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

Lesson 7.2Opposites of Rational Numbers

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 means 3 out of 4 equal parts — like 3 slices of a pizza cut into 4
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 = 2/4 — all name the same point on the number line
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.

Find −(−5.3). Then find the opposite of your answer.

  1. −5.3 is 5.3 units left of 0.
  2. Flip to the other side of 0, keeping the distance 5.3: −(−5.3) = 5.3.
  3. Flip again: the opposite of 5.3 is −5.3.

Answer: 5.3, then −5.3 (two flips return to the start)

Say it and write itSentence starters

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

  • The opposite of is because .
  • After one flip I land on ; after two flips I land on .
  • Both numbers sit units from zero, but on sides.
  • is a rational number because it can be written as .

Word bank oppositefliprational numberdecimalfractionnumber linedistancezeronegativepositivesideequal parts

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 7.2Opposites of Rational Numbers

Apply Day · 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.

  1. 1Complete each step, then write the final answer.

    A point is halfway between −9 and −8. What number is it?

    Show your work

    Hint Halfway between 8 and 9 is 8.5. This point is left of 0.

    Final answer:
  2. 2Complete each step, then write the final answer.

    The space from 0 to −1 has 4 equal parts. What number is 1 part to the left of 0?

    Show your work

    Hint Each part is 1/4. Left of 0 is negative.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Which integer is just to the left of −0.5 on a number line?

    Show your work

    Hint −0.5 is between two integers. Pick the one farther from 0.

    Final answer:
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 7.2Opposites of Rational Numbers

Apply Day · 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.

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

    Ray says −4.5 goes halfway between −4 and −3. Is he right? Where does −4.5 go?

    1. AHalfway between −5 and −4
    2. BHalfway between −4 and −3
    3. CHalfway between 4 and 5
    4. DAt −45
    Show your work
  2. 2Complete 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:
  3. 3Complete each step, then write the final answer.

    A point is halfway between −6 and −5. What number is it?

    Show your work
    Final answer:
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 7.2Opposites of Rational Numbers

Apply Day · 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.

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

    Between which two consecutive integers does −3.5 fall on a number line?

    1. A−3 and −2
    2. B3 and 4
    3. C−4 and −3
    4. D−5 and −4
    Show your work
  2. 2Complete 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:
  3. 3Complete each step, then write the final answer.

    Point R is between −6 and −5. It is 0.3 units from −5. What number is R?

    Show your work
    Final answer:
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