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Common Core for Grade 6

More Lessons for Grade 6

Examples, solutions, videos, and lessons to help Grade 6 students learn how to solve real-world and mathematical problems by writing and solving equations of the form *x* + *p* = *q* and* px* = *q* for cases in which *p*, *q* and *x* are all nonnegative rational numbers.

Common Core: 6.EE.7

### Suggested Learning Targets

**Solving problems with equations x + p = q and px = q (Common Core Standard 6.EE.7)**

Solving Equations

To get the variable by itself, do the opposite operation.

x + 5 = 12

9p = 63

b/8 = 3

Writing and solving equations

Examples:

1. You divide G grapes among 5 people. Each person gets 7 grapes. What does G equal?

2. The temperature in Chicago one winter at noon is T degrees. By midnight, the temperature had dropped 29 degrees, to 18 degrees. What was the temperature at noon? How to solve real world problems involving addition and subtraction, by writing equations that represent the situation described.

Examples:

1. Jessica bought 4 bags of potato chips for a party. When she found out that more people were coming than expected, she went back to the store and bought two more bags of chips. Which number sentence could you use to find out how many bags of chips she bought?

A. 4 + 2 = n

B. 4 - 2 = n

C. 4 ÷ 2 = n

D. 4 × 2 = n

2. Jessica bought 4 bags of potato chips for a party. After the party she had 2 bags of chips left. Which number sentence could you use to find out how many bags of chips were eaten at the party?

A. 4 + 2 = n

B. 4 - 2 = n

C. 4 ÷ 2 = n

D. 4 × 2 = n

Example:

The school copier makes 42 copies per minute. The copier ran for 9 minutes. What equation can the school use to find the total number of copies (c) made during that time?

A. 42 - c = 49

B. c + 9 = 42

C. 42c = 9

D. c/42 = 9 Examples:

1) 130 - f = 70

2) 68/v = 4

3) 25 = 10 + k

4) 95 = 5p

5) 2.5 + m = 8.5

6) 5,600 = 7b

7) 15 1/2 = c - 8

8) 18 ÷ g = 2

1) 56 is equal to the product of 7 and z. What is the value of z? Use mental math and the guess-and-check strategy to help you. Explain your thinking.

2) Jamal is finding the perimeter of this parallelogram. He used the diagram to find the length of one of the sides. Here is his work:

p = 2l + 2w

20 cm = 2(6 cm) + 2 • w

What should Jamal use as the value of w in his equation?

3) Benny is finding the area of a rectangle. He used the diagram to find the width of the rectangle. Here is his work: A = l • w

525 m^{2} = l • 21 m

What should Benny use as the value of l in his equation?

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Common Core for Grade 6

More Lessons for Grade 6

Common Core: 6.EE.7

- I can define an inverse operation.
- I can use inverse operations to solve one step variable equations.
- I can apply rules of the form x + p = q and px = q, for cases in which p, q and x are all nonnegative rational numbers, to solve real world and mathematical problems. (There is only one unknown quantity).
- I can develop a rule for solving one-step equations using inverse operations with

nonnegative rational coefficients. - I can solve and write equations for real-world mathematical problems containing one

unknown. I can solve real world problems using equations.

Solving Equations

To get the variable by itself, do the opposite operation.

x + 5 = 12

9p = 63

b/8 = 3

Writing and solving equations

Examples:

1. You divide G grapes among 5 people. Each person gets 7 grapes. What does G equal?

2. The temperature in Chicago one winter at noon is T degrees. By midnight, the temperature had dropped 29 degrees, to 18 degrees. What was the temperature at noon? How to solve real world problems involving addition and subtraction, by writing equations that represent the situation described.

Examples:

1. Jessica bought 4 bags of potato chips for a party. When she found out that more people were coming than expected, she went back to the store and bought two more bags of chips. Which number sentence could you use to find out how many bags of chips she bought?

A. 4 + 2 = n

B. 4 - 2 = n

C. 4 ÷ 2 = n

D. 4 × 2 = n

2. Jessica bought 4 bags of potato chips for a party. After the party she had 2 bags of chips left. Which number sentence could you use to find out how many bags of chips were eaten at the party?

A. 4 + 2 = n

B. 4 - 2 = n

C. 4 ÷ 2 = n

D. 4 × 2 = n

The school copier makes 42 copies per minute. The copier ran for 9 minutes. What equation can the school use to find the total number of copies (c) made during that time?

A. 42 - c = 49

B. c + 9 = 42

C. 42c = 9

D. c/42 = 9 Examples:

1) 130 - f = 70

2) 68/v = 4

3) 25 = 10 + k

4) 95 = 5p

5) 2.5 + m = 8.5

6) 5,600 = 7b

7) 15 1/2 = c - 8

8) 18 ÷ g = 2

1) 56 is equal to the product of 7 and z. What is the value of z? Use mental math and the guess-and-check strategy to help you. Explain your thinking.

2) Jamal is finding the perimeter of this parallelogram. He used the diagram to find the length of one of the sides. Here is his work:

p = 2l + 2w

20 cm = 2(6 cm) + 2 • w

What should Jamal use as the value of w in his equation?

3) Benny is finding the area of a rectangle. He used the diagram to find the width of the rectangle. Here is his work: A = l • w

525 m

What should Benny use as the value of l in his equation?

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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