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Preparation for AF2.0

Prepare for AF2.0 as students analyze and use tables, graphs, and rules to solve problems involving rates and proportions. Examples provided to identify and extend number patterns, geometric patterns, and use tables to visualize and extend patterns.

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Preparation for AF2.0

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  1. California Standards Preparation forAF2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions.

  2. 3, 12, 48, , , , . . . 3 12 48 Example 1A: Identifying and Extending Number Patterns Identify a possible pattern. Use your pattern to write the next three numbers.  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.

  3. 7 12 17 Example 1B: Identifying and Extending Number Patterns Identify a possible pattern. Use your pattern to write the next three numbers. 7, 12, 17, , , , . . . + 5 + 5 + 5 + 5 + 5 A pattern is to add5 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.

  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. Figure 1 Figure 2 Figure 3 Figure 5 Figure 4 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.

  6. Figure 6 Figure 7 Additional Example 3 Continued Make a table that shows the number of triangles in each figure. 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 7 will have 14 triangles.

  7. 45 41 37 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. Figure 6 Figure 7 Check It Out! Example 3 Continued The table shows the numbers of squares in each figure. A pattern is to add 4 squares each time. 4 8 12 20 24 28 16 +4 +4 +4 +4 +4 +4 Figure 6 has 20 + 4 = 24 squares Figure 7 has 24 + 4 = 28 squares Figure 7 has 28 squares (you also need a picture).

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