Math / 7th Grade / Unit 4: Equations and Inequalities
Students solve equations and inequalities with rational numbers, and encounter real-world situations that can be modeled and solved using equations and inequalities.
Math
Unit 4
7th Grade
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In Unit 4, seventh-grade students continue to build on the last two units by solving equations and inequalities with rational numbers. They use familiar tape diagrams as a way to visually model situations in the form $$px+q=r$$ and $$p(x+q)=r$$. These tape diagrams offer a pathway to solving equations using arithmetic, which students compare to a different approach of solving equations algebraically. Throughout the unit, students encounter word problems and real-world situations, covering the full range of rational numbers, that can be modeled and solved using equations and inequalities (MP.4). As they work with equations and inequalities, they build on their abilities to abstract information with symbols and to interpret those symbols in context (MP.2). Students also practice solving equations throughout the unit, ensuring they are working towards fluency which is an expectation in 7th grade.
In sixth grade, students understood solving equations and inequalities as a process of finding the values that made the equation or inequality true. They wrote and solved equations in the forms $$x+p=q$$ and $$px=q$$, using nonnegative rational numbers. In seventh grade, students reach back to recall these concepts and skills in order to solve one- and two-step equations and inequalities with rational numbers including negatives.
In eighth grade, students explore complex multi-step equations; however, they will discover that these multi-step equations can be simplified into forms that are familiar to what they’ve seen in seventh grade. Eighth-grade students will also investigate situations that result in solutions such as 5 = 5 or 5 = 8, and they will extend their understanding of solution to include no solution and infinite solutions.
Pacing: 16 instructional days (12 lessons, 3 flex days, 1 assessment day)
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The following assessments accompany Unit 4.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Pre-Unit Student Self-Assessment
Have students complete the Mid-Unit Assessment after lesson 4.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Post-Unit Assessment
Post-Unit Assessment Answer Key
Post-Unit Student Self-Assessment
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Suggestions for how to prepare to teach this unit
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
$$3(x+4)=45$$
$$3x+4=45$$
The central mathematical concepts that students will come to understand in this unit
Terms and notation that students learn or use in the unit
equation
inequality
solution
substitution
tape diagram
To see all the vocabulary for Unit 4, view our 7th Grade Vocabulary Glossary.
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.
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.
Solve word problems leading to equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ (Part 1).
Solve word problems leading to equations in the forms $${px+q=r}$$ and $${p(x+q)=r }$$ (Part 2).
Model with equations in the form $${px+q=r}$$ and $${p(x+q)=r}$$.
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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 $${p(x+q)<r.}$$
Solve inequalities with negative coefficients.
Solve word problems leading to inequalities in the forms $${px+q>r}$$ or $${px+q<r}$$ and $${p(x+q)>r}$$ or $${p(x+q)<r}$$.
Model with inequalities.
7.EE.B.3 7.EE.B.4.B
Key
Major Cluster
Supporting Cluster
Additional Cluster
The content standards covered in this unit
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 — 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.
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?
7.EE.B.4.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Standards covered in previous units or grades that are important background for the current unit
6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
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.
6.EE.B.8 — Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Standards in future grades or units that connect to the content in this unit
8.EE.C.7 — Solve linear equations in one variable.
8.EE.C.8 — Analyze and solve pairs of simultaneous linear equations.
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 3
Numerical and Algebraic Expressions
Unit 5
Percent and Scaling