LESSON 1: FINDING COUNTERFEIT COINS...

Copyright © 2014 Pearson Education, Inc. 4

Grade 6 Unit 5: Equations and Inequalities

EXERCISESLESSON 1: FINDING COUNTERFEIT COINS

EXERCISES

• Review your Unit Assessment from the previous unit.

• Write your wonderings about equations and inequalities.

• Write a goal stating what you plan to accomplish in this unit.

• Based on your previous work, write three things you will do differently during this unit to increase your success.



EXERCISESLESSON 2: AN INTRODUCTION

EXERCISES

For problems 1–4, write either Equation or Inequality to describe each statement.

1. 4 = 3 + 1

2. 2 < 9

3. 12 > 10 + 1

4. 9 – 3 < 7

5. Put a check mark next to each statement that is true.

A 5 = 5 B 4 < 2 C 7 < 17 D –2 < –3 E –5 > –2

Choose =, >, or < for each blank in problems 6–12.

6. 9 + 2 8 + 5

7. 7.2 + 2.03 9.3

8. 214

+ 338

625

– 213

9. 5.2 + 3.15 9

10. 23

• 6 4

11. 12

÷ 2 12

• 2

Challenge Problem

12. Fill in the blank with some number that will make the statement true.

3.5 + 2.1 + 5.21 < 12

•



EXERCISES

EXERCISES

For problems 1–7, decide whether the given values of x make each statement true or false, and show your work.

1. x = 3; 6 + 5 = 8 + x

2. x = 5; 4x < 21

3. x = 2; 14 < 7x

4. x = 6; 2x – 12 = 5

5. x = 4.1; 2.1x + 5 > 13.7

6. x = 22; x ÷ 3 + = 10

7. x = 111

; 45

÷ x > 13

+ 8

8. Complete the table by determining which of the given values of x are solutions. (There may be more than one solution for each row. If no solutions make the equation or inequality true, write None.)

Values of x Equation or Inequality Solutions

2, 4, 8 x + 9 = 13

–3, 3, 6 x > 2

3, 5, 9 4 x = 2x + 6

1, 2.1, 612

x + 7 > 7 + x

0, 23

, 312

3x + 4 + 5x = 8 + 2x

Challenge Problem

9. a. Write an equation that has more than one solution.

b. Write an equation that has no solution.

83

LESSON 3: SOLVING WITH SUBSTITUTION



EXERCISES

EXERCISES

In problems 1–7, choose the correct solution for each equation.

1. h + 7.5 = 29

A h = 21.5

B h = 297 5.

C h can be any number.

D There is no solution.

2. 4x = 28

A x = 24

B x = 7

C x can be any number.


3. 7 + 3x = 3x + 16

A x = 8

B x = 256



4. 2b + 10 = 3b + 3 + 6b

A b = 1

B b = 10

C b can be any number.


5. 2y + 7 = 22

A y = 7.5

B y = 11

C y can be any number.


LESSON 4: SOLVE WITH REASONING



EXERCISESLESSON 4: SOLVE WITH REASONING

6. 5(x + 3) = 15 + 5x

A x = 5

B x = 2



7. r – 5 = 5 – r

A r = 5

B r = 10

C r can be any number.


Challenge Problem

8. Determine whether the following equation has one solution, infinitely many solutions, or no solution. Explain your reasoning.

5x + 8 + x = 2(x + 4) + x



EXERCISES

EXERCISES

1. What number can you subtract from both sides of the equation so that x will be by itself on the left?

x + 15 = 29

For problems 2–4, fill in the blanks according to the addition property of equality.

2. x + 9 = 13

x + 9 – = 13 –

x =

3. 11 = x + 2.4

11 – = x + 2.4 –

= x

4. x – 7.6 = 3.4

x – 7.6 + = 3.4 +

x =

Show how to use the addition property of equality to solve each equation in problems 5–8. Use substitution to check your solution.

5. x + 46 = 109

6. x + 6.7 = 9

7. x + 12

= 813

8. 315

= x + 16

Challenge Problem

9. Explain how to use the addition property of equality to solve

0.5x – 6.8 = –0.5x – 1.2.

LESSON 5: THE ADDITION PROPERTY



EXERCISES

EXERCISES

1. What number can you divide both sides of the equation by so that x will be by itself on the left?

7x = 42

For problems 2–4, fill in the blanks according to the multiplication property of equality.

2. 5x =35

5x ÷ = 35 ÷

x =

3. 23

x = 6

23

x • = 6 •

x =

4. 7x

= 15

7x

• = 15

•

x =

Show how to use the multiplication property of equality to solve each equation in problems 5–8. Use substitution to check your solution.

