Combining Opposite Quantities to Get Zero

Module 2 Lesson 1: Opposite Quantities Combine to Make                   Zero

Number lines & Additive Inverse

All numbers on the left (<) of 0 are negative and all numbers to the right (>) of 0 are positive.

Multiple Choice

Counting UP starting at zero corresponding to ________ numbers.

• negative

• rational

• additive inverse

• positive

Multiple Choice

Counting down starting at zero corresponds to ________ numbers.

• negative

• rational

• additive inverse

• positive

Absolute Value

• Always start at zero

• The distance between a number and zero on a number line. Terms used are:

• Additive Inverse

• Opposites

• Equal Distance

Multiple Choice

What do you call the distance between a number and zero on a number line?

• Rational numbers

• Positive numbers

• Negative number

• The absolute value

Open Ended

What is the relationship between 7 and -7? Hint: how many units?

What is the sum of the card values? *sum means to add*

Use the counting on method on the provided number line to justify your answer.

5 minus 5 = 0

0 minus 4 = -4

negative 4 + 8 = 4

Remember to be recording these answers in your Module 2 Mat book

What is the final position on the number line?

Multiple Select

What card or combination of cards would you need to get back to 0 (zero)?

• 3

• -4

• -2-2

• -8

The Absolute Value of 7 is 7 units to the right of zero.

How far is -7 (or the opposite of 7) from 0 (zero) and in which direction?

All black cards (on top) are positive and all the red cards (at the bottom) are negative

Think back to our previous work, explain how you would use the counting on method to represent the following: While playing the Integer Game, the first card is 7, and second card selected is -7.

This is simply asking: If you have 7 and negative 7 where does the dot land?

Multiple Choice

What does this tell us about the sum of 7 and its opposite, -7?

hint: sum means total

• 0 (zero)

• 7

• -7

Multiple Select

What is the relationship between 7 & -7?

• 7 & -7 both have the same absolute values

• They are both the same distance from zero

• they are in equal opposite directions from zero

• 7 & -7 are opposites

Look at the curved arrows you drew for 7 and -7. What relationship exists between these two arrows that would support your claim about the sum of 7 & -7? (answer on the next slide & in your book)

Multiple Choice

What relationship exists between these two arrows that would support your claim about the sum of 7 & -7?

• nothing

• both equal 6

• equal opposites

Multiple Select

Do you think this will hold true for the sum of any number and its opposite? & why?

• Yes, opposites always have an equal number of units

• No, opposites are the sum of ten

• Yes, opposites contain equal absolute values

• No, absolute value means different sums

• Yes, opposites cancel each other out to equal zero

We will play a game much like this when we meet on Thursday or Friday. The goal will be to get your cards to equal zero.

If red cards are negative and black cards are positive

Then what would these cards equal? *answer on the next slide*

Multiple Choice

2 - 3 + 1 =

• 1

• -1

• -2

• 0

• -3

If red cards are negative and black cards are positive

Then what would these cards equal? *answer on the next slide*

Multiple Choice

-9 -1 + 7

• -4

• -3

• 3

• 0

• -2

If red cards are negative and black cards are positive

Then what would these cards equal? *answer on the next slide*

Multiple Choice

10 -6 -9

• -10

• -5

• 10

• -15

• 5