Mathematics Pacing Resource Document 5.AT.8 Standard: 5.AT.8: Teacher Background Information: Expressions

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1 Teacher Background Information: Expressions can be evaluated and not solved. Expressions with variables are a means for expressing patterns and generalizations. Variables can be used as unique unknown values or as quantities that vary. Unfortunately, students often think of the former (the variable is a place holder for one exact number) and not the latter (that a variable could represent multiple, even infinite values). Experiences in elementary and middle school should focus on building meaning for both. Example: The skating rink charges $100 to reserve the place and then $5 per person. Write an expression to represent the cost for any number of people. n = the number of people Connecting writing expressions with story problems and/or drawing pictures will give students a context for this work. It is important for students to read algebraic expressions in a manner that reinforces that the variable represents a number.

2 Teacher Background Information: Example: Maria has three more than twice as many crayons as Elizabeth. Write an algebraic expression to represent the number of crayons that Maria has. Solution: 2c + 3 where c represents the number of crayons that Elizabeth has Example: 2c + 3 where c represents the number of crayons that Elizabeth has Solution: t where t represents the number of tickets purchased Process Standards to Emphasize with Instruction of : 5.PS.1: Make sense of problems and persevere in solving them. 5.PS.2: Reason abstractly and quantitatively. 5.PS.3: Construct a viable argument and critique the reasoning of others. 5.PS.4: Model with mathematics. 5.PS.7: Look for and make use of structure.

3 Lesson Plans/Print Activities: Web-based Practice: Math Expressions Resources: Unit 1, Lesson 1,5 topic-b-overview Patterns in the Coordinate Plane and Graphing Number Patterns from Rules (Lessons 7-12) topic-d-overview Problem Solving in the Coordinate Plane (Lessons 13-20) topic-e-overview Multi-Step Word Problems (Lessons 21-26) Recognize how an equation relates independent and dependent variables Analyze the relationship between independent and dependent variables by graphing In this lesson you will learn how to identify independent and dependent variables by examining. Relate variables using a graph. In this lesson you will learn how to show the relationship between independent and dependent variables by writing an equation. Khan Academy Distinguish dependent from independent variables in real-world situations.

4 To compute the perimeter of a rectangle you add the length, l and width, w and double this sum. Write an expression for the perimeter of a rectangle. Use the expression to find the perimeter of a rectangle with length 30 and width 75. [ Sadie computes the perimeter of a rectangle by adding the length, l, and width, w, and doubling this sum. Eric computes the perimeter of a rectangle by doubling the length, l, doubling the width, w, and adding the doubled amounts. Write an expression for Sadie s way of calculating the perimeter. Write an expression for Eric s way as well. Use both of the expressions to find the perimeter of a rectangle with length 30 and width 75. Explain why Sadie and Eric always get the same answer, no matter what the length and width of the rectangle are. [

5 A pizza costs $9.00. There is also a $3.50 delivery fee for each delivery. Write an expression that shows the cost of a pizza. Expression for the cost of one pizza: What if more one pizza was ordered? What expression could you use to find the price for ordering different amounts of pizza? Use your expression to complete the table. Pizzas Total Cost [Howard County Public Schools, Maryland]

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7 Write an expression for each phrase. Phrase Expression A case of juice boxes has 8 boxes in it. Let c represent a case. How many total juice boxes are there in c cases? Leon is six years younger than Frank. Let f represent Frank s age. How old is Leon? 3 more than y Each table holds the same amount of students. There are 24 students at t tables. How many students are at each table? [Howard County Public Schools, Maryland]

8 A hockey player scored 874 goals in his career. He played for n years. Write an expression that could be used to find the average number of goals scored per year. Justify your expression. [Howard County Public Schools, Maryland]

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10 Zaria earns $6 per hour at her job. She also earned a bonus of $30 this week. To find the total amount she earned this week, Zaria used the expression below, where h is the number of hours she worked this week. 6h + 30 Zaria worked 32 hours this week. What is the total amount of money Zaria earned this week? A. $68 B. $192 C. $222 D. $662

11 Tanya does push-ups and sit-ups every morning. She does p push-ups and 2p + 5 sit-ups. Which statement describes the number of sit-ups Tanya does every morning? A. The number of sit-ups is 5 fewer than half the number of push-ups she does. B. The number of sit-ups is 5 more than half the number of push-ups she does. C. The number of sit-ups is 5 fewer than twice the number of push-ups she does. D. The number of sit-ups is 5 more than twice the number of push-ups she does.

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