we will solve one-step equations using the

We will solve one-step equations using the properties of addition, subtraction, multiplication, and division.

What are we going to learn?

What does solve mean?Solve means __________.

CFU

Students, you already know how to use inverse operations to undo a change in value. Now, we will solve one-step equations using inverse operations.

Make Connection

Inverse operations are operations that undo each other.

Inverse Operations

+ and –

and

What operation would undo the change in value?1. 2.

8 2 = 6 7 3 = 10

12 3 = 4 3 5 = 15

- +

3. 4.

6 + 2 = 8 10 - 3 = 7

4 3 = 12 15 5 = 3

Learning Objective

Activate Prior Knowledge

Think about PEMDAS. What are the operations ?Which operations are grouped together?

CALIFORNIA STANDARD:

6.AF 1.1 Write and Solve One-Step Linear Equations in One Variable.

x + 2 = 3Solution

(1) + 2 = 3?

True3 = 3

x = 1

x + 2 = 3(4) + 2 = 3?

False6 = 3

x = 4

NOT a Solution

A one-step equation contains2 one operation.A one-step equation requires3 one inverse operation to solve for the variable.

• To keep an equation balanced, inverse operations must be done on both sides of the equation.

The solution is the value of the variable that makes the equation true.

Solving One-Step Equations

2 has within it3 needs (synonym)

Vocabulary

x + 2 = 3Inverse

Operation Balance

Which inverse operation would be used to solve the one-step equation 4x = 8? How do you know?A MultiplicationB Division

CFU 2

Go toSkill Dev 1

Go toSkill Dev 2

Inverse Operations

+ and –

and

Which inverse operation would be used to solve the one-step equation x - 4 = 6? How do you know?A AdditionB Subtraction

What is the difference between the solution (x = 1) and the non-solution (x = 4)?

CFU 1

InverseOperation

Balancex4

= 1

divisionx4

= 1

x + 2 = 3addition

Solution

True1 = 1

x = 4 = 1x4

= 1(4)4

?

FlashcardsInverse Operations

Concept Development

Why is 2 subtracted on both sides of the equation?Why is 1 the solution to the equation x + 2 = 3?

CFU

A one-step equation requires one inverse operation to solve for the variable.• To keep an equation balanced, inverse operations must

be done on both sides of the equation.The solution is the value of the variable that makes the equation true.

xxx

x

x = 3

Inverse Operations

+ and –

and

- 2 - 2 x + 2 = 5

=3 + 2 5

Concept Development (Clarification and CFU)

WE WANT TO ISOLATE THE VARIABLE TERM (X) .

Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation.

Check and interpret4 the solution. Hint: Answer the question.

Solve one-step equations.1

23

4 explain (synonym)

Vocabulary

A one-step equation requires one inverse operation to solve for the variable.• To keep an equation balanced, inverse operations must be done on both sides

of the equation.The solution is the value of the variable that makes the equation true.

1. Isabella is baking muffins. The recipe calls for 8 cups of sugar. Isabella has already added 3 cups of sugar. How many more cups of sugar does she need to add?

2. Yesterday, Samuel had $7. He was given more money today and now has $10. How much money was Samuel given today?

3. Shannon had some money in her pocket. She received $4 for school supplies. She now has $11. How much money did she start with?

4. Jessie had a few marbles. He earned 5 of them during a game and now has 8. How many marbles did Jessie start with?

5 + 3 = 8- 3 - 3

c = 5

Isabella needs to add __________________.5 cups of sugar

8 = 8

Samuel was given ________________ today.

3 + 7 = 10- 7 - 7m = 3

$3

10 = 10

7 + 4 = 11- 4 - 4

m = 7

Shannon started with __________________.$7

11 = 11

c + 3 = 8m + 7 = 10

m + 4 = 11 3 + 5 = 8- 5 - 5

m = 3

Jessie started with _____________________.3 marbles

8= 8

m + 5 = 8

How did I/you connect the problem to the equation?How did I/you solve for the variable?How did I/you interpret the solution?

CFU

1

2

3

Back toConcept Dev

Inverse Operations

+ and –

and

c + 3 = 8

m + 7 = 10

m + 4 = 11

m + 5 = 8

Skill Development/Guided Practice I


Check and interpret the solution. Hint: Answer the question.


23


1. Binders cost $2 each. If Miguel has $12, how many binders can he buy?

2. A box of pencils has 6 pencils inside. If Rosalina has 24 pencils, how many boxes does she have?

3. Isabella gave out muffins to her 6 friends. If each friend was given 4 muffins, how many muffins did Isabella give out?

4. Ricky and his two friends earned money doing chores for his neighbor. After splitting the money, they each got $7. How much money did they earn together?

