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

Lesson 7.27.2 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can place rational numbers, including fractions and decimals, on a number line — one step at a time, with support.

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 whole numbers 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 whole numbers 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 7.27.2 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 place rational numbers, including fractions and decimals, on a number line — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    −3−2.5−2−1.5−1−0.500.510
    Find the two integers around −1.5.

    Plot −1.5 on a number line.

    1. 1Is −1.5 to the left or right of 0?
    2. 2Which integer is just to the right of −1.5?
    3. 3Which integer is just to the left of −1.5?
    4. 4The .5 means one half. Where does the dot go?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −101start
    Start at 0. Count parts to the left.

    Plot −3/4 on a number line.

    1. 1Which two integers is −3/4 between?
    2. 2How many equal parts do we split 0 to −1 into?
    3. 3Start at 0. How many parts do you count to the left?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A point is halfway between 2 and 3. What number is it?

    Show your work

    Hint Halfway means one half of a unit past 2.

    Final answer:
  4. 4Complete each step, then write the final answer.
    −4−3−2A
    Each space is one fourth of a unit.

    Point A is on the number line. What number is at point A? Write a decimal.

    Show your work

    Hint Start at −3. Count the small spaces to point A. Each space is 0.25.

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

    At night, the temperature was −6.5°C. Which integer is just to the left of −6.5 on a number line?

    Show your work

    Hint Left means farther from 0 for a negative number.

    Final answer:
  6. 6Circle 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

    Hint Is −4.5 more than 4 units from 0, or less?

    Show your work

Explain your thinkingHow do you find the two integers a negative decimal is between? Use −1.5 or −6.5 to explain.

Sentence starter −6.5 is between ___ and ___. · I put the dot ___ because ___.

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