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

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

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

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 .

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

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 10 + 2 = 12 triangles Figure 7 has 12 + 2 = 14 triangles Figure 6 Figure 7 Figure 7 will have 14 triangles.

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, , , , . . . 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.

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 .

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

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 20 + 4 = 24 squares Figure 7 has 24 + 4 = 28 squares Figure 6 Figure 7 Figure 7 has 28 squares (you also need a picture).