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

Lesson 7.4Compare and Order Integers and Rational Numbers

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can compare and order integers using a number line.

Why This Matters Lucy and Yuzuki are playing a trivia game with these rules: if a player answers a question correctly, they receive 1 point; if they answer incorrectly, they lose 0.25 point. The player with the greatest score wins the game. The final scores for two games are shown in the table. Who is the winner of each game?

Start hereWords for this lesson

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

WordWhat it meansExample
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
CompareSpanish: Comparar To see if a number is bigger, smaller, or equal to another. −7 compared with −3
OrderSpanish: Ordenar To arrange numbers by size, from least to greatest or greatest to least. Least to greatest: -5, -2, 0, 3, 7 (left to right on the number line)
Greater thanSpanish: Mayor que The > sign, showing one number is bigger. −3 > −7
Less thanSpanish: Menor que The < sign, showing one number is smaller. −7 < −3
Negative integerSpanish: Entero negativo A whole number smaller than zero, like -5. −7, −3, −100

How it worksWorked example

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

Compare −14 degrees and −5 degrees.

  1. Plot −14 and −5 on a number line.
  2. −5 is to the right of −14.
  3. Write the comparison: −14 < −5.

Answer: −5 is greater; −14 is colder

Now you trySame steps, your turn

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

Now let's compare -2 and 3. Which one is to the left on the number line? The -2 is left of zero.

Answer:

Say it and write itSentence starters

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

  • On the number line, sits to the of , so is greater.
  • I can write the comparison as .
  • The least number in this set is because .
  • Comparing two negative numbers is different from counting because .

Word bank compareordergreater thanless thannumber lineleftrightnegativepositiveleastgreatestinequality

Watch out!A common mistake

A common mistake in Compare and Order Integers is thinking that a negative number with a bigger digit is the bigger value

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

Lesson 7.4Compare and Order Integers and Rational Numbers

Level 0Most support · every hint printed

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

Learning target I can compare and order integers using a number line.

Why This Matters Lucy and Yuzuki are playing a trivia game with these rules: if a player answers a question correctly, they receive 1 point; if they answer incorrectly, they lose 0.25 point. The player with the greatest score wins the game. The final scores for two games are shown in the table. Who is the winner of each game?

How it worksWorked example

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

Compare −14 degrees and −5 degrees.

  1. Plot −14 and −5 on a number line.
  2. −5 is to the right of −14.
  3. Write the comparison: −14 < −5.

Answer: −5 is greater; −14 is colder

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Which statement is TRUE?

    1. A-5 < -2
    2. B-4 > 0
    3. C-3 > -1
    4. D-1 < -6
    Steps to try
    1. Sketch a quick number line. For negatives, 'greater' means closer to zero, not a bigger digit.
    2. For each statement, place both numbers on the number line: the one farther LEFT is less. Test all four.
    3. First statement: put -3 and -1 on the line. -3 is farther left, so is '-3 > -1' true or false? Keep testing.
    Show your work
  2. 2Write the name of the correct group on each line.

    Drag to order these integers from LEAST to GREATEST.

    Groups:
    • 3
    • -1
    • -6
    • 0
    • -4
    • 5
    Steps to try
    1. Least to greatest reads left to right on a number line — all the negatives come before 0.
    2. Group first: negatives (-1, -6, -4), then 0, then positives (3, 5). Order the negatives by distance below zero.
    3. Among -1, -4, and -6, the one farthest below zero goes first. Place it, then order the other two negatives.
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

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

    1. A-8
    2. B-3
    3. C0
    4. D5
    Steps to try
    1. 'Least' means farthest LEFT on the number line — for negatives, that's the one farthest below zero.
    2. Place all five numbers on a mental number line. Negatives sit left of 0, and the least is the leftmost one.
    3. Compare just the negatives first, -3 and -8: which is farther below zero? Then check it against 0, 2, and 5.
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    What is |−8|?

    1. A0
    2. B8
    3. C−8
    4. D−16
    Steps to try
    1. The bars |...| mean absolute value: the distance from 0, which is never negative.
    2. Find -8 on the number line and count the units between it and 0.
    3. Start at -8 and hop toward 0, counting each hop. The total number of hops is the value.
    Show your work

Explain your thinkingHow does plotting on the number line help you compare and order integers?

Sentence starter On the number line, ___ is to the left of ___, so ___ < ___. The order from least to greatest is ___.

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