Graphing Number Relationships 5.OA.B.3

Graphing Number Relationships 2 4 6 8 10 12 y-axis 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. 2 4 6 8 10 12 14 16 18 20 22 24 x-axis And, here is a grid to help us see more clearly along both axes at the same time. This number line represents the x-axis. This number line represents the y-axis.

(5,9) (6,10) (7,11) 5 9 6 10 7 11 Graphing Number Relationships + 4 2 4 6 8 10 12 y-axis Let’s begin with the number 5 … … and the function + 4. What is 5 + 4? 9 Let’s write the 5 and the 9 as the ordered pair (5,9). Here is the location of (5,9). What is 6 + 4? 10 Here is the ordered pair (6,10). Here is the location of (6,10). What is 7 + 4? 11 Here is the ordered pair (7,11). Here is the location of (7,11). Notice that these ordered pairs form one line. 2 4 6 8 10 12 14 16 18 20 22 24 x-axis 11 What is 7 + 4? Here is the ordered pair (7,11). Notice that these ordered pairs form one line. Here is the location of (6,10). Here is the location of (7,11). … and the function + 4. 9 What is 5 + 4? Let’s begin with the number 5 … Let’s write the 5 and the 9 as the ordered pair (5,9). Here is the location of (5,9). 10 What is 6 + 4? Here is the ordered pair (6,10).

(22,12) (20,10) (18,8) 22 12 20 10 18 8 Graphing Number Relationships – 10 12 (22,12) 20 10 (20,10) 18 8 (18,8) 2 4 6 8 10 12 y-axis Let’s begin with the number 22 … … and the function – 10. What is 22 – 10? 12 Let’s write the 22 and the 12 as the ordered pair (22,12). Here is the location of (22,12). What is 20 – 10? 10 Here is the ordered pair (20,10). What is 18 – 10? 8 Here is the ordered pair (18,8). Here is the location of (18,8). Notice that these ordered pairs form one line. 2 4 6 8 10 12 14 16 18 20 22 24 x-axis What is 18 – 10? 8 Here is the ordered pair (20,10). Here is the location of (18,8). 10 Here is the ordered pair (18,8). Let’s begin with the number 22 … … and the function – 10. Here is the location of (20,10). What is 22 – 10? 12 Let’s write the 22 and the 12 as the ordered pair (22,12). What is 20 – 10? Here is the location of (22,12). Notice that these ordered pairs form one line.

(1,3) (2,6) (3,9) 1 3 2 6 3 9 Graphing Number Relationships × 3 y-axis 4 6 8 10 12 y-axis Let’s begin with the number 1 … … and the function x 3. What is 1 x 3? 3 Let’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? 6 Here is the ordered pair (2,6). Here is the location of (2,6). What is 3 x 3? 9 Here is the ordered pair (3,9). Here is the location of (3,9). Notice that these ordered pairs form one line. 2 4 6 8 10 12 14 16 18 20 22 24 x-axis 9 What is 3 x 3? Here is the ordered pair (3,9). Notice that these ordered pairs form one line. Here is the ordered pair (2,6). Here is the location of (3,9). Let’s begin with the number 1 … What is 1 x 3? … and the function x 3. Here is the location of (2,6). 3 Let’s write the 1 and the 3 as the ordered pair (1,3). What is 2 x 3? Here is the location of (1,3). 6

(24,4) (18,3) (12,2) 24 4 18 3 12 2 Graphing Number Relationships ÷ 6 10 12 y-axis Let’s begin with the number 24 … … and the function ÷ 6. What is 24 ÷ 6? 4 Let’s write the 24 and the 4 as the ordered pair (24,4). Here is the location of (24,4). What is 18 ÷ 6? 3 Here is the ordered pair (18,3). Here is the location of (18,3). What is 12 ÷ 6? 2 Here is the ordered pair (12,2). Here is the location of (12,2). Notice that these ordered pairs form one line. 2 4 6 8 10 12 14 16 18 20 22 24 x-axis 2 Here is the ordered pair (12,2). Notice that these ordered pairs form one line. What is 12 ÷ 6? Here is the location of (12,2). What is 24 ÷ 6? … and the function ÷ 6. Let’s begin with the number 24 … Here is the location of (18,3). 4 Let’s write the 24 and the 4 as the ordered pair (24,4). 3 What is 18 ÷ 6? Here is the location of (24,4). Here is the ordered pair (18,3).

(21,7) (18,6) (15,5) 21 7 18 6 15 5 Graphing Number Relationships ÷ 3 4 6 8 10 12 y-axis Let’s begin with the number 21 … … and the function ÷ 3. What is 21 ÷ 3? 7 Let’s write the 21 and the 7 as the ordered pair (21,7). Here is the location of (21,7). What is 18 ÷ 3? 6 Here is the ordered pair (18,6). Here is the location of (18,6). What is 15 ÷ 3? 5 Here is the ordered pair (15,5). Here is the location of (15,5). Notice that these ordered pairs form one line. 2 4 6 8 10 12 14 16 18 20 22 24 x-axis 5 What is 15 ÷ 3? Here is the ordered pair (15,5). Notice that these ordered pairs form one line. Here is the ordered pair (18,6). Here is the location of (15,5). Let’s begin with the number 21 … What is 21 ÷ 3? … and the function ÷ 3. Here is the location of (18,6). 7 Let’s write the 21 and the 7 as the ordered pair (21,7). What is 18 ÷ 3? Here is the location of (21,7). 6

Graphing Number Relationships Closing Question

(15,4) (12,3) (18,5) 15 4 12 3 18 5 Graphing Number Relationships ÷ 3 – 1 4 (15,4) 12 3 (12,3) 18 5 (18,5) 2 4 6 8 10 12 y-axis Let’s begin with the number 15 … … and the functions ÷ 3 and – 1. What is the final outcome? 4 Let’s write the 15 and the 4 as the ordered pair (15,4). Here is 12. What is the final outcome? 3 Here is the ordered pair (12,3). Here is the location of (12,3). Here is 18. What is the final outcome? 5 Here is the ordered pair (18,5). Here is the location of (18,5). Notice that these ordered pairs form one line. 2 4 6 8 10 12 14 16 18 20 22 24 x-axis 5 Here is 18. What is the final outcome? Notice that these ordered pairs form one line. Here is the ordered pair (12,3). Here is the location of (18,5). Here is the ordered pair (18,5). Let’s write the 15 and the 4 as the ordered pair (15,4). Let’s begin with the number 15 … Here is the location of (12,3). Here is the location of (15,4). … and the functions ÷ 3 and – 1. What is the final outcome? Here is 12. What is the final outcome? 4 3

(24,7) (21,6) (9,2) 24 7 21 6 9 2 Graphing Number Relationships ÷ 3 – 1 7 (24,7) 21 6 (21,6) 9 2 (9,2) 2 4 6 8 10 12 y-axis Let’s use the same functions to add more points to the grid. Here is the number 24. What is the outcome? 7 Let’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? 6 Here is the ordered pair (21,6). Here is the location of (21,6). Here is 9. What is the final outcome? 2 Here 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. 2 4 6 8 10 12 14 16 18 20 22 24 x-axis Here is the ordered pair (9,2). 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. Here is 9. What is the final outcome? Here is the location of (21,6). 7 Here is the number 24. What is the outcome? Let’s write the 24 and the 7 as the ordered pair (24,7). Here is the location of (24,7). 6 Here is 21. What is the final outcome? Here is the ordered pair (21,6).