1. 1-1 Numbers and Patterns Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes Objective: Students identify and extend patterns

2. 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. 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. 1-1 Numbers and Patterns Problem of the Day For each of the following, write the product of three and the number. 3, 7, 12, 18 9, 21, 36, 54

4. 1-1 Numbers and Patterns Learn to identify and extend patterns.

5. 1-1 Numbers and Patterns Vocabulary conjecture

6. 1-1 Numbers and Patterns Identify a possible pattern. Use it to write the next three numbers. Additional Example 1A: Identifying and Extending Number Patterns 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.  4  4  4  4  4 3, 12, 48,,,,... 3 12 48

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

8. 1-1 Numbers and Patterns Additional Example 1C: Identifying and Extending Number Patterns 20, 17, 14,,,,... 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. – 3 – 3 – 3 – 3 – 3 20 17 14 Identify a possible pattern. Use it to write the next three numbers.

9. 1-1 Numbers and Patterns Check It Out: Example 1A 18, 25, 32,,,,... 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. + 7 + 7 + 7 + 7 + 7 18 25 32 Identify a possible pattern. Use it to write the next three numbers.

10. 1-1 Numbers and Patterns Check It Out: Example 1B 45, 41, 37,,,,... 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. – 4 – 4 – 4 – 4 – 4 Identify a possible pattern. Use it to write the next three numbers. 45 41 37

11. 1-1 Numbers and Patterns Check It Out: Example 1C 2, 6, 18,,,,... 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.  3  3  3  3  3 Identify a possible pattern. Use it to write the next three numbers. 2 6 18

12. 1-1 Numbers and Patterns Identify a possible pattern. Use it to draw the next three figures. Additional Example 2: Identifying and Extending Geometric Patterns The pattern is to rotate the figure in a counterclockwise direction. So the next three figures will be.

13. 1-1 Numbers and Patterns Check It Out: Example 2 The pattern is three triangular objects that repeat, while alternating between orange and green. So the next three figures will be Identify a possible pattern. Use it to draw the next three figures..

14. 1-1 Numbers and Patterns You can analyze patterns to make conjectures. A conjecture is a statement believed to be true.

15. 1-1 Numbers and 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. Additional Example 3: Using Tables to Identify and Extend Patterns Figure 2Figure 3 Figure 4 Figure 5 Figure 1

16. 1-1 Numbers and Patterns Additional Example 3 Continued The table shows the numbers of triangles in each figure. The pattern is to add 2 triangles each time. Figure1234567 Number of Triangles 2468101214 +2 Figure 6 Figure 7 Figure 6 has 10 + 2 = 12 triangles Figure 7 has 12 + 2 = 14 triangles 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.

17. 1-1 Numbers and Patterns 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. Check It Out: Additional Example 3 Figure 2Figure 3 Figure 4Figure 5 Figure 1

18. 1-1 Numbers and Patterns Check It Out: Example 3 Continued The table shows the numbers of squares in each figure. The pattern is to add 4 squares each time. Figure1234567 Number of Squares 4812 16 202428 +4 Figure 6 has 20 + 4 = 24 squares Figure 7 has 24 + 4 = 28 squares Figure 6Figure 7 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.

19. 1-1 Numbers and Patterns Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. 1-1 Numbers and Patterns Identify a possible pattern. Use the pattern to write next three numbers. Lesson Quiz: Part I 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.

21. 1-1 Numbers and Patterns Identify a possible pattern. Use the pattern to draw the next three figures. 4. 5. Make a table that shows the number of dots in the figure. Then tell how many dots are in the seventh figure of the pattern. Use drawings to justify your answer. Lesson Quiz: Part II 14