Students solve equations and inequalities with rational numbers, and encounter real-world situations that can be modeled and solved using equations and inequalities.
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)
This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.
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tape diagram
equation
solution
substitution
inequality
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tape diagram
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Tape diagram and equations |
Examples: $$3(x+4)=45$$ $$3x+4=45$$ |
7.EE.B.4.A
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.3
7.EE.B.4.A
Solve 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 $${p(x+q)=r}$$ algebraically.
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 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.4.B
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.3
7.EE.B.4.B
Model with inequalities.
Key: Major Cluster Supporting Cluster Additional Cluster
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