Neft Teacher · Notes Packet

Unit 2 · Standard 6.NS.1

Divide Mixed Numbers

Lesson 2-4

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 Mixed Number: A whole number plus a fraction, like 2 1/2.

2 1/3 means 2 wholes and 1/3 more — picture 2 full circles and 1/3 of another

Mixed Number

A whole number plus a fraction, like 2 1/2.

Illustration of Improper Fraction: A fraction where the top is bigger than or equal to the bottom, like 7/4.

7/3 is improper because 7 > 3. It equals 2 1/3 as a mixed number.

Improper Fraction

A fraction where the top is bigger than or equal to the bottom, like 7/4.

Illustration of Convert: To change a number to a new form but keep the same value.

2 1/3 → multiply 2 × 3 = 6, add 1 → 7/3. Same value, different form.

Convert

To change a number to a new form but keep the same value.

Illustration of Simplify: To make a fraction smaller using the same parts, like 2/4 = 1/2.

8/6: GCF is 2 → 8÷2 / 6÷2 = 4/3 = 1 1/3

Simplify

To make a fraction smaller using the same parts, like 2/4 = 1/2.

Illustration of Reciprocal: A fraction turned upside down. You use it in keep-change-flip.

The reciprocal of 3/4 is 4/3. To divide by 3/4, multiply by 4/3.

Reciprocal

A fraction turned upside down. You use it in keep-change-flip.

Key Ideas & Notes

Think About It

  • What is the total distance of the route?
  • How long is each segment?
  • Will the number of segments be more or less than 3?

My Notes

Guided Examples

Example 1

What is 1 1/2 ÷ 3/4?

Solution: 1 1/2 = 3/2. Then 3/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2.

Answer: A. 2

Example 2

Convert 3 2/5 to an improper fraction.

Solution: 3 × 5 = 15, then 15 + 2 = 17. So 3 2/5 = 17/5.

Answer: A. 17/5

Example 3

What is 2 1/4 ÷ 3/4?

Solution: 2 1/4 = 9/4. Then 9/4 ÷ 3/4 = 9/4 × 4/3 = 36/12 = 3.

Answer: A. 3

Write About the Math The Writing Revolution

I can explain my steps using the words mixed number, improper fraction, convert, reciprocal, and simplify.

1. Kernel Sentence subject + verb

Model: Mixed Number is a whole number plus a fraction, like 2 1/2.Número mixto es un número entero más una fracción, como 2 1/2.

Write a kernel sentence about mixed number. Use a subject and a verb.Escribe una oración base sobre número mixto. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Mixed Number matters in mathNúmero mixto importa en matemáticas

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

becauseporque

Mixed Number matters in math because ___.Número mixto importa en matemáticas porque ___.

butpero

Mixed Number matters in math, but ___.Número mixto importa en matemáticas, pero ___.

soentonces

Mixed Number matters in math, so ___.Número mixto importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about mixed number.Di un hecho verdadero sobre mixed number.

Mixed number ___.

QuestionPregunta

Ask a question about mixed number.Haz una pregunta sobre mixed number.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about mixed number.Muestra entusiasmo sobre mixed number.

Wow, ___ !¡Guau, ___ !

CommandMandato

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

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

First I changed ___ into ___.Primero cambié ___ a ___.

Then I ___.Luego ___.

I would use this when ___.Usaría esto cuando ___.

Try It

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

1. What is 3 1/2 ÷ 1/4?

  1. 14
  2. 3 1/8
  3. 7/8
  4. 13/4
Show your work:

2. A recipe makes 2 1/4 batches of cookies. Each batch uses 3/4 cup of butter. How many cups of butter are needed in total?

  1. 3 cups
  2. 1 1/2 cups
  3. 2 cups
  4. 6 cups
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

A detective has a rope that is 5 1/4 feet long. She needs to cut it into pieces that are each 3/4 foot for tying evidence tags. How many pieces can she cut? Write the equation, show each step (convert, keep-change-flip, multiply, simplify), and verify your answer.

Sentence starter: First I convert 5 1/4 to ___. Then I use KCF: ___ × ___ = ___. The answer is ___ pieces. I can verify because ___ × 3/4 = 5 1/4.

Show your work:

Reflect — Exit Ticket

What is 2 2/3 ÷ 2/3?

  1. 4
  2. 2/3
  3. 8/3
  4. 1 7/9
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. 14 — 3 1/2 = 7/2. Then 7/2 ÷ 1/4 = 7/2 × 4/1 = 28/2 = 14.
  2. Try It 2: A. 3 cups — This is multiplication: 2 1/4 × 3/4 = 9/4 × 3/4 = 27/16. Wait — re-read: we need 2 1/4 batches at 3/4 cup each, but the question for division practice should be: if you have 2 1/4 cups and each batch needs 3/4 cup, how many batches? 2 1/4 ÷ 3/4 = 9/4 × 4/3 = 36/12 = 3.
  3. Exit Ticket: A. 4 — 2 2/3 = 8/3. Then 8/3 ÷ 2/3 = 8/3 × 3/2 = 24/6 = 4.

Writing (TWR) — what to look for