Neft Teacher · Notes Packet

Unit 6 · Standard 6.EE.3

The Distributive Property

Lesson 6-5

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 Distributive Property: Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.

3(4 + 5) = 3×4 + 3×5 = 12 + 15 = 27 — the 3 gets 'distributed' to both the 4 and the 5

Distributive Property

Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.

Illustration of Factor: A number that gets multiplied by another number.

In 3(x + 2), the 3 is the factor outside the parentheses that multiplies each term inside

Factor

A number that gets multiplied by another number.

Illustration of Expand: To multiply out the parentheses in an expression.

Expand 2(n + 6): multiply 2 × n = 2n and 2 × 6 = 12, so 2(n + 6) = 2n + 12

Expand

To multiply out the parentheses in an expression.

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

3(x + 4) and 3x + 12 always give the same answer: when x = 2, both = 18; when x = 10, both = 42

Equivalent

Expressions that always have the same value.

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

In 6x + 15, the coefficient of x is 6 — it came from distributing in 3(2x + 5)

Coefficient

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

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

4x + 2x = 6x (combine coefficients); 4x + 2y cannot be combined (different variables)

Like terms

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

Key Ideas & Notes

Think About It

  • Why do both methods give the same total?
  • What does the 3 represent in 3(15 + 5)?
  • How is 3(15 + 5) related to 3 × 15 + 3 × 5?

My Notes

Guided Examples

Example 1

Expand 6(n + 3) using the distributive property.

Solution: 6(n + 3) = 6 × n + 6 × 3 = 6n + 18.

Answer: A. 6n + 18

Example 2

Expand 4(5 − 2) using the distributive property.

Solution: 4(5 − 2) = 4 × 5 − 4 × 2 = 20 − 8 = 12.

Answer: A. 12

Example 3

Expand 3(x + 4) using the distributive property.

Solution: 3(x + 4) = 3 × x + 3 × 4 = 3x + 12.

Answer: A. 3x + 12

Write About the Math The Writing Revolution

I can explain my steps using the words distributive property, factor, expand, and equivalent.

1. Kernel Sentence subject + verb

Model: Distributive Property is multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.Propiedad distributiva es multiplicar un número por todo lo que está dentro del paréntesis: a(b + c) = ab + ac.

Write a kernel sentence about distributive property. Use a subject and a verb.Escribe una oración base sobre propiedad distributiva. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Distributive Property matters in mathPropiedad distributiva importa en matemáticas

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

becauseporque

Distributive Property matters in math because ___.Propiedad distributiva importa en matemáticas porque ___.

butpero

Distributive Property matters in math, but ___.Propiedad distributiva importa en matemáticas, pero ___.

soentonces

Distributive Property matters in math, so ___.Propiedad distributiva importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about distributive property.Di un hecho verdadero sobre distributive property.

Distributive property ___.

QuestionPregunta

Ask a question about distributive property.Haz una pregunta sobre distributive property.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about distributive property.Muestra entusiasmo sobre distributive property.

Wow, ___ !¡Guau, ___ !

CommandMandato

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

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

I distributed the ___ to ___.Distribuí el ___ a ___.

So ___ equals ___.Entonces ___ es igual a ___.

This helps when ___.Esto ayuda cuando ___.

Try It

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

1. Expand 3(x + 4) using the distributive property.

  1. 3x + 12
  2. 3x + 4
  3. x + 12
  4. 7x
Show your work:

2. When using the distributive property with a(b + c), you must multiply 'a' by:

  1. Both b and c
  2. Only b
  3. Only c
  4. b + c first, then multiply
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

Use the distributive property to explain why 6 × 98 can be calculated as 6 × 100 − 6 × 2 = 588. Then create your own example of using the distributive property to make multiplication easier.

Sentence starter: 6 × 98 = 6(100 − 2) = 6 × ___ − 6 × ___ = ___ − ___ = ___. My example: ___ × ___ = ___(___ ± ___) = ___.

Show your work:

Reflect — Exit Ticket

Which expression is equivalent to 7(x + 3)?

  1. 7x + 21
  2. 7x + 3
  3. x + 21
  4. 7x + 10
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. 3x + 12 — 3(x + 4) = 3 × x + 3 × 4 = 3x + 12.
  2. Try It 2: A. Both b and c — The distributive property says a(b + c) = ab + ac. You multiply the outside factor by EACH term inside the parentheses.
  3. Exit Ticket: A. 7x + 21 — 7(x + 3) = 7 × x + 7 × 3 = 7x + 21.

Writing (TWR) — what to look for