Neft Teacher · Notes Packet

Unit 9 · Standard 6.NS.6

Rational Numbers on the Number Line

Lesson 9-4

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 Rational number: Any number you can write as a fraction. This includes fractions, decimals, and integers.

1/2 = 0.5, -3/4 = -0.75, 6 = 6/1 — all rational numbers

Rational number

Any number you can write as a fraction. This includes fractions, decimals, and integers.

Illustration of Fraction: A number that shows part of a whole, like 3/4.

3/4 means 3 out of 4 equal parts — like 3 slices of a pizza cut into 4

Fraction

A number that shows part of a whole, like 3/4.

Illustration of Decimal: A number with a dot, like 0.5, that shows a part less than one.

0.5 = 1/2 (halfway between 0 and 1 on the number line)

Decimal

A number with a dot, like 0.5, that shows a part less than one.

Illustration of Number line: A straight line with numbers spaced out evenly.

A line with marks at -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2

Number line

A straight line with numbers spaced out evenly.

Illustration of Equivalent: Having the same value, just written a different way.

1/2 = 0.5 = 2/4 — all name the same point on the number line

Equivalent

Having the same value, just written a different way.

Illustration of Integer: Whole numbers and their opposites, like -2, -1, 0, 1, 2.

..., -3, -2, -1, 0, 1, 2, 3, ...

Integer

Whole numbers and their opposites, like -2, -1, 0, 1, 2.

Key Ideas & Notes

Think About It

  • Where would -2.5 fall on a number line between -3 and -2?
  • How is plotting 3/4 different from plotting a whole number?
  • Can a negative number be a fraction or decimal?

My Notes

Guided Examples

Example 1

Which point is located between -1 and -2 on the number line?

Solution: -1.5 is between -1 and -2 because it is 0.5 units to the left of -1 (or 0.5 units to the right of -2).

Answer: B. -1.5

Example 2

Which fraction is equivalent to 0.25?

Solution: 0.25 means 25 hundredths = 25/100 = 1/4.

Answer: A. 1/4

Example 3

Where is -3/4 located on the number line?

Solution: -3/4 = -0.75, which is between 0 and -1. It is 3/4 of the way from 0 toward -1.

Answer: A. Between 0 and -1

Write About the Math The Writing Revolution

I can explain my reasoning using the words rational number, fraction, decimal, and number line.

1. Kernel Sentence subject + verb

Model: Rational number is any number you can write as a fraction. This includes fractions, decimals, and integers.Número racional es cualquier número que puedes escribir como fracción. Incluye fracciones, decimales y enteros.

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

2. Sentence Expansion because · but · so

Kernel: Rational number matters in mathNúmero racional importa en matemáticas

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

becauseporque

Rational number matters in math because ___.Número racional importa en matemáticas porque ___.

butpero

Rational number matters in math, but ___.Número racional importa en matemáticas, pero ___.

soentonces

Rational number matters in math, so ___.Número racional importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

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

Rational number ___.

QuestionPregunta

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

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

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

Wow, ___ !¡Guau, ___ !

CommandMandato

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

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

I placed ___ between ___ and ___.Coloqué ___ entre ___ y ___.

I knew because ___.Lo supe porque ___.

I see this when ___.Veo esto cuando ___.

Try It

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

1. Where is -3/4 located on the number line?

  1. Between 0 and -1
  2. Between -3 and -4
  3. Between -1 and -2
  4. Between 0 and 1
Show your work:

2. Which rational number is closest to 0 on the number line?

  1. -1/4
  2. 0.5
  3. -2
  4. 1.75
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

Name three different rational numbers between -1 and 0. Write each as both a fraction and a decimal. Explain how you know they are between -1 and 0.

Sentence starter: Three rational numbers between -1 and 0 are: ___ = ___, ___ = ___, and ___ = ___. I know they are between -1 and 0 because ___.

Show your work:

Reflect — Exit Ticket

Which rational number is located between -2 and -3 on the number line?

  1. -1.5
  2. -2.75
  3. -3.5
  4. 2.5
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. Between 0 and -1 — -3/4 = -0.75, which is between 0 and -1. It is 3/4 of the way from 0 toward -1.
  2. Try It 2: A. -1/4 — |-1/4| = 0.25, |0.5| = 0.5, |-2| = 2, |1.75| = 1.75. Since 0.25 is the smallest absolute value, -1/4 is closest to zero.
  3. Exit Ticket: B. -2.75 — -2.75 is between -2 and -3 because it is 0.75 units to the left of -2. -1.5 is between -1 and -2, and -3.5 is between -3 and -4.

Writing (TWR) — what to look for