7th Grade Substitute Lesson

Absolute Value and Additive Inverse Review

Rational Numbers

Review what you have learned in Module 2

Number Lines

Math problems and finding distance on a number line

Computing Integers Using a Number Line

by Josephine Bly

​Brain Dump!

• ​Recall:

  • ​Same Signs: add the numbers together and keep the sign​

Distance on a number line

• Distance is always positive so we have to use absolute values to answer

• To find distance we subtract one point from the other

• Once completed you will change your answer to a positive

​Brain Dump!

• ​Recall:

  • ​Different Signs: the answer takes the sign of the value that is the furthest away from zero

Positive & Negative Numbers

Rational numbers that are on a number line.

Absolute Values

Multiple Choice

What would the problem look like for this distance?

• $$\left|-2-6\right|$$

• $$-2-6$$

• $$-2+6$$

• $$\left|-2+6\right|$$

Multiple Select

Select all the true statements about the Additive Inverse.

• 6 is the additive inverse of 6

• -4 is the additive inverse of 4

• 781 is the additive inverse of -781

• -21 is the additive inverse of 22

• 1 is the additive inverse of 0

Multiple Choice

What is the solution?

• -8

• 8

• 4

• -4

Multiple Choice

Which is the least integer?

• 1

• -1

• -2

• -8

Multiple Choice

What would the distance problem look like?

• $$9+\left(-7\right)$$

• $$9-7$$

• $$\left|9-\left(-7\right)\right|$$

• $$\left|9-7\right|$$

Multiple Select

Select all the true statements about the Additive Identity.

• $$12+1=13$$

• $$21+0=21$$

• $$\left(-7\right)+0=\left(-7\right)$$

• $$15+15=30$$

• $$\left(-12\right)+12=0$$

Multiple Choice

What is the solution?

• 2

• -2

• 16

• -16

Multiplying and Dividing With Integers​

Multiple Choice

Which is the greatest integer?

• -33

• -31

• -28

• -17

​Brain Dump!

• An even number of negative signs means the answer will be positive. Why? The negative pairs make a positive​

• ​An odd number of negative signs means the answer will be negative. Why? The negative sign does not have another negative sign to cancel itself out

Multiple Choice

What is the distance problem?

• $$\left|5+1\right|$$
  

• $$\left|1-5\right|$$

• $$1-5$$

• $$5-1$$

Multiple Choice

What is Absolute Value?

• The distance from 0 to a number gives the absolute value of a number.

• Variable or a constant is any number.

• Distance from 0 and it will always be negative.

Multiple Choice

Solve the distance.

• 6

• -6

• 4

• -4

Multiple Choice

Which answer has the integers in order from least to greatest?

• − 9, -5, -3, 0, 4, 3

• − 9, -5, -3, 0, 3, 4

• − 5, -9, -3, 0, 4, 3

• 3, 4, 0, -3, -5, -9

Multiple Choice

What is the distance problem?

• $$\left|-18-4\right|$$

• $$\left|-4-18\right|$$

• $$\left|-4-\left(-18\right)\right|$$

• $$-18-\left(-4\right)$$

Fill in the Blanks

Add rational numbers with the same sign by adding the ______ ______ and using the common sign.

Fill in the Blanks

What is the distance?

Fill in the Blanks

Solve the distance between the 2 points.

Fill in the Blanks

Add rational numbers with opposite signs by subtracting the

absolute value from the larger absolute value and using the sign of the number with the larger absolute value.

Distance

2 key parts to finding distance is to always subtract one point from the other and your answer should always be positive.

Creating math problems from number lines

• Find the starting point where it leaves from zero to the first value

• Follow based on where the previous arrow ended

Multiple Select

What is a rational number?

• Decimals that end

• Decimals that go on forever

• Fractions

• Negative Numbers

• Irrational Numbers

Multiple Choice

What is the first number in the equation?

• 9

• -7

• 0

• 16

Multiple Choice

Compare: 6 ? -3

• =

• >

• <

Multiple Choice

What is the equation?

