovals. There are several ways to describe a pattern! What are two other patterns shown in this set of shapes? Solution: Pair/Share Did you partner describe the pattern in the same way you did? 17 Lana wrote the pattern below. 7, 14, 21, 28, 35 If the pattern continues, what would be the next number in the pattern? Circle the letter of the correct answer. You can check your answer by working backward! A 40 B 42 C 49 D 70 Diego chose D as the correct answer. How did he get that answer? Solution: Pair/Share What would the next 3 numbers in the pattern be? 73

9 Part 5: Common Core Practice Solve the problems. 1 What would be the 99th number in the pattern shown below? 10, 20, 30, 40, 50 A 99 B 900 C 909 D Nia used pattern blocks to make the shape pattern shown below. Which does NOT describe Nia s shape pattern? A B C Each shape has one more side than the shape before it. The shapes in the odd numbered spots have an odd number of sides. The sides in a shape are all the same length. D The hexagon only appears in spots that are multiples of 4. 3 Choose Yes or No to tell whether the pattern follows the rule: 17. a. 7, 17, 27, 37 Yes No b. 1, 7, 49, 343 Yes No c. 3, 10, 17, 24 Yes No d. 7, 77, 777, 7777 Yes No e. 7, 14, 21, 28 Yes No 74

10 Part 5: Common Core Practice 4 Tell whether each sentence is True or False. a. A number pattern that follows the rule add 3 has both odd and even numbers. True False b. A number pattern starts with 5 cannot include the number 3. True False c. The number pattern that follows the rule start at 20 and subtract 4 has only even numbers. True False d. A number pattern that follows the rule multiply by 2 must have even numbers only. True False 5 Draw a shape pattern that follows the rule that the shapes go back and forth between four sides and five sides. Show your work. Answer 6 Write a number pattern that follows the rule subtract 6 and also has all odd numbers. Show your work. Answer Self Check Go back and see what you can check off on the Self Check on page

11 Develop Skills and Strategies (Student Book pages 66 75) Number and Shape Patterns Lesson Objectives Use rules to generate or extend a number pattern. Use manipulatives or drawings to show a shape pattern. Analyze and describe patterns in numbers and shapes. Prerequisite SkilLs Use addition, subtraction, multiplication, and division. Recognize simple patterns. Extend simple patterns. Understand even and odd. The Learning Progression This lesson builds on students previous work with number and shape patterns, including identifying patterns in addition and multiplication tables. In this lesson, students reason about number patterns and see that there may be more than one pattern in a sequence of numbers. For example, a list of numbers with the rule Add 5 also alternates between odd and even numbers. They connect a rule to a sequence of numbers or shapes and either extend or generate numbers or shapes that follow the pattern. The work in this lesson helps build a foundation for examining relationships between ordered pairs and coordinate graphs, and, later on, studying proportional relationships and functions in middle school. Vocabulary There is no new vocabulary. Review the following key terms. rule: a procedure that is followed to go from one number or shape to the next in a pattern shape pattern: a series of shapes that follow a rule to repeat or change number pattern: a series of numbers that follow a rule to repeat or change Teacher Toolbox Prerequisite Skills Ready Lessons Tools for Instruction Interactive Tutorials Teacher-Toolbox.com 4.OA.C.5 4.OA.5 CCSS Focus 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. ADDitionaL standards: 4.OA.B.4 (See page A42 for full text.) standards FOR MatheMaticaL Practice: SMP 2, 3, 4, 5, 7 (See page A9 for full text.) 72