Neft Teacher · Notes Packet

Unit 2 · Standard 6.NS.1

Interpret Division of Fractions Flagship

Lesson 2-1-flagship

Name:Date:Class:

Evidence Lab Mission

The Fraction Vault

You are the lead forensic analyst at the Reyes Detective Agency. A 3-foot strip of evidence tape must be cut into exact 1/4-foot sections before it can be logged — and the vault that holds the case file only opens once you know how many pieces that makes. Interpret fraction division and crack the case.

Key Vocabulary Level 1 support

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

Illustration of Dividend: The number you are splitting up in a division problem.

In 3 ÷ 1/4 = 12, the dividend is 3 — it is the total being split

Dividend

The number you are splitting up in a division problem.

Illustration of Divisor: The number you split by in a division problem.

In 3 ÷ 1/4 = 12, the divisor is 1/4 — it is the size of each piece

Divisor

The number you split by in a division problem.

Illustration of Quotient: The answer when you divide.

In 3 ÷ 1/4 = 12, the quotient is 12 — there are 12 quarter-size pieces in 3

Quotient

The answer when you divide.

Illustration of Reciprocal: A fraction turned upside down.

The reciprocal of 1/4 is 4/1 = 4. Multiplying by the reciprocal gives the same result as dividing.

Reciprocal

A fraction turned upside down.

Illustration of Unit fraction: A fraction with 1 on top, like 1/4.

1/2, 1/3, 1/4, 1/5 — each represents one equal part of a whole

Unit fraction

A fraction with 1 on top, like 1/4.

Key Ideas & Notes

Think About It

  • What total length is being divided?
  • What is the size of each section?
  • Will the answer be greater than or less than 3?

My Notes

Guided Examples

Example 1

What does 3 ÷ 1/4 mean?

Solution: 3 ÷ 1/4 asks: how many 1/4-size pieces fit into 3? The answer is 12, because each whole has 4 fourths, and 3 × 4 = 12.

Answer: A. How many 1/4-size pieces fit into 3

Example 2

Which expression means 'how many 1/3-size pieces are in 2'?

Solution: Finding how many 1/3-size pieces fit into 2 is represented by 2 ÷ 1/3. The answer is 6.

Answer: A. 2 ÷ 1/3

Example 3

A rope is 4 feet long. How many 1/2-foot pieces can be cut from it?

Solution: 4 ÷ 1/2 = 4 × 2 = 8 pieces. Each whole foot contains 2 halves, and 4 × 2 = 8.

Answer: A. 8 pieces

Write About the Math The Writing Revolution

I can explain a fraction division using the words dividend, divisor, quotient, reciprocal, and unit fraction.

1. Kernel Sentence subject + verb

Model: Dividend is the number you are splitting up in a division problem.Dividendo es el número que estás repartiendo en una división.

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

2. Sentence Expansion because · but · so

Kernel: Dividend matters in mathDividendo importa en matemáticas

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

becauseporque

Dividend matters in math because ___.Dividendo importa en matemáticas porque ___.

butpero

Dividend matters in math, but ___.Dividendo importa en matemáticas, pero ___.

soentonces

Dividend matters in math, so ___.Dividendo importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

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

Dividend ___.

QuestionPregunta

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

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about dividend.Muestra entusiasmo sobre dividend.

Wow, ___ !¡Guau, ___ !

CommandMandato

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

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

I know ___ because ___.Sé que ___ porque ___.

First I ___, then I ___.Primero ___, luego ___.

This is important because ___.Esto es importante porque ___.

Try It

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

1. What is 6 ÷ 1/5?

  1. 30
  2. 6/5
  3. 5/6
  4. 1
Show your work:

2. A shelf is 5 feet long. Books are each 1/4 foot wide. How many books fit on the shelf? Which expression represents this?

  1. 5 ÷ 1/4 = 20 books
  2. 5 × 1/4 = 1 1/4 books
  3. 1/4 ÷ 5 = 1/20 book
  4. 5 + 1/4 = 5 1/4 books
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

Dividing 6 by 1/2 gives 12, but dividing 6 by 2 gives 3. How can dividing by a smaller number (1/2) give a bigger answer than dividing by a larger number (2)? Explain using a real-world example.

Sentence starter: When I divide 6 by 2, I am ___. When I divide 6 by 1/2, I am ___. The answer is bigger because ___.

Show your work:

Reflect — Exit Ticket

What does 5 ÷ 1/4 mean, and what is the quotient?

  1. How many 1/4-size pieces fit into 5; quotient is 20
  2. 5 groups of 1/4; quotient is 5/4
  3. 1/4 of 5; quotient is 5/4
  4. 5 minus 1/4; quotient is 4 3/4
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. 30 — 6 ÷ 1/5 means how many 1/5-size pieces fit into 6. Each whole has 5 fifths, so 6 × 5 = 30.
  2. Try It 2: A. 5 ÷ 1/4 = 20 books — You are finding how many 1/4-foot pieces fit into 5 feet, which is 5 ÷ 1/4 = 5 × 4 = 20 books.
  3. Exit Ticket: A. How many 1/4-size pieces fit into 5; quotient is 20 — 5 ÷ 1/4 means 'how many 1/4-size pieces fit into 5.' Since each whole has 4 fourths, 5 × 4 = 20.

Writing (TWR) — what to look for