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Common Core for Grade 7

Common Core for Mathematics

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

Examples, solutions, worksheets, videos, and lessons to help Grade 7 students learn how to use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

A. Solve word problems leading to equations of the form*px* + *q* = *r* and *p*(*x* + *q*) = *r*, where *p*, *q*, and *r* are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. *For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?*

Common Core: 7.EE.4a

### Suggested Learning Targets

**7.EE.4A-4 - Solving Two-Step Equations**

To solve equations, we use inverse (opposite) operations.

Addition and Subtraction

Multiplication and Division

**Solve Two-Step Equations**

This video explains how to solve two-step equations. It first shows how to do it the traditional way and then shows how to think about in terms of the inverse operations.**7.ee.4a**

The Common Core State Standards (CCSS) videos are designed to support states, schools, and teachers in the implementation of the CCSS. Each video is an audiovisual resource that focuses on one or more specific standards and usually includes examples/illustrations geared to enhancing understanding. The intent of each content-focused video is to clarify the meaning of the individual standard rather than to be a guide on how to teach each standard although the examples can be adapted for instructional use.

It compares an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.**Multi-Step Equation Problem Solving**

This video shows how to setup and solve a multi-step word problem using the variable assignment, equation, solution method.

Michael has a total of 92 coins in his coin collection. This is 8 more than three times the number of quarters in the collection. How many quarters does Michael have in his collection?

**Solving Multi-step Word Problems with Equations**

This video demonstrates how to set-up and solve word problems with multiple steps.

1) Karma's age is 2 years less than three eighths of her father's age. If Karma is 13 years old, how old is her father?

2) Last week, Kiwi filled his 16-gallon tank with gas. On average his car burns 0.03 gallon of gas per mile. If Kiwi has 4 gallon left in his tank, how many miles has he driven?

3) The drawing shows a stack of paper cups. The cups are 10 cm high. Each cup after the first adds 0.8 cm to the height of the stack. How many cups will fit in a dispenser that is 30 cm high?

4) Buck rented a truck for $39.95 plus $0.32 per mile. Before returning the truck he filled the tank with gasoline which cost $9.80. If the total cost was $70.23, how far was the truck driven?

5) So far, 37 miles of a new highway have been completed. This is one mile less than two thirds of the entire length. How long will the new highway be when completed?

6) The pressure on a scuba diver at sea level is 14.7 pounds per square inch (psi). The pressure increases 0.445 psi for each foot of depth. Suppose the pressure on a diver is 41.4 psi. How deep is she?

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 7

Common Core for Mathematics

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

A. Solve word problems leading to equations of the form

Common Core: 7.EE.4a

- I can solve simple equations.
- I can solve two step linear equations of the form px+ q = r and p(x+q)=r, where p, q, and r are specific rational numbers.
- I can solve word problems (two-step linear equation problems) with rational coefficients (ex, px +q = r).
- I can fluently solve multi-step linear equations and word problems with rational coefficients (ex: p(x+q)=r).
- I can compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

To solve equations, we use inverse (opposite) operations.

Addition and Subtraction

Multiplication and Division

This video explains how to solve two-step equations. It first shows how to do it the traditional way and then shows how to think about in terms of the inverse operations.

The Common Core State Standards (CCSS) videos are designed to support states, schools, and teachers in the implementation of the CCSS. Each video is an audiovisual resource that focuses on one or more specific standards and usually includes examples/illustrations geared to enhancing understanding. The intent of each content-focused video is to clarify the meaning of the individual standard rather than to be a guide on how to teach each standard although the examples can be adapted for instructional use.

It compares an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

This video shows how to setup and solve a multi-step word problem using the variable assignment, equation, solution method.

Michael has a total of 92 coins in his coin collection. This is 8 more than three times the number of quarters in the collection. How many quarters does Michael have in his collection?

This video demonstrates how to set-up and solve word problems with multiple steps.

1) Karma's age is 2 years less than three eighths of her father's age. If Karma is 13 years old, how old is her father?

2) Last week, Kiwi filled his 16-gallon tank with gas. On average his car burns 0.03 gallon of gas per mile. If Kiwi has 4 gallon left in his tank, how many miles has he driven?

3) The drawing shows a stack of paper cups. The cups are 10 cm high. Each cup after the first adds 0.8 cm to the height of the stack. How many cups will fit in a dispenser that is 30 cm high?

4) Buck rented a truck for $39.95 plus $0.32 per mile. Before returning the truck he filled the tank with gasoline which cost $9.80. If the total cost was $70.23, how far was the truck driven?

5) So far, 37 miles of a new highway have been completed. This is one mile less than two thirds of the entire length. How long will the new highway be when completed?

6) The pressure on a scuba diver at sea level is 14.7 pounds per square inch (psi). The pressure increases 0.445 psi for each foot of depth. Suppose the pressure on a diver is 41.4 psi. How deep is she?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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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