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.

Why This Matters Arihi planted a flower. The height and depth of the plant are shown. How do the height of the plant and the depth of the roots compare?

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 example

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

Plot 1.5 and −3.5 on a number line.

  1. Mark the integers from −4 to 4.
  2. Split each gap into halves.
  3. 1.5 is halfway between 1 and 2. −3.5 is halfway between −4 and −3.

Answer: 1.5 is right of 0; −3.5 is left of 0

Now you trySame steps, your turn

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

Now let's plot 0.75. Which two integers is it between? It is between 0 and 1.

Answer:

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 out!A 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

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.

Why This Matters Arihi planted a flower. The height and depth of the plant are shown. How do the height of the plant and the depth of the roots compare?

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 ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
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.

Why This Matters Arihi planted a flower. The height and depth of the plant are shown. How do the height of the plant and the depth of the roots compare?

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?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
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.

Why This Matters Arihi planted a flower. The height and depth of the plant are shown. How do the height of the plant and the depth of the roots compare?

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?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help