1. Standards California Preparation for AF2.0
Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions.
California
Standards

2. Example 1A: Identifying and Extending Number Patterns
Identify a possible pattern. Use your pattern to write the next three numbers.
3, 12, 48, , , , . . .
 4  4  4  4  4
A pattern is to multiply each number by 4 to get the next number.
48  4 = 192,  4 = 768,  4 = 3072
The next numbers will be 192, 768, and 3072.

3. Example 1B: Identifying and Extending Number Patterns
Identify a possible pattern. Use your pattern to write the next three numbers.
7, 12, 17, , , , . . .
A pattern is to add 5 to each number to get the next number.
= 22, = 27, = 32
The next numbers will be 22, 27, and 32.

4. Additional Example 2A: Identifying and Extending Geometric Patterns
Identify a possible pattern. Use your pattern to draw the next three figures.
A pattern is to rotate the purple triangle in a counterclockwise direction.
The next three figures will be .

5. Example 3: Using Tables to Identify and Extend Patterns
Make a table that shows the number of triangles in figure 1-5. Tell how many triangles are in the seventh figure of a possible pattern. Use drawings to justify your answer.
Figure 2
Figure 3
Figure 4
Figure 5
Figure 1

6. Additional Example 3 Continued
Make a table that shows the number of triangles in each figure.
Figure 1 2 3 4 5 6 7
Number of Triangles 2 4 6 8 10 12 14 +2 +2 +2 +2 +2 +2
A pattern is to add 2 triangles each time.
Figure 6 has = 12 triangles
Figure 7 has = 14 triangles
Figure 6
Figure 7
Figure 7 will have 14 triangles.

7. A pattern is to subtract 4 from each number to get the next number.
Check It Out! Example 1
Identify a possible pattern. Use your pattern to write the next three numbers.
45, 41, 37, , , , . . .
– 4 – 4 – 4 – 4 – 4
A pattern is to subtract 4 from each number to get the next number.
37 – 4 = 33, 33 – 4 = 29, 29 – 4 = 25
The next numbers will be 33, 29, and 25.

8. Check It Out! Example 2
Identify a possible pattern. Use your pattern to draw the next three figures.
A pattern is three triangular objects that repeat, while alternating between orange and green.
The next three figures will be .

9. Check It Out! Example 3
Make a table that shows the number of squares in each figure. Tell how many squares are in the seventh figure of a possible pattern. Use drawings to justify your answer.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

10. Check It Out! Example 3 Continued
The table shows the numbers of squares in each figure.
Figure 1 2 3 4 5 6 7
Number of Squares
A pattern is to add 4 squares each time. 4 8 12 16 20 24 28 +4 +4 +4 +4 +4 +4
Figure 6 has = 24 squares
Figure 7 has = 28 squares
Figure 6
Figure 7
Figure 7 has 28 squares (you also need a picture).