Lesson 15 CCLS Writing Linear Expressions - Weeblyhaaslei.weebly.com/.../6/3266655/writing_linear_expressions_cc_ny7m... · Write an expression that represents this ... correct answer

©Curriculum Associates, LLC Copying is not permitted.L15: Writing Linear Expressions136

Writing Linear ExpressionsLesson 15 Part 1: Introduction

You’ve learned how different expressions can represent the same situation. Take a look at this problem.

This swimming pool was designed so that sections of the pool can be used for different activities. The dimensions are given in meters. Write three different expressions to represent the total surface area of the pool.

Explore It

Use the math you already know to solve the problem.

You can think about the total surface area of the pool as the sum of the surface areas of the swimming sections and the other sections. Write an expression that represents this way of thinking about the total surface area.

8 1 x8 1 x

1

x25

area of swimmers sections area of other sections

You can think about the total surface area as 25(8) 1 8x 1 25x 1 x2. Draw and label a picture that shows this way of thinking about the total surface area.

You can think about the total surface area as (25 1 x)(8 1 x). Explain the thinking behind this expression.

8

x

lap swimmerswater

therapy

kids’area

swim lessons

x25

CCLS7.EE.2

©Curriculum Associates, LLC Copying is not permitted.137L15: Writing Linear Expressions

Lesson 15Part 1: Introduction

Find Out More

The expressions that you wrote to represent the surface area of the pool are equivalent expressions. Each expression shows a different way of looking at the situation.

You can use properties of operations to show that expressions are equivalent. Another way to test whether two or more expressions are equivalent is to evaluate them for specific values of the variable. For example, you could evaluate each expression for x 5 10.

25(8 1 x) 1 x(8 + x) 5 25(8 1 10) 1 10(8 1 10) 5 25(18) 1 10(18) 5 450 1 180 5 630

25(8) 1 8x 1 25x + x2 5 25(8) 1 8(10) 1 25(10) 1 102

5 200 1 80 1 250 1 100 5 630

(25 1 x)(8 + x) 5 (25 1 10)(8 1 10) 5 35(18) 5 630

No matter which expression you use to find the total surface area of the pool, you get 630 square meters as your answer. The three expressions are equivalent.

Reflect

1 If you know the value of x, which expression would you use to find the total surface area of the pool? Explain.

Lesson 15

©Curriculum Associates, LLC Copying is not permitted.

L15: Writing Linear Expressions138

Part 2: Modeled Instruction

Read the problem below. Then explore different ways to write an expression to solve the problem.

A group of rectangular community gardens is being built on an empty city block. The length of each garden will be 90 feet, but the widths of the gardens will vary. Let g stand for the width of a garden. Think about different ways to find the perimeter of each garden. Then write an expression to represent the different ways.

Picture It

You can think about the perimeter of the rectangle as the sum of its sides.

You can think about walking around the rectangle. The sum of its sides equals:

90 1 g 1 90 1 g

90

gg

90

Picture It

You can think about the perimeter of the rectangle as the sum of twice its length and twice its width.

If you see the perimeter as the sum of two equal lengths and two equal widths, you can multiply the length by 2 and the width by 2 and then add the products.

2(90) 1 2g

90

gg

90

Lesson 15


Part 2: Guided Instruction

Connect It

Now you will write the perimeter in a third way and show that all the expressions are equivalent.

2 Look at the diagrams on the previous page. Find the lengths of two adjacent sides. Write an expression for the sum of two adjacent sides.

3 The other pair of adjacent sides have the same sum. Explain how you could think of the perimeter of the rectangular garden as a product of the sum of two sides.

4 Write an expression for the perimeter of the rectangular garden as a product of the sum of two sides.

5 Now use all three ways to show how to find the perimeter of a rectangular garden that is 16 feet long and 5 feet wide.

6 Does it matter which expression you use to find the perimeter? Explain.

Try It

Use what you just learned to solve these problems. Show your work.

7 Students in Jay’s school plant vegetables in one of the rectangular gardens with length

90 feet and width 7 1 ·· 2 feet. Use each of the expressions above to find the garden’s

perimeter. Show that all three expressions produce the same measurement.

8 Write the following expression in two different ways: 1 ·· 2 (a 1 b).

Lesson 15



Read the problem below. Then explore how to write different expressions to represent and solve it.

The price of a $40.90 backpack is discounted 30%. Write two different expressions to represent its sale price.

Picture It

You can draw a bar diagram to represent the situation.

