Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.27.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can place rational numbers, including fractions and decimals, on a number line, explain why the method works, and use it on a problem I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Rational numberSpanish: Número racional A number that can be written as a fraction of two integers, with a bottom number that is not zero. −3/4, 0.5, 7, −2.85
FractionSpanish: Fracción A number that shows part of a whole, like 3/4. 3/4 of a cup
DecimalSpanish: Decimal A number with a dot, like 0.5, that shows a part less than one. 0.5 is half of one
Number lineSpanish: Recta numérica A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right. left is less, right is more
EquivalentSpanish: Equivalente Having the same value, just written a different way. 1/2 = 0.5
IntegerSpanish: Número entero Whole numbers and their opposites, like -2, -1, 0, 1, 2. ..., -3, -2, -1, 0, 1, 2, 3, ...

How it worksWorked exampleplotting a rational number and its opposite

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A tree trunk rises 1.8 meters above the ground. Its taproot reaches the opposite value. Plot both on a vertical number line.

  1. The ground is 0. Above the ground is positive; below the ground is negative.
  2. The height is 1.8, so the root value is its opposite: −1.8
  3. Between each pair of integers, mark ten equal parts so you can count tenths.
  4. Plot 1.8 eight tenths above 1, and plot −1.8 eight tenths below −1.

Answer: The trunk is 1.8 m and the root is −1.8 m; both sit 1.8 units from 0.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A dock post rises 2.4 meters above the water. Its anchor sits at the opposite value. Plot both on a vertical number line.

  1. The water surface is . Above it is and below it is .
  2. The post height is , so the anchor value is its opposite:
  3. Mark equal parts between each pair of integers so you can count tenths.
  4. Plot both points. Each one sits units from 0.
Answer:post height and anchor value

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The number is rational because it can be written as .
  • On the number line, falls between and .
  • I split each unit into equal parts because .
  • The opposite of is , so it sits to the of zero.

Word bank rational numberfractiondecimaloppositenumber lineintegerbetweenequal partsdenominatorabovebelowzero

Watch outA common mistake

A common mistake in Rational Numbers on the Number Line is treating the numerator and denominator of a negative fraction as two separate whole numbers instead of one value between two integers — for example, plotting -3/4 by going to -3 and then counting 4 more units to the left, landing (incorrectly) at -7, instead of recognizing that -3/4 = -0.75, which sits between 0 and -1. Before you submit an answer, find the two whole numbers your value falls between, then split that space into equal parts.

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.27.2 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can place rational numbers, including fractions and decimals, on a number line, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    −3−2−1start
    Count away from 0, to the left.

    Plot −2 1/4 on a number line.

    1. 1Which two integers is −2 1/4 between?
    2. 2How many equal parts do we split −2 to −3 into?
    3. 3Start at −2. How many parts do you count to the left?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −2−1start
    −2 to −1 has 5 equal parts.

    Point M is between −1 and −2. It is 2 of 5 equal parts from −1. What number is M? Write a decimal.

    1. 1How long is each part?
    2. 2Count 2 parts to the left of −1. What is M?
    3. 3Why do you count to the left from −1, not to the right?
    Final answer:
  3. 3Complete each step, then write the final answer.

    What number is 3 of 10 equal parts from 0 toward −1? Write a decimal.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Point K is between −4 and −3. It is 0.4 units from −4. What number is K?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    On a trail map, the ranger station is at 0. A lake is at −1 2/3 miles. Each mile is split into 3 equal parts. How many parts from 0 is the lake?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Lia plots −1 1/3. She splits −1 to −2 into 3 parts. Then she counts 1 part to the right of −1. What number did she really plot?

    Show your work
    Final answer:

Explain your thinkingFor a negative mixed number like −21/4, why do you count the fraction part away from 0? Use Lia's mistake.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help