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

Lesson 7.2Represent Rational Numbers and Their Opposites on the Number Line

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.

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 integers 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 integers 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 7.2Represent Rational Numbers and Their Opposites on the Number Line

Version ASupported 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.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each fraction to its decimal equivalent.

    1. 1/2
    2. -3/4
    3. 1 1/4
    4. -2 1/2
    5. 3/10
    6. -1/5
    • A0.5
    • B-0.75
    • C1.25
    • D-2.5
    • E0.3
    • F-0.2

    Hint Each fraction equals a decimal. Halves, quarters, fifths, and tenths all have decimal partners you know.

  2. 2Mark and label each value on the number line.

    Plot these rational numbers: -1, 0.5, -0.5, 1, -1.5

    -3-2.5-2-1.5-1-0.500.511.522.53

    Hint The tick marks count by 0.5 — each hop is a HALF, not a whole unit.

    Show your thinking
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

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

    1. A-2.5
    2. B-1.5
    3. C-0.5
    4. D1.5

    Hint 'Between -1 and -2' is on the NEGATIVE side, in the gap from -1 to -2.

    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Which fraction is equivalent to 0.25?

    1. A1/4
    2. B1/2
    3. C1/3
    4. D2/5

    Hint Read 0.25 as a place-value number: 25 hundredths.

    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

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

    1. ABetween -3 and -4
    2. BBetween -1 and -2
    3. CBetween 0 and -1
    4. DBetween 0 and 1

    Hint The size of -3/4 is less than 1 whole — its distance from zero is under 1.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Mistake: Plotting 1.5

    1. 1ProblemPlot 1.5 on the number line.
    2. 2Student thinking1.5 has a 1 and a 5, so I will plot it between 1 and 5.
    3. 3Student answerPoint plotted at about 3, halfway between 1 and 5.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint What does the .5 in 1.5 mean — is it a separate whole number or a part of one?

    Correct work
    Correct answer:

Explain your thinkingHow did you decide exactly where to place rational numbers that fall between integers?

Sentence starter To plot ___, I found the integers it falls between, which are ___ and ___. Then I estimated ___ of the way between them because ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.2Represent Rational Numbers and Their Opposites on the Number Line

Version BCore 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.

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    Plot these rational numbers: -3.5, -1/4, 2.75, -2, 1 1/2

    -5-4-3-2-1012345
    Show your thinking
  2. 2Complete the table. Show how you found each value.

    Convert between fraction and decimal form. Then plot on a mental number line to compare.

    FractionDecimalBetween Which Two Integers?
    3/4
    -7/2
    0.6
    -1.25
    2 1/5
    Show your work
  3. 3Write the name of the correct group on each line.

    Order these rational numbers from LEAST to GREATEST.

    Groups:
    • 1/2
    • -2.5
    • 0.75
    • -1/4
    • 3
    • -1.5
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

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

    1. A-2
    2. B-1/4
    3. C0.5
    4. D1.75
    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    Which number is farthest to the LEFT on a number line?

    1. A-4
    2. B-1
    3. C0
    4. D2
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Mistake: Plotting -2.25

    1. 1ProblemPlot -2.25 on the number line.
    2. 2Student thinkingIt is negative, so I go past -2. The .25 is one quarter, so I count toward 0 (to the right) by a quarter unit and land between -2 and -1.
    3. 3Student answerPoint plotted at -1.75, between -2 and -1.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingHow did you decide exactly where to place rational numbers that fall between integers?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.2Represent Rational Numbers and Their Opposites on the Number Line

ChallengeExtension

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.

Part 1Understand the ideamodels and meaning
  1. 1Decide whether each pair balances. Check Yes or No, then explain.

    Which side is greater? Compare -2/3 and -3/4.

    Left sideRight sideBalanced?
    Explain your choice
  2. 2Circle the letter of the best answer. Show how you know.

    On a number line, point P is located at -2.5. Which statement describes its location best?

    1. AAt -3
    2. BAt -2
    3. CHalfway between -2 and -3
    4. DHalfway between 2 and 3
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Which list of numbers is ordered from LEAST to GREATEST?

    1. A-5, -2, 0, 3
    2. B-2, -5, 0, 3
    3. C0, -2, 3, -5
    4. D3, 0, -2, -5
    Show your work
Part 3Explain and correctreasoning
  1. 4Find the mistake. Explain it, then show the correct work.

    Find the Plotting Error

    1. 1ProblemPlot -3/4 on the number line
    2. 2Student thinking-3/4 has a 3 and a 4, so I go to -3 on the number line and then count 4 more to the left
    3. 3Student answerPoint plotted at -7

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 5Answer in complete 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.

    Write your answer

Explain your thinkingHow did you decide exactly where to place rational numbers that fall between integers?

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