The whole bar represents the price of the backpack.

The shaded section represents the 30% discount.

0.30($40.90)

30% 70%

0.70($40.90)

$40.90

Model It

You can calculate the sale price by subtracting the 30% discount from the original price.

sale price 5 original price 2 discount

sale price 5 original price 2 30% of the original price

5 40.90 2 0.30 (40.90)

Model It

You can calculate the sale price by finding 70% of original price.

sale price 5 70% of the original price

5 0.70 (40.90)

Part 3: Modeled Instruction

Lesson 15


Connect It

Now you will show that both expressions give you the same sale price.

9 Explain how you could find the sale price of the backpack using two operations.

10 Calculate the sale price of the backpack using two operations. Show your work.

11 Explain how you could find the sale price of the backpack using one operation.

12 Calculate the sale price of the backpack using one operation. Show your work.

13 Suppose the price of the backpack was p dollars. Write two different expressions to represent the sale price.

Try It

Use what you just learned to solve these problems. Show your work.

14 The price of a flash drive that regularly sells for $16 is increased by 15%. Write two different expressions to find the new price.

15 The original price of a DVD is represented by the variable x. If the DVD is discounted 45%, write a subtraction expression and a multiplication expression to represent its sale price.

Part 3: Guided Instruction

Student Model

Part 4: Guided Practice Lesson 15



Study the student model below. Then solve problems 16–18.

A store manager paid $15 for a computer case and sells it in the store for 65% more than she paid. What expression represents the price of the computer case in the store?

Look at one way you could write an expression.

original price 1 65% of original price 5 sale price

15 1 0.65 • 15 5 sale price

Solution:

16 A hand-woven rectangular rug measures x ft long and 2 4 ·· 5 ft wide. Write an expression to represent the perimeter of the rug.

Show your work.

Solution:

15 1 0.65(15)

What is another way to write an expression to represent the sale price?

Pair/Share

The student wrote an expression by finding the increase and adding it to the original cost.

How many different ways can you represent the perimeter of the rug?

Pair/Share

What do I know about a rectangle that will help me solve this problem?

Part 4: Guided Practice Lesson 15


17 A customer calculated the cost of a new jacket, c, including a 7% sales tax, by multiplying 0.07 times the cost of the jacket and adding the product to the cost of the jacket. What is another way to calculate the price including tax? What expression represents the total cost?

Show your work.

Solution:

18 The price of a $198.00 smart phone is discounted 40% for a special promotion. What is its sale price during the promotion? Circle the correct answer.

A $190.08

B $120.80

C $118.80

D $79.20

Courtney chose D as the correct answer. How did she get that answer?

Which method would you use to solve the problem?

Pair/Share

I know that sales tax is added to the original cost of the jacket to find the total cost.

How could you explain to Courtney the way to find the correct answer?

Pair/Share

Will the sale price be more or less than $198.00?

Part 5: Common Core Practice Lesson 15



Solve the problems. Mark your answers to problems 1–3 on the Answer Form to the right. Be sure to show your work.

1 A music store manager advertises a 40% off sale. The manager lets x represent the regular price of any CD in the store. Which expression does NOT represent the sale price of a CD?

A 0.6x

B 0.4x

C x (1 2 0.4)

D x 2 0.4x

2 Jonathan and Trina both earn $12 per hour, but Trina earned a $15 bonus this week for being on time every day. Let J 5 number of hours that Jonathan worked this week and T 5 number of hours that Trina worked this week. Which expression represents the total amount that Jonathan and Trina earned this week?

A 12 (J 1 T 1 15)

B 12 (J 1 15) 1 12 (T 1 15)

C 15 (J 1 T) 1 12

D 12 (J 1 T) 1 15

3 Jayne’s mom bought a new folding chair that cost $14. She was charged an 8% sales tax. Which expression below represents the final price of the chair, including sales tax?

A 8 (1.14)

B 14 2 0.08 (1.14)

C 14 (1.08)

D 14 (0.08 1 14)

Answer Form

Number Correct 3

1 B C D

2 B C D

3 B C D



Self Check Go back and see what you can check off on the Self Check on page 125.

4 The length of a rectangle is x feet. Its width is (x 2 7) feet. Draw and label a rectangle to represent this situation. Then write three different expressions you could use to find its perimeter.

Show your work.

Answer

5 The perimeter of an equilateral triangle is 6x 2 6.3. Draw and label a triangle to represent this situation. Then write an expression to represent its perimeter as a sum. Then write an expression to represent its perimeter as a product.

