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Word Problems
Additive Inverse
Absolute Value
Number lines
Add/Subtract Integers
100
What is the additive inverse of 6 ?
-6
100
What is the absolute value of -17?
17
100
What is -9 – (-3)?
-9 - (-3) becomes -9 +3 which is -6
200
If it says -5 degrees outside and the weatherman says it will be 10 degrees colder tomorrow what will the temperature be tomorrow?
-15 degrees
200
Rewrite this subtraction problem as an addition problem: -5 - 3
Using 3's additive inverse which is -3, and the process of keep change change, that subtraction problem becomes -5 + (-3)
200
Why is absolute value always positive?
Because it's the distance a number is away from zero!
200
If its currently negative degrees outside and it gets colder will the degrees the following day be negative or positive? Explain using a number line
See demonstration
200
Are 10 + (-2) and -10-2 the same problem?
No, 10 + (-2) equals 8, but -10-2 equals -12
300
If you are traveling 100ft below sea level on the top of a mountain and then you travel down the hill 50ft, at what height will you be traveling?
50 ft above sea level
300
Use a number line to illustrate the solution to these two problems: 7 – 4 and 7 + (– 4) Explain why your answer is the same for both problems.
For the first problem, starting at 7 on the number line, and subtracting 4 would end up on the 3 of the number line. For the second, starting at 7 and going toward the negative 4 times
300
|-16-(-4)| =
First you do the operation inside the absolute value lines, so -16-(-4) is -16+4 which is -12. Then the absolute value of -12 is 12!
300
Use a number line to solve -10.5 – 5.5 =
See example
300
Answer whether this statement is sometimes true, always true, or never true: The sum of two negative integers is negative.
ALWAYS true
400
What is the total amount the temperature dropped in this scenario: On Monday morning Chris and his friends hit the slope while the temperature was -2.25°F. When they finally left the slopes that evening to go home and pack, the temperature had dropped to -21.5°F. What was the total drop in temperature?
19.25°F
400
Create two equations that are written two different ways but use all of the same number and have the same solution
4+ (-2) and 4 - 2
400
Answer true or false: The absolute value of any number will always be a positive number
FALSE: zero is the exception since the absolute value of zero is zero, and zero is not positive
400
A submarine was under water at 250 feet. The crew dove 400 feet deeper into the ocean. How far under the ocean is the submarine after the crew dove deeper? Use a number line to show your answer with hash marks of at least 50 feet apart.
400 feet!
500
Describe a real world math problem involving you borrowing money from a friend when two opposite values cancel out and make zero.
If I owe my friend 52 dollars, how much should I pay her over four days to make my debt cancel out to zero?
500
Answer true or false AND give an example: The distance between two numbers on a number line is the same as the difference between them
TRUE The distance between 10 and -6 on the number line is 16 and the difference between them is 10- (-6) which is 10+ 6 which is also 16.
500
Fill in the blank: As you approach zero from the left of the number line, the integers ____, but the absolute value of those integers ____.
As you approach zero from the left of the number line the integers increase (you're going right so theyre getting bigger), but the absolute value of those integers decreases. Let's say it's like -3, 2, 1 which are getting bigger, but the absolute values (3, 2, 1) are getting smaller.
500
Take us through the very specific steps of writing a number line and solving a problem using a number line. 11-2 +3
=12
500
Erika says you get a positive answer when you subtract a negative number from a negative number. Edith says you get zero and Ramiro says you get a negative answer. Show that they can all be right.
You can get a positive answer when you subtract a negative number from a negative number that has fewer negatives in it (it is bigger). For example, -3 - (-5) becomes -3+5 which then becomes 2 because there are two more positives than negative. You can get zero when you subtract a negative number from the same negative number. For example, when you have the problem -3- (-3), it becomes -3 +3 which is zero. You can get a negative answer when you subtract a negative number from a negative number that has more negatives than it. For instance, -7 - (-2) becomes -7 +2 which is -5, which is still negative.