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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 2).

## 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 student work to understand different approaches in simplifying expressions and to identify mistakes.
3. Simplify expressions involving adding, subtracting, and expanding expressions with rational numbers.

## Tips for Teachers

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The numbers used in the problems in this lesson require skills working with positive and negative rational numbers. This is a good opportunity to spiral in skills from the previous unit aligned to 7.NS.1 and 7.NS.2. Resources in the Problem Set Guidance include a range of problems from simpler, with just integers, to more complex, with fractions and decimals. Students should get exposure to a wide range of difficulty levels.

#### 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

A student solved the problem below as part of her homework. Review her work and check for any mistakes. For each line in her work, explain what she did to get her next step.

Homework Problem:

${-\frac{1}{3}(5x-2y)-2\left ( \frac{1}{2}x+\frac{1}{3}y \right )}$

Student’s Work:

${-\frac{5}{3}x+\frac{2}{3}y-x-\frac{2}{3}y}$

${-\frac{5}{3}x-x+\frac{2}{3}y-\frac{2}{3}y}$

${\left ( -\frac{5}{3}-1 \right )x+0}$

${-\frac{8}{3}x}$

### Problem 2

Find the perimeter of the parallelogram.

### Problem 3

An expression is given.

${-2y+\frac{3}{2}x+\frac{7}{4}}$

Which are equivalent to the given expression? Select each correct answer.

a.     ${-\frac{1}{2}xy+\frac{7}{4}}$

b.     ${\frac{3}{2}x-2\left ( y+\frac{7}{2} \right )}$

c.     ${-\frac{1}{4}y+\frac{3}{2}(y+x)}$

d.     ${-2y+\frac{1}{2}\left ( 3x+\frac{7}{2} \right )}$

e.     ${\frac{1}{4}(-8y+6x+7)}$

#### References

PARCC Released Items Math Spring Operational 2016 Grade 7 Released ItemsProblem 4

## 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.

• Have students swap work every now and then to check and correct each other’s work (without an answer key).

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Which expressions are equivalent to the expression $n+\frac{5}{6}(m-n)-\frac{1}{3}m$? Select all that apply.

1. $\frac{1}{2}m$
2. $\frac{1}{6}n+\frac{1}{2}m$
3. $\frac{1}{6}n+1\frac{1}{6}m$
4. $1\frac{5}{6}n-1\frac{1}{6}m$
5. $n-\frac{5}{6}n+\frac{5}{6}m-\frac{1}{3}m$

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