Show your work.

Answer

Writing Linear expressionsLesson 15

L15: Writing Linear Expressions 139©Curriculum Associates, LLC Copying is not permitted.

(Student Book pages 136–145)

Lesson objeCtives• Rewrite expressions in different forms to better

understand relationships within contexts.

• Incorporate expressions representing length and width into the formulas for perimeter and area of triangles and rectangles.

Prerequisite skiLLs • Understand the concept of equivalent expressions.

• Simplify expressions.

• Write expressions to represent problem situations.

voCabuLaryequivalent expressions: expressions that have the same value

the Learning ProgressionMathematically proficient students represent situations mathematically, perform necessary calculations, and understand the result in terms of the original situation.

In this lesson, students learn that while equivalent expressions describe the same situation, different expressions can give different perspectives and might be more useful for certain purposes.

For example, if an item costs x dollars, the sale price after a 30% discount could be given by either x 2 0.3x or 0.7x. One expression describes the sale price as a discount subtracted from the original price; the other describes the sale price as a percentage of the original. Both methods are equally valid.

The lesson builds on work from Grade 6 to represent situations with expressions and equations. It draws on understanding of properties of operations. In later grades, students work with situations involving functions and integer exponents.

CCLs Focus

7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a 1 0.05a 5 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

aDDitionaL stanDarDs: 7.EE.1 (see page A32 for full text)

stanDarDs For MatheMatiCaL PraCtiCe: SMP 2, 4, 6–8 (see page A9 for full text)

Toolbox Teacher-Toolbox.com

✓ ✓

✓ ✓

✓

✓ ✓

Prerequisite Skills 7.EE.2

Ready Lessons

Tools for Instruction

Interactive Tutorials

L15: Writing Linear Expressions140©Curriculum Associates, LLC Copying is not permitted.

Lesson 15Part 1: introduction

at a gLanCeStudents explore ways to describe the area of a rectangle using algebraic expressions.

steP by steP• Tell students that this page models finding different

algebraic ways of representing one situation.

• Have students read the problem at the top of the page.

• Work through Explore It as a class.

• Point out that in the first bullet they are dividing the pool into two rectangles.

• Next, they add the areas of the separate rectangles to find the total area.

• Ask student pairs or groups to explain their answers for the last two bulleted items.

Model dimensions of a swimming pool.

Materials: large sheets of paper (packing or butcher) measuring at least 60 cm by 60 cm, markers, centimeter rulers; if large paper is unavailable, use scissors to cut rectangles and tape them together

• Discuss what happens to the swimming pool on page 136 when the value of x changes. Does any part of the pool not change? [Yes. The section for lap swimmers will always be 25 meters by 8 meters.]

• In the upper left corner of the packing paper, have students draw a rectangle measuring 25 cm by 8 cm.

• Ask students to choose a value for x. You may want to encourage them to use more reasonable values, say, less than 30 meters.

• Have students draw the rest of the swimming pool using their chosen value for x.

• Let students share some models. Discuss how small or large values of x affect the shape and size of the model. Are there values of x that would be unreasonable? [Yes. For example: 1 would probably be too small, and 50, while possible, would seem unreasonable.]

hands-on activity

• Which of these algebraic expressions makes the most sense to you. Why?

Students’ answers may vary. They might like the expression in the second bullet because it’s easier for them to see the area of each section of the pool separately. Alternately, they might like the expression in the third bullet because it uses the whole rectangle’s length and width.

• Do you think one of these expressions is more correct than the others? Explain.

Some of the expressions look more complicated than others and could be simplified, but they all accurately describe the area, and all could be used to get accurate results.

Mathematical Discourse

©Curriculum Associates, LLC Copying is not permitted.L15: Writing Linear Expressions136

Writing Linear expressionsLesson 15 Part 1: introduction

you’ve learned how different expressions can represent the same situation. take a look at this problem.

This swimming pool was designed so that sections of the pool can be used for different activities. The dimensions are given in meters. Write three different expressions to represent the total surface area of the pool.

explore it

use the math you already know to solve the problem.

You can think about the total surface area of the pool as the sum of the surface areas of the swimming sections and the other sections. Write an expression that represents this way of thinking about the total surface area.

8 1 x8 1 x

1

x25

area of swimmers sections area of other sections

You can think about the total surface area as 25(8) 1 8x 1 25x 1 x2. Draw and label a picture that shows this way of thinking about the total surface area.

