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
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.
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.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge studentsâ€™ facility with foundational skills and concepts, as well as their progress with unit content.
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.
Model | Example |
Tape diagram and equations |
$$3(x+4)=45$$ $$3x+4=45$$ |
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
Topic B: Solving and Modeling with Inequalities
Key
Major Cluster
Supporting Cluster
Additional Cluster
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