Graphing Number Relationships

5.OA.B.3

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This number line represents the x-axis.This number line represents the y-axis.And, here is a grid to help us see more clearly along both axes at the same time.

Graphing Number Relationships

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5 + 4 9 (5,9)6 10 (6,10)7 11 (7,11)

Let’s begin with the number 5 …… and the function + 4.What is 5 + 4?9Let’s write the 5 and the 9 as the ordered pair (5,9).Here is the location of (5,9).What is 6 + 4?10Here is the ordered pair (6,10).Here is the location of (6,10).What is 7 + 4?11Here is the ordered pair (7,11).Here is the location of (7,11).Notice that these ordered pairs form one line.

Graphing Number Relationships

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Here is the location of (20,10).

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22 – 10 12 (22,12)

20 10 (20,10)18 8 (18,8)

Let’s begin with the number 22 …… and the function – 10.What is 22 – 10?12Let’s write the 22 and the 12 as the ordered pair (22,12).Here is the location of (22,12).What is 20 – 10?10Here is the ordered pair (20,10).What is 18 – 10?8Here is the ordered pair (18,8).Here is the location of (18,8).Notice that these ordered pairs form one line.

Graphing Number Relationships

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1 × 3 3 (1,3)2 6 (2,6)3 9 (3,9)

Here is the location of (2,6).Let’s begin with the number 1 …… and the function x 3.What is 1 x 3?3Let’s write the 1 and the 3 as the ordered pair (1,3).Here is the location of (1,3).What is 2 x 3?6Here is the ordered pair (2,6).What is 3 x 3?9Here is the ordered pair (3,9).Here is the location of (3,9).Notice that these ordered pairs form one line.

Graphing Number Relationships

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24 ÷ 6 4 (24,4)18 3 (18,3)12 2 (12,2)

Here is the location of (18,3).Let’s begin with the number 24 …… and the function ÷ 6.What is 24 ÷ 6?4Let’s write the 24 and the 4 as the ordered pair (24,4).Here is the location of (24,4).What is 18 ÷ 6?3Here is the ordered pair (18,3).What is 12 ÷ 6?2Here is the ordered pair (12,2).Here is the location of (12,2).Notice that these ordered pairs form one line.

Graphing Number Relationships

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21 ÷ 3 7 (21,7)18 6 (18,6)15 5 (15,5)

Here is the location of (18,6).Let’s begin with the number 21 …… and the function ÷ 3.What is 21 ÷ 3?7Let’s write the 21 and the 7 as the ordered pair (21,7).Here is the location of (21,7).What is 18 ÷ 3?6Here is the ordered pair (18,6).What is 15 ÷ 3?5Here is the ordered pair (15,5).Here is the location of (15,5).Notice that these ordered pairs form one line.

Graphing Number Relationships

Closing Question

Graphing Number Relationships

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Here is the location of (15,4).

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15 ÷ 3 4– 1 (15,4)12 3 (12,3)18 5 (18,5)

Here is the location of (12,3).Let’s begin with the number 15 …… and the functions ÷ 3 and – 1.What is the final outcome?4Let’s write the 15 and the 4 as the ordered pair (15,4).Here is 12. What is the final outcome?3Here is the ordered pair (12,3).Here is 18. What is the final outcome?5Here is the ordered pair (18,5).Here is the location of (18,5).Notice that these ordered pairs form one line.

Graphing Number Relationships

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24 ÷ 3 7– 1 (24,7)21 6 (21,6)9 2 (9,2)

Here is the location of (21,6).Here is the number 24. What is the outcome?7Let’s write the 24 and the 7 as the ordered pair (24,7).Here is the location of (24,7).Here is 21. What is the final outcome?6Here is the ordered pair (21,6).Here is 9. What is the final outcome?2Here is the ordered pair (9,2).Here is the location of (9,2).As long as we use the same functions, the points remain on the same line.Let’s use the same functions to add more points to the grid.

Graphing Number Relationships