You can think about the total surface area as (25 1 x)(8 1 x). Explain the thinking behind this expression.

8

x

lap swimmerswater

therapy

kids’area

swim lessons

x25

CCLs7.ee.2

25(8 1 x) 1 x(8 1 x)

1 1lap swimmers

25

8

kids’s area

x

x

water therapy

x

8

1swim lessons

25

x

you can think about the total surface area as the area of the large rectangle. you

can multiply the length and width of the whole pool.



at a gLanCeStudents use a given value for x to evaluate the three different expressions for the surface area of the pool on page 136.

steP by steP• Read Find Out More as a class.

• Review how each expression is a different representation of the area of the swimming pool on page 136.

• Point out the use of the order of operations. Time permitting, display the order of operations and have one volunteer describe what happens in each step.

• Discuss Reflect. Lead a discussion about which expression students would prefer to calculate with and why.

• Display the word equivalent for students.

• Tell students to look at the word parts—specifically, the prefix and root word.

• Ask students to identify the prefix. [equi-] Ask what equi- means. [“equal”]

• Now ask students to identify the root word. [valent] Tell students that valent developed from a Latin word meaning “worth” or “value.”

• Have a volunteer define equivalent. [“being of equal worth”]

eLL support

sMP tip: Showing the area as a whole and as the sum of different parts illustrates to students how to use the structure of a shape (SMP 7). Here and in later lessons, point out where areas can be divided into shapes that are easy to work with. ©Curriculum Associates, LLC Copying is not permitted.

137L15: Writing Linear Expressions


Find out More

The expressions that you wrote to represent the surface area of the pool are equivalent expressions. Each expression shows a different way of looking at the situation.

You can use properties of operations to show that expressions are equivalent. Another way to test whether two or more expressions are equivalent is to evaluate them for specific values of the variable. For example, you could evaluate each expression for x 5 10.

25(8 1 x) 1 x(8 + x) 5 25(8 1 10) 1 10(8 1 10) 5 25(18) 1 10(18) 5 450 1 180 5 630

25(8) 1 8x 1 25x + x2 5 25(8) 1 8(10) 1 25(10) 1 102

5 200 1 80 1 250 1 100 5 630

(25 1 x)(8 + x) 5 (25 1 10)(8 1 10) 5 35(18) 5 630

No matter which expression you use to find the total surface area of the pool, you get 630 square meters as your answer. The three expressions are equivalent.

reflect

1 If you know the value of x, which expression would you use to fi nd the total surface area of the pool? Explain.

responses will vary. students may choose the third expression because there are

fewer operations to perform. they may choose the second expression because

the numbers are smaller and easier to work with.

142 L15: Writing Linear Expressions©Curriculum Associates, LLC Copying is not permitted.

Part 2: Modeled instruction Lesson 15

at a gLanCeStudents explore different ways to express the perimeter of rectangular community gardens.

steP by steP• Read the problem at the top of the page as a class.

• Read the first Picture It. Point out that this method simply adds the lengths of each side.

• Read the second Picture It. Remind students that opposite sides of a rectangle are always equal in length.

Find perimeter of a rectangle.

Materials: rectangular desk, string of sufficient length to measure the perimeter of the desk’s surface at least twice, scissors, tape

• Point out the surface of a desk in the classroom. Ask students what the perimeter of the desk’s surface would be. [The distance around the outside of the desk’s surface.]

• Use a piece of string to measure the entire perimeter of the desk’s surface. Cut the string at that perimeter length, and tape it, straightened out, to a wall.

• Ask students what other ways you could find the perimeter. [You could measure all sides and then add their lengths. Or, knowing that the opposite sides are the same length, you could measure two adjacent sides and multiply their sum by two.]

hands-on activity

• Ask students why it might be important to know the perimeter of a rectangle. One application is purchasing materials for fencing. Other examples might include borders for sidewalks or gardens.

• Encourage students to think of situations where one measurement of the rectangle might be unknown, and what conditions might have an effect on that measurement.

• For example, suppose a horse needs a fenced area that is at least 50 m by 80 m, but the owner has space to extend the length. The perimeter would be given by 2(50 1 80 1 x) or some equivalent expression, and x could be determined both by the available space and the fencing budget.

real-World Connection

Lesson 15



Part 2: Modeled instruction

read the problem below. then explore different ways to write an expression to solve the problem.

