Lesson 2.7 - Problem Solving - Look For A Pattern

Five-Minute Check (over Lesson 2–6) Main Idea Example 1:Look For a Pattern

• Solve problems by looking for a pattern.

Look For a Pattern HAIR Lelani wants to grow an 11-inch ponytail to cut off and donate to a program that makes wigs for children with cancer. She has a 3-inch ponytail now, and her hair grows about one inch every two months. How long will it take for her ponytail to reach 11 inches? Understand

You know the length of Lelani’s ponytail now. You know how long Lelani wants her ponytail to grow and you know how fast her hair grows. You need to know how long it will take for her ponytail to reach 11 inches.

Plan

Look for a pattern. Then extend the pattern to find the solution.

Look For a Pattern Solve After the first two months, Lelani’s ponytail will be 3 inches + 1 inch, or 4 inches. Her hair grows according to the pattern below. 3 in. 4 in. 5 in. 6 in. 7 in. +1

+1

+1

+1

+1

8 in. +1

9 in. +1

10 in. 11 in. +1

Answer: It will take eight sets of two months, or 16 months total, for Lelani’s ponytail to reach 11 inches. Check Lelani’s ponytail grew from 3 inches to 11 inches, a difference of eight inches, in 16 months. Since one inch of growth requires two months and 8 × 2 = 16, the answer is correct.

RUNNING Samuel ran 2 miles on his first day of training to run a marathon. On the third day, Samuel increased the length of his run by 1.5 miles. If this pattern continues for every other day, how many miles will Samuel run on the 27th day? A. 13 mi B. 15 mi

1. 2. 3. 4.

D. 23 mi

0%

0% D

0%

C

A

0%

B

C. 21.5 mi

A B C D

End of the Lesson

Pg 112-113, # 4-14 all

Five-Minute Check (over Lesson 2–6) Image Bank Math Tools

Adding Integers Comparing and Ordering Integers Subtracting Positive and Negative Integers

(over Lesson 2-6)

Find 21(–5). A. 26 B. 16

A B C 0% D

0% D

A

D. –125

0% B

0%

1. 2. 3. 4.

C

C. –105

(over Lesson 2-6)

Find –7(–4). A. 28 B. 3

A B C 0% D

0% D

A

D. –28

0% B

0%

1. 2. 3. 4.

C

C. –3

(over Lesson 2-6)

Find (–9)2. A. –81 B. –18

A B C 0% D

0% D

A

D. 81

0% B

0%

1. 2. 3. 4.

C

C. 18

(over Lesson 2-6)

Evaluate the expression 9(x2 + y2) for x = –4 and y = 11. A. 1,233 B. 1,105

A B C 0% D

0% D

0% B

D. 265

A

0%

1. 2. 3. 4.

C

C. 441

(over Lesson 2-6)

Find the product of –x and y if x = –4, and y = 11. A. –44 B. –15

A B C 0% D

0% D

A

D. 44

0% B

0%

1. 2. 3. 4.

C

C. 15

(over Lesson 2-6)

What is –3(8g) simplified? A. –38g B. –24g A B C 0% D

0% D

0% B

D. –24 + 3g

A

0%

1. 2. 3. 4.

C

C. –24 + g