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# Numerical and Algebraic Expressions

## Objective

Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).

## Common Core Standards

### Core Standards

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• 7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

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• 6.EE.A.3

• 6.EE.A.4

• 7.NS.A.1

• 7.NS.A.2

## Criteria for Success

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1. Look for and make use of structure in expressions (MP.7).
2. Analyze incorrect answers to highlight and correct misconceptions.
3. Simplify expressions involving adding, subtracting, and expanding expressions with rational numbers.

## Tips for Teachers

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Lessons 7 and 8 pull together the concepts from the previous four lessons and engage students in simplifying complex expressions. In Lesson 7, students look at and discuss common misconceptions, and the problems become progressively more complex and challenging by the end of Lesson 8. Students will need to draw on their skills of computing with rational numbers from Unit 2.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from discussion) and Anchor Problem 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

In math class, students are attempting to simplify the expression written on the board:

${7-2(3-8x)}$

Three students make an attempt at a first step:

Len writes:  ${5(3-8x)}$

Monty writes: ${7-2(-5x)}$

Nailany writes:  ${7-6-16x}$

1. Do you agree with any of the students? Explain your reasoning for each one.
2. Oscar is a little stuck, so he rewrites the problem in a different way to help him determine what to do. He writes ${ 7+(-2)(3-8x)}$. How might this new expression help Oscar simplify the expression?

#### References

Institute for Mathematics and Education Draft 6–8 Progression on Expressions and Equations

Modified by Fishtank Learning, Inc.

### Problem 2

Which expressions below are equivalent to ${4-3(6x-3)}$? Select all that apply.

a.     ${(4-18)x+9}$

b.     ${(4+9)-18x}$

c.     ${4-(18x-9)}$

d.     ${4-18x-3}$

e.     ${4-18x+9}$

f.     ${6x-3 }$

### Problem 3

Determine which expression is equivalent to ${\frac{3}{4}-x\left ( \frac{1}{2}-\frac{5}{8} \right )+\left ( -\frac{3}{8}x \right )}$.

a.     ${-\frac{3}{4} x}$

b.     ${\frac{1}{2} x}$

c.     ${\frac{1}{8}-\frac{7}{8}x}$

d.     ${\frac{3}{4}-\frac{1}{4}x}$

#### References

PARCC Released Items Math Spring Operational 2015 Grade 7 End of Year Released ItemsProblem 13

## Problem Set

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

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Simplify the expressions.

a.     ${-2x+15-4(3x-1)}$

b.     ${-(a+b)-\frac{3}{2}(a-b)}$

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