A group of rectangular community gardens is being built on an empty city block. The length of each garden will be 90 feet, but the widths of the gardens will vary. Let g stand for the width of a garden. Think about different ways to find the perimeter of each garden. Then write an expression to represent the different ways.

Picture it

you can think about the perimeter of the rectangle as the sum of its sides.

You can think about walking around the rectangle. The sum of its sides equals:

90 1 g 1 90 1 g

90

gg

90

Picture it

you can think about the perimeter of the rectangle as the sum of twice its length and twice its width.

If you see the perimeter as the sum of two equal lengths and two equal widths, you can multiply the length by 2 and the width by 2 and then add the products.

2(90) 1 2g

90

gg

90


Part 2: guided instruction Lesson 15

at a gLanCeStudents revisit the problem on page 138. They explore a third way to describe perimeter and find that all three methods are equivalent.

steP by steP• Be sure to note that Connect It refers to the problem

on page 138.

• In problem 2, point out that the order of the terms does not matter.

• Before students address problem 5, review three different ways to find perimeter:

find the sum of all side lengths (l 1 w 1 l 1 w);

find the sum of two times the length and two times the width (2l 1 2w); and

multiply the sum of the length and the width by 2 (2[w 1 l]).

• Have students work through Try It and discuss their answers.

try it soLutions 7 Solution: 1st Way: 90 1 7 1

·· 

2 1 90 1 7 1

·· 

2 5 195;

2nd Way: 2(90) 1 2 1 7 1 ··

 2 2 5 180 1 15 5 195;

3rd Way: 1 290 1 7 1 ··

 2 2 5 2 1 97 1

·· 

2 2 1 195

8 Solution: 1 ··

 2 a 1 1

·· 

2 b, or (a 1 b)

······ 

2 ; Students may use the

distributive property or recognize that multiplying

by 1 ··

 2 is the same as dividing by 2.

sMP tip: Students reason abstractly and quantitatively (SMP 2) when they recognize different ways to represent the problem and manipulate the values accurately to find the perimeter. Occasionally ask students to think of a different method for a calculation or to listen to and restate the method of a classmate.

ERROR ALERT: Students who wrote 675 feet may

have multiplied 90 by 7 1 ··

 2 and found the area instead

of the perimeter.

Lesson 15


Part 2: guided instruction

Connect it

now you will write the perimeter in a third way and show that all the expressions are equivalent.

2 Look at the diagrams on the previous page. Find the lengths of two adjacent sides. Write an expression for the sum of two adjacent sides.

3 The other pair of adjacent sides have the same sum. Explain how you could think of the perimeter of the rectangular garden as a product of the sum of two sides.

4 Write an expression for the perimeter of the rectangular garden as a product of the sum of two sides.

5 Now use all three ways to show how to fi nd the perimeter of a rectangular garden that is 16 feet long and 5 feet wide.

6 Does it matter which expression you use to fi nd the perimeter? Explain.

try it

use what you just learned to solve these problems. show your work.

7 Students in Jay’s school plant vegetables in one of the rectangular gardens with length

90 feet and width 7 1 ·· 2 feet. Use each of the expressions above to fi nd the garden’s

perimeter. Show that all three expressions produce the same measurement.

8 Write the following expression in two diff erent ways: 1 ·· 2 (a 1 b).

90 1 g or g 1 90

since the two sums are the same, i can multiply the sum by 2.

2(90 1 g) or 2(g 1 90)

1st way: 16 1 5 1 16 1 5; 2nd way: 2(16) 1 2(5); 3rd way: 2(16 1 5)

no; the expressions are all equivalent, so i can choose any one of them. in each

case, the result is 42 feet.

1st way: 90 1 7 1 ·· 2 1 90 1 7 1 ·· 2 5 195; 2nd way: 2(90) 1 2 1 7 1 ·· 2 2 5 180 1 15 5 195;

3rd way: 2 1 90 1 7 1 ·· 2 2 5 2 1 97 1 ·· 2 2 5 195; the perimeter is 195 feet

a 1 b ····· 2 ; 1 ·· 2 a 1 1 ·· 2 b


Part 3: Modeled instruction Lesson 15

at a gLanCeStudents explore two methods of finding the sale price of a backpack with a 30% discount.

steP by steP• Read the problem at the top of the page as a class.

• Discuss Picture It. Guide students to understand how the entire bar represents the original price of the backpack, and the shaded part represents the part of the price to be subtracted from the original price.

• If necessary, review percentages briefly with students. 30% is equivalent to 0.30, and 3% is equivalent to 0.03.

