Lesson 7.1Integers in Real Situations
Start hereWords, worked example, and sentence starters
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.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| IntegerSpanish: Número entero | The counting numbers, their opposites, and 0. | −14, 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. | a loss, a drop, a withdrawal |
| Positive numberSpanish: Número positivo | A number greater than 0. On a number line it sits to the right of 0. | 9°C is 9 degrees ABOVE zero |
| 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 exampletaking the opposite twice
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A freezer gauge read −33 degrees. It changed to the opposite of that reading, then changed again to the opposite of the new reading.
- Start with the first reading. −33 It sits 33 units to the left of 0.
- Take the opposite: same distance, other side. second reading = 33
- Take the opposite again: flip back across 0. third reading = −33
- Check: two flips land you on the number you started with.
Answer: The readings are 33, then −33 — the opposite of the opposite is the original number.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A vault gauge read −58 degrees. It changed to the opposite of that reading, then changed again to the opposite of the new reading.
- Start with the first reading. It sits units from 0.
- Take the opposite: same distance, side. second reading =
- Take the opposite again. third reading =
- Check: the opposite of the opposite of a number is .
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- A is negative here because .
- Zero represents in this situation.
- The opposite of is , so the flip moves me to the .
- After two opposites I am back at because .
Word bank integeroppositeflipnegativepositivezerogainlossdistancenumber lineleftright
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.
Lesson 7.1Integers in Real Situations
Apply Day · Version ASupported practice
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.
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1Complete each step, then write the final answer.
What is the opposite of 27?
Show your workHint Find the number 27 units from 0 on the other side.
Final answer: -
2Complete each step, then write the final answer.
A cave is 30 meters under the ground. The ground is 0. Write the cave's position as an integer.
Show your workHint Under the ground means less than 0. Use a − sign.
Final answer: -
3Complete each step, then write the final answer.
Mia owes her brother $35. Zero means she owes nothing. Write what Mia owes as an integer.
Show your workHint Owing money is less than having nothing. Use a − sign.
Final answer:
Lesson 7.1Integers in Real Situations
Apply Day · Version BCore practice
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.
-
1Complete each step, then write the final answer.
Leo says the opposite of −11 is −11, because it is the same number. Is he right? What is the opposite of −11?
Show your workFinal answer: -
2Complete each step, then write the final answer.
Find −(−(−(−4))). Each − sign means "the opposite of."
Show your workFinal answer: -
3Complete each step, then write the final answer.
What is the opposite of 18?
Show your workFinal answer:
Lesson 7.1Integers in Real Situations
Apply Day · ChallengeExtension
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.
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1Circle the letter of the best answer. Show how you know.
Badwater Basin sits 86 meters below sea level, where sea level is defined as 0. Which integer represents this elevation?
- A0
- B−8.6
- C−86
- D86
Show your work -
2Complete each step, then write the final answer.
Kai says −(−17) is negative because it has a − sign in front. What is −(−17)?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Find −(−(−19)).
Show your workFinal answer: