Neft Teacher · Notes Packet

Unit 1 · Standard 6.NS.4

Prime Factorization

Lesson 1-1

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 Prime number: A number bigger than 1 that you can only divide by 1 and itself.

7 has only two factors: 1 × 7. So 7 is prime.

Prime number

A number bigger than 1 that you can only divide by 1 and itself.

Illustration of Composite number: A number bigger than 1 that you can divide by more than just 1 and itself.

12 = 1 × 12, 2 × 6, 3 × 4 — six factors, so 12 is composite

Composite number

A number bigger than 1 that you can divide by more than just 1 and itself.

Illustration of Prime factorization: Writing a number as prime numbers multiplied together.

36 = 2 × 2 × 3 × 3 = 2² × 3²

Prime factorization

Writing a number as prime numbers multiplied together.

Illustration of Factor tree: A picture that splits a number into its prime numbers, step by step.

24 → 4 × 6 → (2 × 2) × (2 × 3) → 2 × 2 × 2 × 3

Factor tree

A picture that splits a number into its prime numbers, step by step.

Illustration of Exponent: A small number that tells how many times to multiply a number by itself.

2³ means 2 × 2 × 2 = 8

Exponent

A small number that tells how many times to multiply a number by itself.

Key Ideas & Notes

Think About It

  • What number are we breaking down into factors?
  • What's the difference between a factor and a prime factor?
  • How many different ways can we start breaking 60 apart?

My Notes

Guided Examples

Example 1

Which of the following is a prime number?

Solution: 17 has exactly two factors: 1 and 17. 15 = 3 × 5, 21 = 3 × 7, and 9 = 3 × 3, so they are all composite.

Answer: A. 17

Example 2

What is the prime factorization of 30?

Solution: 30 = 2 × 15 = 2 × 3 × 5. All three factors (2, 3, 5) are prime, so 2 × 3 × 5 is the prime factorization.

Answer: A. 2 × 3 × 5

Example 3

What is the prime factorization of 18?

Solution: 18 = 2 × 9 = 2 × 3 × 3. Both 2 and 3 are prime, so 2 × 3 × 3 is the prime factorization.

Answer: A. 2 × 3 × 3

Write About the Math The Writing Revolution

I can explain how I broke a number down using the words prime number, composite number, factor, and exponent.

1. Kernel Sentence subject + verb

Model: Prime factorization is writing a number as prime numbers multiplied together.Factorización prima es escribir un número como números primos multiplicados.

Write a kernel sentence about prime factorization. Use a subject and a verb.Escribe una oración base sobre factorización prima. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Prime factorization matters in mathFactorización prima importa en matemáticas

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

becauseporque

Prime factorization matters in math because ___.Factorización prima importa en matemáticas porque ___.

butpero

Prime factorization matters in math, but ___.Factorización prima importa en matemáticas, pero ___.

soentonces

Prime factorization matters in math, so ___.Factorización prima importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about prime factorization.Di un hecho verdadero sobre prime factorization.

Prime factorization ___.

QuestionPregunta

Ask a question about prime factorization.Haz una pregunta sobre prime factorization.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about prime factorization.Muestra entusiasmo sobre prime factorization.

Wow, ___ !¡Guau, ___ !

CommandMandato

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

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

I broke ___ into ___ because ___.Separé ___ en ___ porque ___.

A prime number is ___.Un número primo es ___.

This helps in real life when ___.Esto ayuda en la vida real cuando ___.

Try It

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

1. Which of these numbers is composite?

  1. 27
  2. 23
  3. 29
  4. 31
Show your work:

2. Two students found different factor trees for 60. Student A started with 2 × 30. Student B started with 6 × 10. Which statement is true?

  1. Both get the same prime factorization: 2 × 2 × 3 × 5
  2. Only Student A gets the correct prime factorization
  3. Only Student B gets the correct prime factorization
  4. They will get different prime factorizations
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

Choose any two-digit composite number. Show TWO different factor trees that both lead to the same prime factorization. Explain why every composite number has only one prime factorization.

Sentence starter: I chose the number ___. My first factor tree starts with ___ × ___, and my second starts with ___ × ___. Both give the same prime factorization: ___. This happens because ___.

Show your work:

Reflect — Exit Ticket

What is the prime factorization of 40?

  1. 2 × 2 × 2 × 5
  2. 4 × 10
  3. 5 × 8
  4. 2 × 20
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. 27 — 27 = 3 × 9 = 3 × 3 × 3, so it has more than two factors. 23, 29, and 31 are all prime.
  2. Try It 2: A. Both get the same prime factorization: 2 × 2 × 3 × 5 — The Fundamental Theorem of Arithmetic says every composite number has exactly one prime factorization. No matter how you start the factor tree, you always end with 2 × 2 × 3 × 5.
  3. Exit Ticket: A. 2 × 2 × 2 × 5 — 40 = 2 × 20 = 2 × 2 × 10 = 2 × 2 × 2 × 5. All factors (2, 2, 2, 5) are prime.

Writing (TWR) — what to look for