• Discuss the first Model It. Point out that 30% is the same as 0.30.

• Discuss the second Model It. Ask, Why can you find the sale price by multiplying 0.70 by 40.90? [because the sale price is 70% of the original price]

• Which method for calculating the sale price do you think is the best to use? Why?

Students may prefer either method. Some may like the first because it makes more intuitive sense to them or because 0.3 is an easy number for them to multiply. Others may prefer the second method because it uses fewer calculations.

• Can you think of a problem where you would use the method you prefer less?

Many students will prefer one method. Listen for responses that indicate selecting a method based on the numbers in the problem, either the price or the discount amount.

Mathematical Discourse

sMP tip: Bar models help students model everyday situations with mathematics (SMP 4) and understand the relationships among the quantities in the problem. Encourage students to use bar models or diagrams help them understand a problem or decide on a solution method.

Lesson 15



read the problem below. then explore how to write different expressions to represent and solve it.

The price of a $40.90 backpack is discounted 30%. Write two different expressions to represent its sale price.

Picture it

you can draw a bar diagram to represent the situation.

The whole bar represents the price of the backpack.

The shaded section represents the 30% discount.

0.30($40.90)

30% 70%

0.70($40.90)

$40.90

Model it

you can calculate the sale price by subtracting the 30% discount from the original price.

sale price 5 original price 2 discount

sale price 5 original price 2 30% of the original price

5 40.90 2 0.30 (40.90)

Model it

you can calculate the sale price by finding 70% of original price.

sale price 5 70% of the original price

5 0.70 (40.90)

Part 3: Modeled instruction


Part 3: guided instruction Lesson 15

at a gLanCeStudents revisit the problem on page 140 and explore two different methods of finding a sale price. They calculate the sale price using both methods.

steP by steP• Point out that Connect It refers to the problem on

page 140.

• Emphasize that both methods describe the same sale price and that p 2 0.30p is equivalent to 0.70p.

• Ask students if there would be a reason to use two operations instead of one. [If you did not have a calculator, it might be easier to calculate a 10% discount and subtract it than to calculate 90% of the original price.]

• Make sure students understand an operation means a calculation.

eLL support

Find the sale price, with sales tax, after a discount.

Jess wonders whether she has enough cash to buy some art supplies. A sign says they are discounted 30% from the original price of $34. The sales tax is 5%. If Jess has $25, does she have enough money?

• Ask, What is the first step to solve the problem? [Sales tax is charged on the sale price, so find the sale price first.]

• Ask, How do you find the sale price? [Find 30% of the original price and subtract that from the original price, or find 70% of the original price to get $23.80.]

• Ask, What is the next step? [Find the price with sales tax. They may find 5% of $23.80 and add it to the sale price, or they may multiply by 1.05.]

• Ask, If Jess has $25, does she have enough money? [The total price is $24.99. She has enough.]

Concept extensiontry it soLutions 14 Solution: 16 1 0.15(16); 1.15(16)

15 Solution: x 2 0.45x; 0.55x

ERROR ALERT:Students who wrote 16 2 0.15(16) and 0.85(16) are not paying attention to the situation in the problem. The price is increased, not discounted by a percentage.

Lesson 15


Connect it

now you will show that both expressions give you the same sale price.

9 Explain how you could fi nd the sale price of the backpack using two operations.

10 Calculate the sale price of the backpack using two operations. Show your work.

11 Explain how you could fi nd the sale price of the backpack using one operation.

12 Calculate the sale price of the backpack using one operation. Show your work.

13 Suppose the price of the backpack was p dollars. Write two diff erent expressions to represent the sale price.

try it

use what you just learned to solve these problems. show your work.

14 The price of a fl ash drive that regularly sells for $16 is increased by 15%. Write two diff erent expressions to fi nd the new price.

15 The original price of a DVD is represented by the variable x. If the DVD is discounted 45%, write a subtraction expression and a multiplication expression to represent its sale price.

Part 3: guided instruction

i could multiply $40.90 by 0.30 to get the discount. then i could subtract the

discount from $40.90 to get the sale price.

Multiply: 0.30 3 $40.90 5 $12.27; then subtract: $40.90 2 $12.27 5 $28.63.

i could multiply $40.90 by 0.70 to get the sale price.

