Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.5

Lesson 7.17.1 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use integers to represent quantities in everyday life, explain what 0 means in each situation, and name the opposite of an integer on the number line, explain what each part stands for, and build one for a situation I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
IntegerSpanish: Número entero The counting numbers, their opposites, and 0. −9, −1, 0, 6, 230
OppositeSpanish: Opuesto A number that is the same distance from 0 as another number, but on the other side of 0. −6 and 6 are opposites
Negative numberSpanish: Número negativo A number less than 0, written with a − sign. On a number line it sits to the left of 0. −9 is read negative nine
Positive numberSpanish: Número positivo A number greater than 0. On a number line it sits to the right of 0. 6, 19, 230
Number lineSpanish: Recta numérica A straight line where numbers are placed in order. It extends to the left of 0 to show values less than 0. left is less, right is more
Opposite of the oppositeSpanish: Opuesto del opuesto Taking the opposite twice brings you back to the first number. −(−6) = 6

How it worksWorked examplewriting an integer and naming its opposite

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

A submarine sits 47 meters below the surface of the water. Write an integer for its depth, then name the opposite.

  1. Decide the direction. Below the surface is less than 0, so the integer is negative.
  2. Write the integer with a negative sign. depth = −47
  3. The opposite sits the same distance from 0 on the other side. 47
  4. Check on a number line: one point is left of 0, one is right, both 47 units away.

Answer: The depth is −47 meters and its opposite is 47.

Now you trySame steps, your turn

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

A drone hovers 26 meters above the ground. Write an integer for its height, then name the opposite.

  1. Decide the direction. Above the ground is than 0, so the sign is .
  2. Write the integer. height =
  3. The opposite sits on the side of 0. opposite =
  4. Check on a number line: both points are units from 0.
Answer:height and its opposite

Say it and write itSentence starters

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

  • The integer represents .
  • Zero stands for in this situation.
  • The opposite of is because .
  • On the number line, sits units to the of 0.

Word bank integeroppositenegativepositivenumber linezerodistanceabovebelowleftrightsign

Watch outA common mistake

The most common mistake in this lesson is thinking that the opposite of a negative integer is still negative — for example, saying the opposite of -7 is -7, or that the opposite of -12 is -24. Opposites are the same DISTANCE from 0 but on OPPOSITE sides of 0, so taking an opposite always changes the direction and never changes the distance: the opposite of -7 is 7 and the opposite of -12 is 12. The one exception is 0, which is 0 units from itself and is therefore its own opposite. Before you submit, count the units from 0 and check that your answer is on the other side.

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.5

Lesson 7.17.1 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can use integers to represent quantities in everyday life, explain what 0 means in each situation, and name the opposite of an integer on the number line, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    −30−25−20−15−10−5051015202530flip 1flip 2−23?
    Two flips across 0.

    In Fairbanks, the temperature is −23°F. Find the opposite of the opposite of −23.

    1. 1What is the opposite of −23?
    2. 2What is the opposite of 23?
    3. 3Write this with − signs.
    Final answer:
  2. 2Complete each step, then write the final answer.
    −15−10−50510150
    P and Q are 26 units apart.

    Points P and Q are opposites. They are 26 units apart. Q is to the right of 0. Find P.

    1. 1Opposites are the same distance from 0. How far from 0 is each one?
    2. 2P is on the left side of 0. What is P?
    3. 3Why do you split 26 in half?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find −(−(−(−4))). Each − sign means "the opposite of."

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

    −(−n) = −31. What is n?

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

    A company's change in profit was $0 in May. In June it lost $1,250. In July the change was the opposite of June's. Write July's change as an integer.

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

    Kai says −(−17) is negative because it has a − sign in front. What is −(−17)?

    Show your work
    Final answer:

Explain your thinkingIs the opposite of a number always negative? Use −(−23) or the points P and Q to defend your answer.

ChallengeWrite your own problem

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

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