5. 6x = 73

6. x = 21

7. 6.4 = 4x

8.

=

Challenge Problem

9. Explain how to use both the multiplication and addition properties of equality to solve 4x + 5 = x + 20.6.

34

5x 3

8

LESSON 6: THE MULTIPLICATION PROPERTY



EXERCISES

EXERCISES

1. Determine whether the solution to each equation can be found by adding 2, subtracting 2, multiplying by 2, or dividing by 2.

a. 2x = 15b. x + 2 = 6c. 0.5x = 8d. 7.3 = x – 2

For problems 2–10, explain whether you would use the addition or multiplication properties of equality to solve the given equation. Then, solve the equation and check using substitution.

2. 5 + a = 7

3. 6y = 39

4. m + 8 = 56

5. 25

b = 16

6. 6x

= 78

7. 153 = 16x

8. 59

= 8x

9. 15 = n + 3.8

10. 21 = 12

x

Challenge Problem

11. Use the properties of equality to solve the ratio 34

= 10x

. Explain your steps.

LESSON 7: SOLVING EQUATIONS



EXERCISES

EXERCISES

1. Write an equation for each statement. Let n be your variable.

a. The sum of 3 and some number is 9.b. The product of 4 and some number is 10.c. One-half of some number is 8.

Choose a variable to represent the unknowns in problems 2–7. Then write and solve an equation for each exercise.

2. Some number increased by 4 is equal to 11. What is the number?

3. The product of some number and 5 is 223

. What is the number?

4. The perimeter of a square is 48 in. What is the length of one side?

5. At the beginning of a trip, the odometer on a car reads 146,201 km. At the end of the trip, it reads:

How many kilometers did the car travel during the trip?

LESSON 8: EQUATIONS TO SOLVE PROBLEMS



EXERCISES

6.

This is a photo of the headquarters of the U.S. Department of Defense. It is called the Pentagon because of its geometrical shape (penta means “five”). The sum of the measures of the five equal interior angles is 540 degrees. What is the measure of each angle?

7. Two and a half pounds of potato salad cost $8.75.

At that rate, what is the cost of 512

lb?

Challenge Problem

8. The lengths of the sides of a triangle are a + 5 units, a + 7 units, and 3a + 3 units. The sides of a square are each 2a units. What is the value of a if the perimeter of the square is equal to the perimeter of the triangle?

LESSON 8: EQUATIONS TO SOLVE PROBLEMS



EXERCISES

EXERCISES

1. Decide whether each value of x is a solution to the inequality x ≥ 6.

a. x = 6b. x = 4c. x = 8d. x = –8

Write an inequality to represent each scenario in problems 2–6. Define your variables and include at least three solutions for each inequality.

2. Gasoline is selling for more than $3 per gallon.

3. You must be at least 5 years old to attend the show.

4. More than 50,000 votes were cast in the election.

5. There are at least 2 gallons of milk in the refrigerator.

6. The maximum capacity of the room is 250 people.

Challenge Problem

7. You are building a soccer field. The length has to be 30 m longer than the width, and the total perimeter must be between 320 m and 360 m.

What are some possible dimensions for the field? Represent your answer with an inequality.

LESSON 9: INEQUALITIES



EXERCISESLESSON 10: ON THE NUMBER LINE

EXERCISES

1. Which of the following inequalities is represented by this number line?

–5 –4 –3 –2 –1 0 1 2 3 4 5

A x > –2

B x < –2

C x ≥ –2

D x ≥ 2

For each inequality in problems 2–6:

• Represent the inequality on a number line.

• Write three values that make the inequality true.

• Write the inequality using words—for example, “x is less than 5.”

2. y ≥ 6

3. x < 3

4. 212

≥ m

5. n ≤ – 412

6. p < 3.5



EXERCISES

Challenge Problem

7. Let x represent Mia’s height in inches, and let y represent Denzel’s height in inches. Put a check mark next to each inequality that is true.

72

66

60

54

48

42

36

30

24

18

12

6

0

a. x > yb. y < x + 9c. x < 66d. x > 63e. x + y < 138f. y – x < 3

LESSON 10: ON THE NUMBER LINE



EXERCISESLESSON 11: PUTTING IT TOGETHER

• Read through your work on the Self Check task and think about your other work in this lesson.

• Write what you have learned.

• What would you do differently if you were starting the Self Check task now?

• Record your ideas. Keep track of any strategies you have learned.

• Complete any exercises that you have not finished from this unit.

LESSON 1: FINDING COUNTERFEIT COINS...

Documents

Transcript of LESSON 1: FINDING COUNTERFEIT COINS...