Multiply: 0.70 3 $40.90 5 $28.63.

sale price 5 p 2 0.30p; sale price 5 0.70p

16 1 0.15(16); 1.15(16)

x 2 0.45x; 0.55x


Part 4: guided Practice Lesson 15

at a gLanCeStudents write algebraic expressions to help solve problems.

steP by steP• Ask students to solve the problems individually.

• When students have completed each problem, have them Pair/Share to discuss their solutions with a partner or in a group.

soLutions Ex Solution: 15 1 0.65(15); The expression finds the

amount of increase and adds it to the original cost.

16 Solution: 2 1 x 1 2 4 ··

 5 2 ft or any equivalent expression;

Students could solve the problem by drawing and

labeling a rectangle or by using a formula for

perimeter of a rectangle.

17 Solution:Multiply the cost by 1.07; 1.07c; Students could solve the problem by realizing that adding a 7% increase is the same as multiplying by 1.07.

18 Solution: C; Courtney found the discount by multiplying the original price $198.00 by 0.4 but forgot to subtract the discount from original price.

Explain to students why the other two answer choices are not correct:

Ais not correct because the discount was found by multiplying by 0.04, not 0.4.

Bis not correct because there was a mistake made in the subtraction.



17 A customer calculated the cost of a new jacket, c, including a 7% sales tax, by multiplying 0.07 times the cost of the jacket and adding the product to the cost of the jacket. What is another way to calculate the price including tax? What expression represents the total cost?

Show your work.

Solution:

18 The price of a $198.00 smart phone is discounted 40% for a special promotion. What is its sale price during the promotion? Circle the correct answer.

a $190.08

b $120.80

C $118.80

D $79.20

Courtney chose D as the correct answer. How did she get that answer?

Which method would you use to solve the problem?

Pair/share

I know that sales tax is added to the original cost of the jacket to find the total cost.

How could you explain to Courtney the way to find the correct answer?

Pair/share

Will the sale price be more or less than $198.00?

Multiply the cost of the jacket by 1.07; 1.07c

she found the discount, $79.20, by multiplying the original

price, $198.00, by 0.4, but she forgot to subtract the discount

from the original price.

Possible answer:

cost of the jacket plus tax:

c 1 0.07c

c(1 1 0.07)

c(1.07)

StudentModel




study the student model below. then solve problems 16–18.

A store manager paid $15 for a computer case and sells it in the store for 65% more than she paid. What expression represents the price of the computer case in the store?

Look at one way you could write an expression.

original price 1 65% of original price 5 sale price

15 1 0.65 • 15 5 sale price

Solution:

16 A hand-woven rectangular rug measures x ft long and 2 4 ·· 5 ft wide. Write an expression to represent the perimeter of the rug.

Show your work.

Solution:

15 1 0.65(15)

What is another way to write an expression to represent the sale price?

Pair/share

The student wrote an expression by finding the increase and adding it to the original cost.

How many different ways can you represent the perimeter of the rug?

Pair/share

What do I know about a rectangle that will help me solve this problem?

2 1 x 1 2 4 ·· 5 2 ft or any equivalent expression

Possible answer:

perimeter 5 2(length 1 width)

length 5 x

width 5 2 4 ·· 5



at a gLanCeStudents use algebraic expressions to solve word problems that might appear on a mathematics test.

steP by steP• First, tell students that they will use algebraic

expressions to solve word problems. Then have students read the directions and answer the questions independently. Remind students to fill in the correct answer choices on the Answer Form.

• After students have completed the Common Core Practice problems, review and discuss correct answers. Have students record the number of correct answers in the box provided.

soLutions 1 Solution:B; 0.4x would represent only the discount,

not the sale price.

2 Solution: D; Multiply their hourly wage, 12, by the sum of their hours, ( J 1 T), then add the bonus of 15.

3 Solution:C; Multiply the cost of the chair, 14, by 1.08, which represents 100% of the original cost plus a sales tax of 8% of the original cost.

4 Solution: x 1 x 2 7 1 x 1 x 2 7, 2x 1 2(x 2 7), 2(2x 2 7) or other equivalent expressions. See possible student work above.

5 Solution:For example:Sum: 2x 2 2.1 1 2x 2 2.1 1 2x 2 2.1;Product: 3(2x 2 2.1); or other equivalent expressions. See possible student work above.



self Check Go back and see what you can check off on the Self Check on page 125.

4 The length of a rectangle is x feet. Its width is (x 2 7) feet. Draw and label a rectangle to represent this situation. Then write three different expressions you could use to fi nd its perimeter.

Show your work.

