Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.8

Lesson 7.37.3 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero — one step at a time, with support.

Why This Matters This is your support small group for Lesson 7.3. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

Start hereWords for this lesson

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

WordWhat it meansExample
IntegerSpanish: Número entero Whole numbers and their opposites, like -2, -1, 0, 1, 2. ... -3, -2, -1, 0, 1, 2, 3 ... shown on a number line with 0 in the center
PositiveSpanish: Positivo A number bigger than zero, to the right of zero on a number line. +5 means 5 above zero, like 5 floors above ground level
NegativeSpanish: Negativo A number smaller than zero, to the left of zero on a number line. -3 means 3 below zero, like 3 floors underground
Absolute valueSpanish: Valor absoluto How far a number is from zero. It is never negative. |−3| = 3 and |3| = 3
OppositeSpanish: Opuesto Two numbers the same distance from zero, on opposite sides, like 3 and -3. −3 and 3 are opposites
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, −50

How it worksWorked example

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

Find |−13| and |6|. Which number is farther from 0?

  1. −13 is 13 units left of 0, so |−13| = 13.
  2. 6 is 6 units right of 0, so |6| = 6.
  3. Compare the distances: 13 > 6.

Answer: −13 is farther from 0

Now you trySame steps, your turn

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

Find |3|, the absolute value of 3.

Answer:

Say it and write itSentence starters

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

  • The absolute value of is because it sits units from zero.
  • and share the same absolute value because .
  • An absolute value is never negative because .
  • The number closer to zero is because its distance is .

Word bank absolute valuedistancemagnitudezeronumber lineoppositeunitscloserfarthernegativepositivesign

Watch out!A common mistake

A common mistake in Integers and Absolute Value is judging size by the digits alone instead of position on the number line

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.8

Lesson 7.37.3 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero — one step at a time, with support.

Why This Matters This is your support small group for Lesson 7.3. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

  1. 1Complete each step, then write the final answer.
    −10−8−6−4−20246810? units−8
    Count from −8 to 0.

    Find |−8|, the absolute value of −8.

    1. 1Is −8 to the left or right of 0?
    2. 2Count the units from −8 to 0. How many?
    3. 3So what is |−8|?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −5−4−3−2−1012345? units−3.5
    This time the number is a decimal.

    Find |−3.5|, the absolute value of −3.5.

    1. 1Where is −3.5 on the number line?
    2. 2How many units is −3.5 from 0?
    3. 3Can a distance be negative?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find |−11|.

    Show your work

    Hint How many units is −11 from 0?

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

    Find |−3/4|.

    Show your work

    Hint −3/4 is between −1 and 0. How far is it from 0?

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

    A town is at an elevation of −20 feet. Sea level is 0. How far is the town from sea level?

    Show your work

    Hint Distance from sea level is the absolute value of the elevation.

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

    Ben says |−5| = −5. Is he right? What is |−5|?

    Show your work

    Hint Absolute value is a distance. Can a distance be negative?

    Final answer:

Explain your thinkingBen wrote |−5| = −5. Explain his mistake. Why is an absolute value never negative?

Sentence starter An absolute value is never negative because ___. · |−5| = ___ because −5 is ___ units from 0.

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