(7.2) Number, operation, and quantitative reasoning.

The student adds, subtracts, multiplies, or divides to solve problems and justify solutions.

The student is expected to: (C) use models to add, subtract, multiply, and divide integers and connect the actions to

algorithms.

7.2C Addition and Subtraction of Integers

7.2C INSTRUCTIONAL ACTIVITY #1

Addition and subtraction of integers can be modeled using different colors of tiles to represent integers. For example, use blue tiles to represent positive integers and red tiles to represent negative integers.

EXAMPLE 1: Use color tiles to model the addition problem ˉ7 + 3.

• Place 7 red tiles to represent ˉ7, then place 3 blue color tiles below them to represent 3.

• A tile representing a positive 1 and a negative 1 can be combined to represent a “zero pair”.

• Remove the tiles representing the “zero pairs”.

• The remaining tiles represent ˉ7 + 3, therefore ˉ7 + 3 = -4.

7.2C INSTRUCTIONAL ACTIVITY #1

Addition and subtraction of integers can be modeled using different colors of tiles to represent integers. For example, use blue tiles to represent positive integers and red tiles to represent negative integers.

EXAMPLE 2: Use color tiles to model the subtraction problem ˉ4 - ˉ3.• Place 4 red tiles to represent ˉ4.

• Remove 3 red tiles representing the subtraction of ˉ3.

• The remaining tile represents ˉ4 - ˉ3, therefore ˉ4 - ˉ3 = ˉ1.

7.2C INSTRUCTIONAL ACTIVITY #1

Addition and subtraction of integers can be modeled using a number line.• Always begin the model at zero.

• Draw an arrow to the right to represent a positive integer or draw an arrow to the left to represent a negative integer as the first number in the problem.

Next

• Draw an arrow to the right to represent adding a positive integer or draw an arrow to the left to represent adding a negative integer.or

• Draw an arrow to the right to represent subtracting a negative integer because you are adding “the opposite of” the negative integer.

0-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10987654321

Example: ˉ2 - ˉ2 can be changed to addition and becomes ˉ2 + 2.

7.2C INSTRUCTIONAL ACTIVITY #1

Use the number line below to model the addition problem ˉ7 + 3.

0-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10987654321

ˉ7

+3

• Begin to model the addition problem at 0.

• Since ˉ7 is a negative integer, it can be modeled with an arrow ˉ7 units to the left of 0. Draw an arrow from 0 to ˉ7, which is 7 units to the left of 0.

• Since 3 is a positive integer, it can be modeled with an arrow 3 units to the right of ˉ7. Draw an arrow from ˉ7 to ˉ4, which is 3 units to the right of ˉ7.

The model shows that the sum of ˉ7 and 3 is ˉ4.

7.2C INSTRUCTIONAL ACTIVITY #1

Use the number line below to model the addition problem ˉ6 + ˉ2.

• Start to model the addition problem at 0.

0-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10987654321

ˉ6

ˉ2

• Since ˉ6 is a negative integer, it can be modeled with an arrow 6 units to the left of 0. Draw an arrow from 0 to ˉ6, which is 6 units to the left of 0.

• Since ˉ2 is a negative integer, and is being added to ˉ6, it can be modeled with an arrow 2 units to the left of ˉ6. Draw an arrow from ˉ6 to ˉ8, which is 2 units to the left of ˉ6.

The model shows that the sum of ˉ6 and ˉ2 is ˉ8.

7.2C INSTRUCTIONAL ACTIVITY #1

Use the number line below to model the addition problem ˉ5 - 2.

• Start to model the addition problem at 0.

0-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10987654321

ˉ5

2

• Since ˉ5 is a negative integer, it can be modeled with an arrow 5 units to the left of 0. Draw an arrow from 0 to ˉ5, which is 5 units to the left of 0.

• Since 2 is a positive integer, and is being subtracted from ˉ5, it can be modeled with an arrow 2 units to the left of ˉ5. Draw an arrow from ˉ5 to ˉ7, which is 2 units to the left of ˉ5.