How did I/you connect the problem to the equation?How did I/you solve for the variable?How did I/you interpret the solution?

CFU

1

2

3

2(6) = 12

Miguel can buy ______________________.6 binders

12 = 12 2 2

2b = 12

b = 66(4) = 24

She has ______________________.4 boxes of pencils

24 = 24 6 6

6b = 24

b = 4

4 ● ● 4

m = 24

Isabella gave out ______________________.24 muffins

46m

244

66 = 6

3 ● ● 3

m = 21

Ricky and his friends earned _____________.$21

37m

213

77 = 7

Inverse Operations

+ and –

and

2b = 12 6b = 24

m4

= 6 m3

= 7


of the equation.

Skill Development/Guided Practice 2

Solving one-step equations will help you solve more complex equations.

Solving one-step equations will help you do well on tests.

1

Does anyone else have another reason why it is relevant to solve one-step equations? (Pair-Share) Why is it relevant to solve one-step equations? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?

CFU

2

5x – 6 = 4 + 6 + 6 5x = 10 5 5

x = 2

A one-step equation requires one inverse operation to solve for the variable.• To keep an equation balanced, inverse operations must be done on both

sides of the equation.The solution is the value of the variable that makes the equation true.

Sample Test Question:

37. What value of k makes the following equation true?

k 3 = 36

A 108 B 98 C 39 D 12

Relevance

What did you learn today about solving one-step equations? (Pair-Share) Use words from the word bank.




23


1. Angelina needs to save $20. She has already saved $9. How much more money does Angelina need to save?

2. A can of tennis balls has 3 tennis balls inside. If Frank has 18 tennis balls, how many cans of tennis balls does he have?

11 + 9 = 20- 9 - 9

m = 11

Angelina needs to save ______________________.$11

20 = 20

m + 9 = 20 3(6) = 18

Frank has ______________________.6 cans of tennis balls

18 = 18 3 3

3c = 18

b = 6

2 = 6m

m 8

Sam is trying to solve the equation on the left. After applying one inverse operation, his solution was m = 8. Explain why his solution is incorrect and what possible error he may have made.

Sam’s solution

Inverse Operations

+ and –

and

3c = 18m + 9 = 20


of the equation.

Skill Closure

Access Common Core

Summary Closure

Word Bankequationone-stepbalancedinverse

operation




23


1. Gabriel is baking cookies. The recipe calls for 6 cups of flour. If Gabriel has already added 2 cups of flour, how much more flour does he need to add?

2. Louisa had a handful of nickels. She found 8 more and now has 14 nickels. How many nickels did Louisa start with?

3. Books cost $5 each. If Mathew has $35, how many books can he buy?

4. Jenny and her 4 friends earned money selling sugar-free lemonade. After splitting the money, they each got $9. How much money did they earn together?

4 + 2 = 6- 2 - 2

c = 4

Gabriel needs to add ______________________.4 cups of flour

6 = 6

c + 2 = 6 12 + 8 = 14- 8 - 8

n = 6

Louisa started with ______________________.6 nickels

14 = 14

n + 8 = 14

5(7) = 35

Mathew can buy ______________________.7 books

35 = 35 5 5

5b = 35

b = 75 ● ● 5

m = 45

Jenny and her friends earned ___________________.

$45

59m

455

99 = 9

Inverse Operations

+ and –

and

c + 2 = 6

5b = 35

n + 8 = 14

m5

= 9


of the equation.

Independent Practice

Periodic Review 1

1. Carmella is baking biscuits. The recipe calls for 11 cups of flour. She has already added 6 cups. How much does she still have to add?

2. Fernando is building a bookshelf. He has used 26 pieces. He has 12 of the pieces left. How many pieces does the bookshelf have?

3. Claire made 6 batches of meatballs. She made a total of 48 meatballs. How many meatballs does each batch make?

4. Tyrone and his three friends are going to split a box of crackers. They each get 14 crackers. How many crackers were in the box?

6 11f5 + 6 = 11- 6 - 6

c = 5

Carmella needs to add ______________________.5 cups of flour

11 = 11

c + 6 = 11 26 12p

38 - 26 = 12+ 26 + 26

n = 38

The bookshelf has ______________________.38 pieces

12 = 12

n – 26 = 12

6 48m6(8) = 48

Claire made ______________________.8 meatballs

48 = 48 6 6

6m = 48

b = 8

414c

4 ● ● 4

m = 56

There were ______________________.56 crackers in the box

4

14c

564

14

14 = 14

1. Geoffrey earns $7 for mowing lawns. Last month, he earned $42. How many lawns did he mow?

Which of the following statements is true? How do you know?

a. The inverse operation used to solve this problem is division (÷).

b. The meaning of the solution to this problem is the amount of money earned.

c. The meaning of the solution to this problem is the number of lawns mowed. d. The first step in isolating the variable is to divide both sides of the equation by m.

