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

Lesson 7.27.2 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 7.2. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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.

Plot 0.75 on a number line.

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 whole numbers instead of one value between two integers

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

Lesson 7.27.2 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 7.2. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    −3−2−1start
    Count away from 0, to the left.

    Plot −2 1/4 on a number line.

    1. 1Which two integers is −2 1/4 between?
    2. 2How many equal parts do we split −2 to −3 into?
    3. 3Start at −2. How many parts do you count to the left?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −2−1start
    −2 to −1 has 5 equal parts.

    Point M is between −1 and −2. It is 2 of 5 equal parts from −1. What number is M? Write a decimal.

    1. 1How long is each part?
    2. 2Count 2 parts to the left of −1. What is M?
    3. 3Why do you count to the left from −1, not to the right?
    Final answer:
  3. 3Complete 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:
  4. 4Complete each step, then write the final answer.

    Point K is between −4 and −3. It is 0.4 units from −4. What number is K?

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

    On a trail map, the ranger station is at 0. A lake is at −1 2/3 miles. Each mile is split into 3 equal parts. How many parts from 0 is the lake?

    Show your work
    Final answer:
  6. 6Complete 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:

Explain your thinkingFor a negative mixed number like −21/4, why do you count the fraction part away from 0? Use Lia's mistake.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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