1-1 Numbers and Patterns

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Objective: Students identify and extend patterns

1-1 Numbers and Patterns

Warm UpWrite 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

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

1-1 Numbers and Patterns

Learn to identify and extend patterns.

1-1 Numbers and Patterns

Vocabulary

conjecture

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

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.

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.

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.

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

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

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

.

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.

.

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

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 2 Figure 3

Figure 4 Figure 5

Figure 1

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.

Figure 1 2 3 4 5 6 7

Number of Triangles

2 4 6 8 10 12 14

+2 +2 +2 +2 +2 +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.

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 2 Figure 3

Figure 4 Figure 5

Figure 1

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.

Figure 1 2 3 4 5 6 7

Number of Squares

4 8 12 16 20 24 28

+4 +4 +4 +4 +4 +4Figure 6 has 20 + 4 = 24 squares Figure 7 has 24 + 4 = 28 squares

Figure 6 Figure 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.

1-1 Numbers and Patterns

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

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.

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

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