Modeling Integer Operations

Modeling Integer Operations

​Adding Integers

​Adding integers on the number line.

• ​The bottom arrow is the first number.

• ​The top arrow is the second number.

• ​It ends on the sum.

• ​The arrows are straight lines.

• ​This model represents

-4 + (-2) = -6

Multiple Choice

Look at the number line.

• –2 + 4 =  –2
• –2 + (–4) =  –6
• 4 + (–6) =  –2
• 4 + (–2) =  6

Multiple Choice

• 7 + 10 = 3
• -7 + 10 = 3
• -7 - 10 = 3
• -7 + 3 = 10

Multiplying Integers

Multiplying integers on the number line.

• ​The arrows are curves or groups of arrows

• ​Count number of arrows. That will be the first number.

• ​The length of the arrow is the second number.

• ​It ends on the answer.

• ​This model represents

2(-3) = -6

Multiple Choice

• 4 x 4 = 16
• -4 x (-4) = -16
• -4 x (-4) = 16
• 4 x (-4) = -16

Multiple Choice

• 5 × 2 = 10
• -5 × 2 = 10
• 5 × (-2) = -10
• -5 × (-2) = -10

​Adding Integers Part 2

• Sometimes on adding integers there is only one arrow.

• ​The first number is where the arrow starts.

• ​The length of the arrow is the second number.

• ​The sum is where it stops.

• ​Pay attention to the direction of the arrows!

• ​This model represents

3 + (-5) = -2

Multiple Choice

Which equation matches the number line model?

• -1 + (-6) = -7

• -1 + 6 = 5

• 1 + (-6) = -5

• 1 + 6 = 7

Multiple Choice

Which equation matches the number line model?

• 3 + (-6) = -3

• -3 + (-6) = -9

• -3 + 6 = 3

• 3 + 6 = 9

Multiple Choice

Which equation is represented by the model?

• 8 + (-5) = 3
• -8 + 5 = -3
• 8 + 5 = 13
• -8 + (-5) = -13

Multiple Choice

Which equation is represented by the model?

• 9 + 4 = 13
• 9 + (-4) = 5
• -9 + 4 = -5
• -9 + (-4) = -13

Multiple Choice

• -5 + 3 = -2
• 5 + (-3) = 2
• 5 + 3 = 8
• -5 + (-3) = -8

Multiple Choice

Choose the equation that best represents the model.

• 2 + (–6) =  –4
• 0 – 6 = –6
• –6 + 8 = 2
• 8 + (–6) = 2

Multiple Choice

• -5 - 4 = -1
• -5 + 1 = -1
• -5 + 4 = -1
• 5 + (-4) = 1

Multiple Choice

• -7 - 4 = -28
• 7 x 4 = 28
• 7 x (-4) = -28
• -7 x (-4) = -28