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

Set B · Version ASecond form · supported 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?

RememberRepresent Rational Numbers and Their Opposites on the Number Line

Rational Numbers on the Number Line A rational number can be written as a ratio of two integers with a nonzero denominator. Integers and terminating or repeating decimals are rational. A rational number that is not an integer lies between two neighboring integers.

  1. Find the two consecutive integers the rational number falls between.
  2. Divide the segment between integers into equal parts matching the denominator.
  3. Negative numbers move to the left of zero; positive numbers move to the right

Words: Rational number (Número racional)Fraction (Fracción)Decimal (Decimal)Number line (Recta numérica)Equivalent (Equivalente)

  1. 1Circle the letter of the best answer. Show how you know.

    What is the opposite of -3/4?

    1. A-3/4
    2. B0
    3. C3/4
    4. D4/3

    Hint 'Opposite' means the mirror image across zero — same distance, other side.

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  2. 2Circle the letter of the best answer. Show how you know.

    What is the opposite of −6?

    1. A0
    2. B6
    3. C−6
    4. D−12
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    On a number line, which number is farther to the LEFT: −8 or −3?

    1. A−3
    2. BThey are the same
    3. C−8
    4. DNeither is on the line
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Which integer is the LEAST: −3, 5, −8, 2, 0?

    1. A0
    2. B−3
    3. C5
    4. D−8
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A point sits 5 units to the LEFT of 0 on a number line. What number is it?

    1. A0
    2. B−5
    3. C5
    4. D−10
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    The boat ramp at Miller Lake has a full mark painted on it. When the water sits exactly on that mark, the ramp keeper writes 0 — the mark IS zero. Above the mark is positive, below it is negative. Last week she wrote: Monday +0.75 ft, Tuesday −1.25 ft, Wednesday −0.5 ft, Thursday +1.5 ft. Where does −1.25 fall on the number line?

    1. ABetween −1 and −2
    2. BBetween −1 and 0
    3. CBetween 1 and 2
    4. DExactly at −1
    Show your work

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

Set B · Version BSecond form · core 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 decimal trail marker to its equal fraction.

    1. 0.5
    2. 0.25
    3. -0.5
    4. 0.2
    • A1/2
    • B1/4
    • C-1/2
    • D1/5
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    The boat ramp at Miller Lake has a full mark painted on it. When the water sits exactly on that mark, the ramp keeper writes 0 — the mark IS zero. Above the mark is positive, below it is negative. Last week she wrote: Monday +0.75 ft, Tuesday −1.25 ft, Wednesday −0.5 ft, Thursday +1.5 ft. Which day had the water level closest to the painted mark?

    1. AWednesday at −0.5 ft
    2. BMonday at +0.75 ft
    3. CTuesday at −1.25 ft
    4. DThursday at +1.5 ft
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    The boat ramp at Miller Lake has a full mark painted on it. When the water sits exactly on that mark, the ramp keeper writes 0 — the mark IS zero. Above the mark is positive, below it is negative. Last week she wrote: Monday +0.75 ft, Tuesday −1.25 ft, Wednesday −0.5 ft, Thursday +1.5 ft. Why are rational numbers more useful here than integers alone?

    1. AThey let the scientist record part-of-a-foot changes like 0.75 and −1.25
    2. BThey are easier to add
    3. CIntegers cannot be negative
    4. DThey make the lake bigger
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    The first trail marker sits between 0 and 1. Which rational number belongs there?

    1. A-1/2
    2. B1.5
    3. C2
    4. D3/4
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Order these three trail markers from least to greatest: -1.5, 0.5, -0.5.

    1. A-1.5, -0.5, 0.5
    2. B-1.5, 0.5, -0.5
    3. C-0.5, -1.5, 0.5
    4. D0.5, -0.5, -1.5
    Show your work
  5. 6Circle the letter of the best answer. Show how you know.

    On the trail map, -3/4 sits to the LEFT of which marker?

    1. A-7/8
    2. B-2
    3. C-1/4
    4. D-1
    Rewrite each fraction
    Work it out
    Simplify

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