7m = 42

2. A set of colored pencils had 29 pencils added to it. There are currently 45 pencils altogether. How many pencils were there to start with?


a. The inverse operation used to solve this problem is subtraction (-).

b. The meaning of the solution to this problem is the original number of pencils.

c. The meaning of the solution to this problem is the number of pencils left.

d. The first step in isolating the variable is to add 29 to each side of the equation.

p + 29 = 45

Yes/No

Yes/No

Yes/NoYes/No

Yes/No

Yes/No

Yes/NoYes/No

Access Common Core

Periodic Review 2

1. Larissa has 17 dollars. She gets her allowance. Now she has 28 dollars. How much was her allowance?

2. A set of colored pencils has 45 pencils taken out. There are currently 29 pencils left. How many pencils were there originally?

3. Geoffrey earns $7 for mowing lawns. Last month, he earned $42. How many lawns did he mow?

4. Thomas and his 5 friends made cookies. They shared them equally and each got 13. How many cookies did they make altogether?

17 28a17 + 11 = 28- 17 - 17

a = 11

Larissa’s allowance is ______________________.$11

28 = 28

17 + a = 28 45 29p

74 - 45 = 29+ 45 + 45

n = 74

There were __________________ originally.74 pencils in the set

29 = 29

p - 45 = 29

7 42m7(6) = 42

Geoffrey mowed ______________________.6 lawns

42 = 42 7 7

7m = 42

b = 6

613c

6 ● ● 6

c = 78

Thomas and his friends made __________________.78 cookies

6

13m

786

13

13 = 13

1. Estevan worked on his English homework for 25 minutes. He finished all his homework in 57 minutes. He worked out how long it took him to finish the rest of his homework below, but his older sister told him his answer was incorrect. Where did Estevan make a mistake? How can he fix it?

2. Javier can make 7 paper airplanes each hour. He made 28 airplanes and has calculated how long he spent making them. Explain how he can check that his answer is correct. Is his answer correct?

+ 25 + 25

7 7 a = 4

25 + h = 57

h = 82

7a = 28

Access Common Core

Periodic Review 3

1. Estevan worked on his English homework for 25 minutes. He finished all his homework in 57 minutes. How long did it take him to finish the rest of his homework?

2. Elizabeth had several colored pencils. She gave out 14 of them to her friends and how has 13. How many pencils did she start with?

3. Javier can make 7 paper airplanes each hour. If he made 28 airplanes, how long did he spend making them?

4. Adolfo and his six friends earn money doing yard work. After splitting up the money, they each got 15 dollars. How much money did they earn together?

25 57h25 + 32 = 57- 25 - 25

h = 32

It took Estevan ______________________.32 minutes

57 = 57

25 + h = 57 14 13c

27 - 14 = 13+ 14 + 14

c = 27

Elizabeth had ______________________.27 pencils

13 = 13

c - 14 = 13

7 28a7(4) = 28

Javier spent ______________________.4 hours making airplanes

28 = 28 7 7

7a = 28

a = 4

715y

7 ● ● 7

y = 105

Adolfo and his friends earned ___________________.

$105

7

15y

1057

15

15 = 15

1. Thomas and his 5 friends made cookies. They shared them equally and each got 13. How many cookies did they make?


2. Claire made 6 batches of meatballs. She made a total of 48 meatballs. How many meatballs does each batch make?


a. The inverse operation used to solve this problem is multiplication ().b. The meaning of the solution to this problem is the amount of cookies made.

c. The meaning of the solution to this problem is the number of cookies shared

equally.

d. The first step in isolating the variable is to multiply each side of the

equation by c.

a. The inverse operation used to solve this problem is multiplication ().b. The meaning of the solution to this problem is the number of meatballs made in each batch.

c. The meaning of the solution to this problem is the number of meatballs made in total.

d. The first step in isolating the variable is to divide both sides of the equation by m.

c ÷ 13 = 6.

m 6 = 48.

Yes/No

Yes/No

Yes/NoYes/No

Yes/No

Yes/No

Yes/No

Yes/No

Access Common Core

A one-step equation requires one inverse operation to solve for the variable.

What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know?

Addition Subtraction

x + 4 = 7

Flash Cards (Inverse Operations)





x + 6 = 13




Multiplication Division

5x = 25




Division Multiplication

2 8x





x + 7 = 8




Multiplication Division

7x = 49

Back toConcept Dev

we will solve one-step equations using the

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cfua onestep equation

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