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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Write a number in which no digit is repeated for each description. 1. 4-digit number divisible by 5 and 10. 2. 4-digit number divisible by 3 and 5. 3. 4-digit number divisible by 2, 3, and 6. Possible answer: 1,230.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Write a number in which no digit is repeated for each description. 1. 4-digit number divisible by 5 and 10. 2. 4-digit number divisible by 3 and 5. 3. 4-digit number divisible by 2, 3, and 6. Possible answer: 1,230 Possible answer: 1,245 Possible answer: 1,356

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

  4. 3, 12, 48, , , , . . . 3 12 48 Additional 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.

  5. 7 12 17 Additional 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 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.

  6. . 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

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

  8. Figure 6 Figure 7 Additional Example 3 Continued The table shows the numbers of triangles in each figure. A pattern is to add 2 triangles each time. 2 4 6 8 10 12 14 +2 +2 +2 +2 +2 +2 Figure 6 has 10 + 2 = 12 triangles Figure 7 has 12 + 2 = 14 triangles

  9. 45 41 37 Check It Out! Example 1B 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.

  10. 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 .

  11. 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

  12. 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

  13. 20 17 14 Additional Example 1C: Identifying and Extending Number Patterns Identify a possible pattern. Use your pattern to write the next three numbers. 20, 17, 14, , , , . . . – 3 – 3 – 3 – 3 – 3 A pattern is to subtract 3 from each number to get the next number. 14 – 3 = 11, 11 – 3 = 8, 8 – 3 = 5 The next numbers will be 11, 8, and 5.

  14. 2 6 18 Check It Out! Example 1C Identify a possible pattern. Use your pattern to write the next three numbers. 2, 6, 18, , , , . . .  3  3  3  3  3 A pattern is to multiply each number by 3 to get the next number. 18  3 = 54, 54  3 = 162, 162  3 = 486 The next numbers will be 54, 162, and 486.

  15. 18 25 32 Check It Out! Example 1A Identify a possible pattern. Use your pattern to write the next three numbers. 18, 25, 32, , , , . . . + 7 + 7 + 7 + 7 + 7 A pattern is to add 7 to each number to get the next number. 32 + 7 = 39, 39 + 7 = 46, 46 + 7 = 53 The next numbers will be 39, 46, and 53.

  16. The next three figures will be . Additional Example 2B: Identifying and Extending Geometric Patterns Identify a possible pattern. Use your pattern to draw the next three figures. A pattern is to rotate the arrow in a counterclockwise direction while alternating colors of orange and blue.

  17. Lesson Quiz: Part I Identify a possible pattern. Use your pattern to write next three numbers. 1. –8, –6, –4, , , , … Add 2; –2, 0, 2 2. –3, 6, –12, 24, , , , … Multiply by –2; –48, 96, –192 3. 0, 1, 3, 6, 10, , , , … Add 1 more than the number previously added; 15, 21, 28.

  18. Lesson Quiz: Part II Identify a possible pattern. Use your pattern to draw the next three figures. 4. 5. Make a table that shows the number of dots in the figure. Tell how many dots are in the seventh figure of a possible pattern. Use drawings to justify your answer. 14

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