Lesson 7 | Equations and Inequalities | 7th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

7.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Expressions and Equations

7.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
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

Analyze real-world situations and identify important information needed to solve a problem.
Create equations to model real-world applications and efficiently solve a problem (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

In this lesson, students have the opportunity to tackle novel challenges and discover how equations are effective tools to model and solve problems. In place of Anchor Problems, there are four options for activities listed in the Additional Practice section, two of which require students to have computers. Choose one or two activities to use.
In terms of pacing, and depending on the number of activities used, this lesson may extend over more than one day.

Problem Set

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

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

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

A batch of 8 cookie ice cream sandwiches weighs 1,092 grams. On average, each cookie weighs 12 grams, and the same amount of ice cream is used for each sandwich. A pint of ice cream has approximately 450–460 grams of ice cream. How many pints of ice cream would you need to make another batch of 8 cookie ice cream sandwiches?

References

Wikimedia Commons Photo: Toll House Chocolate Chip Cookie Sandwich.jpg by Thomson200

Toll House Chocolate Chip Cookie Sandwich.jpg by Thomson200 is made available on Wikimedia Commons under the CC0 1.0 license. Accessed May 14, 2018, 4:44 p.m..

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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.

SERP Poster Problems On the Download — This problem explores speed and delayed start time in the context of downloading files on different cell phones. Students write and solve equations and create posters to share and discuss student work.
Desmos Central Park — Using computers, students explore creating equally spaced parking spaces by dragging dividers into the right locations. They eventually use variables and equations to find efficient ways to tackle the challenges.
Desmos Picture Perfect — Using computers, students explore placing pictures on hooks that are equally spaced from one another. They develop equations to find efficient ways to solve the challenges. This is similar to Central Park.
Andrew Stadel's 3-Act Math Tasks Styrofoam Cups — Students guess how many Styrofoam cups it will take to reach the top of a doorway. Then, given measurements, they use equations to determine a way to find an exact answer.

Lesson 6

Lesson 8

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

Expressions and Equations

Foundational Standards

Expressions and Equations

Criteria for Success

Tips for Teachers

Problem Set

Target Task

References

Student Response

Additional Practice

Lesson Map

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