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

Learn to identify and extend patterns.

Vocabulary conjecture

Additional Example 1A: Identifying and Extending Number Patterns Identify a possible pattern. Use it 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 So the next numbers will be 192, 768, and 3072.

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

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

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

Identify a possible pattern. Use it to write the next three numbers. Check It Out: Example 1B Identify a possible pattern. Use it to write the next three numbers. 45, 41, 37, , , , . . . 45 41 37 – 4 – 4 – 4 – 4 – 4 A pattern is to subtract each number by 4 to get the next number. 37 – 4 = 33, 33 – 4 = 29, 29 – 4 = 25 So the next numbers will be 33, 29, and 25.

Identify a possible pattern. Use it to write the next three numbers. Check It Out: Example 1C Identify a possible pattern. Use it to write the next three numbers. 2, 6, 18, , , , . . . 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 So the next numbers will be 54, 162, and 486.

Additional Example 2: Identifying and Extending Geometric Patterns Identify a possible pattern. Use it to draw the next three figures. The pattern is to rotate the figure in a counterclockwise direction. So the next three figures will be .

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

You can analyze patterns to make conjectures You can analyze patterns to make conjectures. A conjecture is a statement believed to be true.

Additional Example 3: Using Tables to Identify and Extend Patterns Make a table that shows the number of triangles in each figure. Then make a conjecture about the number of triangles in the seventh figure of the pattern. Complete the table, and 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. Then make a conjecture about the number of triangles in the seventh figure of the pattern. Complete the table, and use drawings to justify your answer. The table shows the numbers of triangles in each figure. Figure 1 2 3 4 5 6 7 Number of Triangles The 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 Figure 6 Figure 7

Check It Out: Additional Example 3 Make a table that shows the number of squares in each figure. Then make a conjecture about the number of squares in the seventh figure of the pattern. Complete the table, and use drawings to justify your answer. Figure 1 Figure 2 Figure 3 Figure 4 Figure 5

Check It Out: Example 3 Continued Make a table that shows the number of squares in each figure. Then make a conjecture about the number of squares in the seventh figure of the pattern. Complete the table, and use drawings to justify your answer. The table shows the numbers of squares in each figure. Figure 1 2 3 4 5 6 7 Number of Squares The 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

Lesson Quizzes Lesson Quiz for Student Response Systems

Lesson Quiz for Student Response Systems 1. Identify a possible pattern. Use the pattern to identify the next three numbers. 3, 8, 13, … A. Multiply by 5; 18, 23, 38 B. Add 5; 18, 23, 28 C. Subtract 5; 13, 8, 3 D. Multiply by 5; 15, 40, 65

Lesson Quiz for Student Response Systems 2. Identify a possible pattern. Use the pattern to identify the next three numbers. 7, 21, 63, … A. Add 14; 77, 91, 105 B. Divide by 7; 1, 3, 9 C. Multiply by 3; 189, 567, 1701 D. Multiply by 3; 66, 69, 72

Lesson Quiz for Student Response Systems 3. Identify a possible pattern. Use the pattern to identify the next three numbers. 0, 1, 3, 6, … A. Add one more than the number previously added; 10, 15, 21 B. Add 1; 7, 8, 9 C. Add one more than the number previously added; 9, 13, 18 D. Multiply by 2; 12, 24, 48

Lesson Quiz for Student Response Systems 4. Identify a possible pattern. Use the pattern to identify the next three figures. A. C. B. D.

Lesson Quiz for Student Response Systems 5. Make a table that shows the number of arrows in the figure. Then tell how many arrows are in the fifth figure of the pattern. Use drawings to justify your answer. A. B.