The model shows the difference between ˉ5 and 2 is ˉ7.

7.2C INSTRUCTIONAL ACTIVITY #1

Use the number line below to model the addition problem ˉ4 - ˉ3.

• Start to model the addition problem at 0.

0-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10987654321

ˉ4

ˉ3

• Since ˉ4 is a negative integer, it can be modeled with an arrow 4 units to the left of 0. Draw an arrow from 0 to ˉ4, which is 4 units to the left of 0.

• Since ˉ3 is a negative integer that is being subtracted from ˉ4, it can be modeled with an arrow 3 units to the right of ˉ4 to represent subtracting a negative integer because you are adding “the opposite of the negative integer” or finding the difference between ˉ4 and ˉ3. Draw an arrow from ˉ4 to ˉ1, which is 3 units to the right of ˉ4.

The model shows the difference between ˉ4 and ˉ 3 is ˉ1.

7.2C INSTRUCTIONAL ACTIVITY #1

• Addition and subtraction of integers can be modeled using sketches to represent the integers.

Use to represent +1 and to represent ˉ1 to model the addition problem ˉ6 + 2.

• Start to model the addition problem by representing ˉ6 and adding 2.

• Form “zero pairs” by grouping a representation of a ˉ 1 and +1.

• Mark off and remove the “zero pairs” that are equal to zero.

• Four tiles representing ˉ1’s remain. The model shows that the sum of ˉ6 and 2 is ˉ4.

7.2C STUDENT ACTIVITY #1

Problem #1: Lyle scored 15 points in a board game. On his next turn he lost 5 points, and then he lost 6 more points. On his final turn Lyle gained 9 points. Determine Lyle’s final score by modeling the problem on a number line. Be sure to mark moves above the number line by using arrows and identifying the direction and the amount of the move.

• Start at 0 on the number line. Lyle’s beginning score is 15. Represent this score with the integer _______. To add 15, count 15 places to the right from 0.

• On his next turn Lyle lost 5 points. Represent this with the integer _______. To add -5, count 5 places to the left from 15 to _______.

• On his next turn Lyle lost 6 points. Represent this with the integer _______. To add -6, count 6 places to the left from 10 to _______.

• On his final turn Lyle gained 9 points. Represent this with the integer _______. To add 9, count 9 places to the right from 4 to _______.

• Represent Lyle’s final score with the expression _______ +_______ +_______ +_______.

Lyle’s final score was _______.

0 2 4 6 8 10 12 14 1615

+15

-510

-64

+913

13

15 -5 -6 9

13

7.2C STUDENT ACTIVITY #1

Problem #2: Leslie made $12 babysitting on Friday night. On Saturday afternoon she spent $4 for a movie ticket and $3 for popcorn and a cold drink. On Saturday night she made another $5 babysitting. Determine the amount of money Leslie had after babysitting on Saturday night drawing a sketch to model the problem using to represent +1 and to represent -1 . Be sure to identify and remove “zero pairs” in your model. Write an explanation for each step in your model below each sketch.

Step 1: Identify my positive and negative integers and use colored dots as symbols to identify them.Step 2: Combine my “zero pairs”. Step 3: Remove tiles representing “zero pairs”.

Step 4: Remaining tiles represent the amount of money Leslie had after babysitting on Saturday night.

$10

7.2C STUDENT ACTIVITY #1

Problem #2: Leslie made $12 babysitting on Friday night. On Saturday afternoon she spent $4 for a movie ticket and $3 for popcorn and a cold drink. On Saturday night she made another $5 babysitting.Draw a number line to represent the amount of money Leslie had after babysitting on Saturday night. Be sure to mark moves above the number line by using arrows and identifying the direction and the amount of the move.

0 2 4 6 8 10 12 14 16

The following expression represents how much money Leslie had after babysitting on Saturday night. _______ +_______ +_______ +_______.

Leslie had $_____ after babysitting on Saturday night.

+12

-4-3

+5

12 -4 -3 9

10