1 1 Numbers and Patterns Warm Up Write

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

1 -1 Numbers and Patterns Learn to identify and extend patterns.

1 -1 Numbers and Patterns Vocabulary conjecture

1 -1 Numbers and Patterns Additional Example 1 A: Identifying and Extending Number Patterns Identify a possible pattern. Use it to write the next three numbers. 3, 12, 48, , , 3 , . . . 12 4 48 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.

1 -1 Numbers and Patterns Additional Example 1 B: Identifying and Extending Number Patterns Identify a possible pattern. Use it to write the next three numbers. 7, 12, 17, , , 7 , . . . 12 +5 17 +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.

1 -1 Numbers and Patterns Additional Example 1 C: Identifying and Extending Number Patterns Identify a possible pattern. Use it to write the next three numbers. 20, 17, 14, , , 20 – 3 , . . . 17 – 3 14 – 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.

1 -1 Numbers and Patterns Check It Out: Example 1 A Identify a possible pattern. Use it to write the next three numbers. 18, 25, 32, , . . . 18 25 32 +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.

1 -1 Numbers and Patterns Check It Out: Example 1 B Identify a possible pattern. Use it to write the next three numbers. 45, 41, 37, , , 45 – 4 , . . . 41 – 4 37 – 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.

1 -1 Numbers and Patterns Check It Out: Example 1 C Identify a possible pattern. Use it to write the next three numbers. 2, 6, 18, , . . . 2 3 6 18 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.

1 -1 Numbers and Patterns 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.

1 -1 Numbers and Patterns 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.

1 -1 Numbers and Patterns You can analyze patterns to make conjectures. A conjecture is a statement believed to be true.

1 -1 Numbers and Patterns 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 1 Figure 2 Figure 4 Figure 3 Figure 5

1 -1 Numbers and Patterns 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 2 4 6 8 10 12 14 +2 +2 Figure 6 has 10 + 2 = 12 triangles Figure 6 +2 The pattern is to add 2 triangles each time. +2 Figure 7 has 12 + 2 = 14 triangles Figure 7

1 -1 Numbers and Patterns 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 4 Figure 3 Figure 5

1 -1 Numbers and Patterns 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 4 8 12 16 20 24 28 +4 +4 Figure 6 has 20 + 4 = 24 squares Figure 6 The pattern is to add 4 squares each time. +4 +4 Figure 7 has 24 + 4 = 28 squares Figure 7

1 -1 Numbers and Patterns Lesson Quizzes Lesson Quiz for Student Response Systems

1 -1 Numbers and Patterns 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

1 -1 Numbers and Patterns 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

1 -1 Numbers and Patterns 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

1 -1 Numbers and Patterns Lesson Quiz for Student Response Systems 4. Identify a possible pattern. Use the pattern to identify the next three figures. A. C. B. D.

1 -1 Numbers and Patterns 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.