Lesson 2 | Equations and Inequalities | 7th Grade Mathematics

Objective

Represent equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ using tape diagrams.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.EE.B.4.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?

Expressions and Equations

7.EE.B.4.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?

Foundational Standards

The foundational standards covered in this lesson

6.EE.B.7

Expressions and Equations

6.EE.B.7 — 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.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Represent story situations and equations using tape diagrams.
Write equations to represent tape diagrams and situations.
Write story situations for tape diagrams and equations.
Understand how a tape diagram can be helpful to visualize a solution pathway for an equation (MP.1).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 2 and 3 engage students in representing and solving two-step equations using tape diagrams. In this lesson, students shift between stories, diagrams, and equations, understanding how each connects to the others and helps shed light on the situation. In Lesson 3, students will use the tape diagrams to solve equations.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Which tape diagram matches the situation described below? For the other tape diagram, write a story situation that matches it.

Situation:

Five friends go to a fall festival and they each pay an entry fee of $10. The friends each spend the same amount of money on lunch at the festival and don’t spend any other money. Altogether, the friends have spent $120.

Tape Diagrams:

Guiding Questions

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Problem 2

Which equation matches the tape diagram shown below? For the other equation, draw a tape diagram to represent it.

Tape Diagram:

Equations:

Equation A: $${3x+4=45}$$
Equation B: $${3(x+4)=45}$$

Guiding Questions

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Problem 3

For each situation described below, draw a tape diagram and write an equation. Define any variables you use.

a. Situation A:
A book has 6 chapters in it, each with the same number of pages. The book also has an introduction that is 8 pages long. The whole book is 194 pages long.

b. Situation B:
Eight baskets have some apples in them, and the same number of apples are in each basket. Six apples are added to each basket to make a total of 144 apples.

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

A family of 5 went to a matinee movie on a Saturday afternoon. The movie tickets for the matinee were a special price for each person. The family spent a combined $25 at the concession stand on drinks and popcorn. Altogether, the family spent $57.50 at the movies.

a. Draw a tape diagram to represent the situation above. Then write an equation.

b. How does the tape diagram help you understand how much the special price was?

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Given an equation in the form $${px+q=r}$$ or $${p(x+q)=r}$$, draw a tape diagram and write a story situation.

Kuta Software Free Pre-Algebra Worksheets Two-Step Equation Word Problems — Students do not need to solve; rather, have them draw tape diagrams and write equations for the word problems.
Open Up Resources Grade 7 Unit 6 Practice Problems — Lessons 2 and 3, skip the review questions

Lesson 1

Lesson 3

Lesson Map

Topic A: Solving and Modeling with Equations

Solve one-step equations with rational numbers.

7.EE.B.4.A

Represent equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ using tape diagrams.

7.EE.B.4.A

Solve equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ using tape diagrams.

7.EE.B.3 7.EE.B.4.A

Solve equations in the forms $${px+q=r }$$ and $${p(x+q)=r}$$ algebraically.

7.EE.B.4.A

Solve word problems leading to equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ (Part 1).

7.EE.B.3 7.EE.B.4.A

Solve word problems leading to equations in the forms $${px+q=r}$$ and $${p(x+q)=r }$$ (Part 2).

7.EE.B.3 7.EE.B.4.A

Model with equations in the form $${px+q=r}$$ and $${p(x+q)=r}$$.

7.EE.B.3 7.EE.B.4.A

Topic B: Solving and Modeling with Inequalities

Solve and graph one-step inequalities.

7.EE.B.4.B

Write and solve inequalities in the forms $${px+q>r}$$ or $${px+q<r}$$ and $${p(x+q)>r }$$ or $${p(x+q)<r.}$$

7.EE.B.4.B

Solve inequalities with negative coefficients.

7.EE.B.4.B

Solve word problems leading to inequalities in the forms $${px+q>r}$$ or $${px+q<r}$$ and $${p(x+q)>r}$$ or $${p(x+q)<r}$$.

7.EE.B.4.B

Model with inequalities.

7.EE.B.3 7.EE.B.4.B

Equations and Inequalities

Objective

Common Core Standards

Core Standards

Expressions and Equations

Foundational Standards

Expressions and Equations

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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