Neft Teacher · Notes Packet

Unit 6 · Standard 6.EE.4

Equivalent Expressions

Lesson 6-6

Name:Date:Class:

Key Vocabulary Level 1 support

Picture first, then the word, then a plain-language meaning. Say each word out loud.

Illustration of Equivalent: Expressions that always have the same value.

2x + 4 and 2(x + 2): when x = 3, both = 10; when x = 7, both = 18 — always the same

Equivalent

Expressions that always have the same value.

Illustration of Simplify: To write an expression in a shorter, simpler way.

3x + 2x + 5 simplifies to 5x + 5 — fewer terms, same value

Simplify

To write an expression in a shorter, simpler way.

Illustration of Like Terms: Terms with the same letter, like 2x and 5x.

3x and 7x are like terms (both x); 3x and 3y are NOT (x vs y); 3x and 3x² are NOT (x vs x²)

Like Terms

Terms with the same letter, like 2x and 5x.

Illustration of Combine: To add or subtract terms with the same letter.

4n + 3n = 7n — add the coefficients (4 + 3 = 7) and keep the variable (n)

Combine

To add or subtract terms with the same letter.

Illustration of Coefficient: The number in front of a letter, like the 3 in 3x.

In 5x + 3, the coefficient of x is 5 — when x = 2, the 5x part equals 10

Coefficient

The number in front of a letter, like the 3 in 3x.

Key Ideas & Notes

Think About It

  • Why did both formulas give the same answer?
  • What did Producer B do differently from Producer A?
  • Would they still match if x = 10?

My Notes

Guided Examples

Example 1

Which expression is equivalent to 4x + 3x?

Solution: 4x + 3x = 7x. Combine the coefficients: 4 + 3 = 7.

Answer: A. 7x

Example 2

Which expression is equivalent to 2(m + 5)?

Solution: 2(m + 5) = 2m + 10 using the distributive property.

Answer: A. 2m + 10

Example 3

Which property is shown: 3(x + 7) = 3x + 21?

Solution: Multiplying 3 by each term inside the parentheses is the distributive property.

Answer: A. Distributive

Write About the Math The Writing Revolution

I can explain my work using the words equivalent, simplify, like terms, and combine.

1. Kernel Sentence subject + verb

Model: Equivalent is expressions that always have the same value.Equivalente es expresiones que siempre tienen el mismo valor.

Write a kernel sentence about equivalent. Use a subject and a verb.Escribe una oración base sobre equivalente. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Equivalent matters in mathEquivalente importa en matemáticas

Expand the kernel three ways. Add a reason, a contrast, and a result.

becauseporque

Equivalent matters in math because ___.Equivalente importa en matemáticas porque ___.

butpero

Equivalent matters in math, but ___.Equivalente importa en matemáticas, pero ___.

soentonces

Equivalent matters in math, so ___.Equivalente importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about equivalent.Di un hecho verdadero sobre equivalent.

Equivalent ___.

QuestionPregunta

Ask a question about equivalent.Haz una pregunta sobre equivalent.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about equivalent.Muestra entusiasmo sobre equivalent.

Wow, ___ !¡Guau, ___ !

CommandMandato

Tell a partner what to do with equivalent.Dile a un compañero qué hacer con equivalent.

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

These expressions are equal because ___.Estas expresiones son iguales porque ___.

I checked by ___.Lo comprobé al ___.

Rewriting helps when ___.Reescribir ayuda cuando ___.

Try It

Solve on your own. Check the answer key when you are done.

1. Which property is shown: 3(x + 7) = 3x + 21?

  1. Distributive
  2. Commutative
  3. Associative
  4. Identity
Show your work:

2. Simplify: 5n + 2n

  1. 7n
  2. 10n
  3. 7n²
  4. 52n
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

A student says 2x + 3 and 5x are equivalent because both equal 5 when x = 1. Is the student correct? Explain why testing one value is not enough to prove equivalence, and find a value of x where they give different results.

Sentence starter: The student is ___ because ___. When x = 1: 2(1) + 3 = ___ and 5(1) = ___. But when x = ___: 2(___) + 3 = ___ and 5(___) = ___. To prove equivalence, expressions must be equal for ___ values of x.

Show your work:

Reflect — Exit Ticket

Which expression is equivalent to 6n + 4 + 3n − 1?

  1. 9n + 3
  2. 9n + 5
  3. 63n
  4. 18n + 4
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. Distributive — Multiplying 3 by each term inside the parentheses is the distributive property.
  2. Try It 2: A. 7n — 5n + 2n = 7n. Add the coefficients: 5 + 2 = 7. The variable stays as n.
  3. Exit Ticket: A. 9n + 3 — 6n + 3n = 9n and 4 − 1 = 3, so the simplified expression is 9n + 3.

Writing (TWR) — what to look for