Answer

5 The perimeter of an equilateral triangle is 6x 2 6.3. Draw and label a triangle to represent this situation. Then write an expression to represent its perimeter as a sum. Then write an expression to represent its perimeter as a product.

Show your work.

Answer

Possible answer:

x 2 7x 2 7

x

x

Possible answer:

6x 2 6.3 }}}} 3 5 2x 2 2.1

x 1 x 2 7 1 x 1 x 2 7, 2x 1 2(x 2 7), 2(2x 2 7) or other equivalent expressions

P 5 6x 2 6.3

2x 2 2.1 2x 2 2.1

2x 2 2.1

sum: 2x 2 2.1 1 2x 2 2.1 1 2x 2 2.1

product: 3(2x 2 2.1)




Solve the problems. Mark your answers to problems 1–3 on the Answer Form to the right. Be sure to show your work.

1 A music store manager advertises a 40% off sale. The manager lets x represent the regular price of any CD in the store. Which expression does NOT represent the sale price of a CD?

A 0.6x

B 0.4x

C x (1 2 0.4)

D x 2 0.4x

2 Jonathan and Trina both earn $12 per hour, but Trina earned a $15 bonus this week for being on time every day. Let J 5 number of hours that Jonathan worked this week and T 5 number of hours that Trina worked this week. Which expression represents the total amount that Jonathan and Trina earned this week?

A 12 (J 1 T 1 15)

B 12 (J 1 15) 1 12 (T 1 15)

C 15 (J 1 T) 1 12

D 12 (J 1 T) 1 15

3 Jayne’s mom bought a new folding chair that cost $14. She was charged an 8% sales tax. Which expression below represents the fi nal price of the chair, including sales tax?

A 8 (1.14)

B 14 2 0.08 (1.14)

C 14 (1.08)

D 14 (0.08 1 14)

answer Form

numberCorrect 3

1 A B C D

2 A B C D

3 A B C D


Differentiated instruction Lesson 15

assessment and remediation• Ask students to find the sale price of a CD that was marked at $14 but was sold at a 20% discount. [$11.20]

• For students who are struggling, use the chart below to guide remediation.

• After providing remediation, check students’ understanding. Ask students to find the sale price of a shirt that was originally marked at $25 but was sold at a 15% discount. [$21.25]

• If a student is still having difficulty, use Ready Instruction, Level 6, Lesson 5.

if the error is . . . students may . . . to remediate . . .

$2.80 have found the discount without subtracting it from the original price.

Review that a 20% discount means 20 ··· 100 or 2 ·· 10 of the original price was subtracted. Ask them to compare their answer to the original price and decide if the answer makes sense. Then have students set up the expression using words: original price 2 discount 5 sale price.

$16.80 have added the discount to the original price.

Ask them to think about whether it makes sense for a discounted price to be more than the original price. Then have students set up the expression using words: original price 2 discount 5 sale price.

$13.72 have found a discount of 2% instead of 20%.

Review percentages with students. Discuss that 20% means the same thing as 20 ··· 100 or 20 hundredths, which is the same as 0.20.

$1.12 have found a sale price using 8% of the original price instead of 80%.

Review percentages with students. Discuss that 80% means the same thing as 80 ··· 100 or 80 hundredths, which is the same as 0.80. Ask students to check their answer for reasonableness.

hands-on activity Challenge activityhow much do you save?Materials: paper, pencil, ruler, scissors

• Have students draw a 1-by-8-in. rectangle, then cut it out. Tell them that the 8-inch strip of paper represents the whole cost of a poster marked $8.

• Now tell students the poster goes on sale for 25% off. Tell them to draw a section representing 25% of the rectangle’s area. [1 in. 3 2 in.] Tell students to label this area “25%” and then cut it.

• Ask students what the remaining section should be labeled, as a percent. [75%]

• Point out that the original rectangle was 8 inches long, and the original cost of the poster was $8. Point out that the new rectangle is 6 inches long. What is the new cost of the poster? [$6]

Find the percent discount.

• Tell students that a shirt is on sale for a discounted price of $12.00.

• Say that the original price of the shirt was $30.

• Display this formula:

percent discount 5 1 1 2 discounted price ·············

  original price

2 3 100

• Challenge students to find the percent discount of the original price. [The discount is 60%.]

Documents

Lesson 15 CCLS Writing Linear Expressions - Weeblyhaaslei.weebly.com/.../6/3266655/writing_linear_expressions_cc_ny7m... · Write an expression that represents this ... correct answer