• -9+7=16

• 16-7=9

• -7+16=9

Fill in the Blanks

The rule of subtraction is Subtracting a number is the same as adding its

.

Poll

What is the first number in the problem?

• 8

• 16

• -16

• -8

Multiple Choice

Compare: -3 ? -5

• >

• <

• =

Multiple Choice

What does the equation look like?

• $$8-16=-8$$

• $$16-8=8$$

• $$8-16=8$$

• $$-16+8=-8$$

Open Ended

How do you find the distance between 2 numbers on a Number Line?

Multiple Choice

Write the equation.

• -16+12+7

• -16+12+7=3

• 7+12-16=3

• 3-7-12=-16

Multiple Select

What is the Communicative Property?

• Moving numbers

• Moving Parenthesis

• $$a\times b=b\times a$$

• $$\left(a+b\right)+c=a+\left(b+c\right)$$

• Works for Multiplication & Addition

Multiple Choice

What is the absolute value of 87?

• -87

• 87

Multiple Select

What is the Associative Property?

• Moving numbers

• Moving Parenthesis

• $$a\times b=b\times a$$

• $$\left(a+b\right)+c=a+\left(b+c\right)$$

• Works for Multiplication & Addition

Multiple Choice

What is the absolute value of -77?

• 77

• -77

Multiple Choice

$$\left(+\right)\times\left(+\right)\ =?$$  

• POSITIVE 

• NEGATIVE

Multiple Choice

What does the absolute value symbol look like?

Multiple Choice

$$\left(-\right)\times\left(+\right)\ =?$$  

• POSITIVE 

• NEGATIVE

Multiple Choice

• -13

• 13

Multiple Choice

$$\left(-\right)\times\left(-\right)\ =?$$  

• POSITIVE 

• NEGATIVE

Multiple Choice

• -50

• 50

Multiple Choice

$$\left(+\right)\times\left(-\right)\ =?$$  

• POSITIVE 

• NEGATIVE

Multiple Select

What does absolute value mean? Choose ALL that are correct.

• The number itself

• The number needed to make zero when you add

• A number's distance from zero

• The opposite of a number

Poll

So far do you understand majority of the questions in this slideshow?

• YES

• NO

• KINDA

The END

Now you have to complete a quiz against your classmates!

Multiple Choice

What is the additive inverse of -13?

• -13

• 13

Multiple Choice

What is the additive inverse of 8?

• 8
• 0
• -0
• -8

Multiple Select

What does additive inverse mean? Choose ALL that are correct.

• The number itself

• The number needed to make zero when you add

• A number's distance from zero

• The opposite of a number

Multiple Choice

What is the difference between additive inverse and absolute value?

• Nothing. They are the same thing.

• One is a distance so it's always positive.

• One is more difficult than the other.

Multiple Choice

______________ are the set of whole numbers, their opposites, and zero.

• Rational Numbers

• Opposites

• Integers

• Absolute Values

Multiple Choice

______________ is the distance between a number and zero.

• Additive inverse

• Opposites

• Integers

• Absolute value

Multiple Choice

Additive Inverse example

• -5 + 5 = 0

• |-4| = 4

• -2 + -2 = -4

Multiple Choice

What is the additive inverse of -77?

• 77

• -77

Multiple Choice

|-3| - |1| =

• -4
• 2
• -2
• -4

Multiple Select

Which pair(s) of numbers are opposites? Choose ALL correct answers.

• 4 and -4

• 3.6 and -6.3

• 9/11 and -9/11

Multiple Choice

• -44

• 44

• I have no idea.

Multiple Choice

• <

• >

• =

Multiple Choice

• <

• >

• =

Fill in the Blanks

You start 5 feet below sea level. You walk 12 feet up a hill. You then trip and fall 10 feet down the hill. What integer represents your height in relation to sea level?

Multiple Choice

A) Which city is the closest to sea level (0 ft)?

B) Which city has the coldest average temperature?

• A) New Orleans and B) Cleveland

• A) Cleveland and B) Miami

• A) Miami and B) Burlington

• A) Miami and B) Cleveland