ALGEBRA Name Lesson 6 - Stafford Township School District

Name

Patterns with Fractions

Essential Question How can you use addition or subtraction to describe a pattern or create a sequence with fractions?

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ALGEBRA

Lesson 6.8

Number and Operations-- Fractions--5.NF.A.1 MATHEMATICAL PRACTICES MP5, MP7, MP8

Mr. Patrick wants to develop a new chili recipe for his restaurant. Each

batch he makes uses a different amount of chili powder. The first batch

uses

3

1 _

2

ounces,

the

second

batch

uses

4

5 _

6

ounces,

the

third

uses

6

1 _

6

ounces,

and the fourth uses 71_2 ounces. If this pattern continues, how much chili

powder will he use in the sixth batch?

You can find the pattern in a sequence by comparing one term with the next term.

STEP 1

Write the terms in the sequence as equivalent fractions with a common denominator. Then examine the sequence and compare the consecutive terms to find the rule used to make the sequence of fractions.

+12_6_

difference between terms

31_2_, 45_6_, 61_6_, 71_2_,...

oz,

oz,

oz,

oz

batch 1 batch 2 batch 3 batch 4

terms with common denominator

STEP 2 Write a rule that describes the pattern in the sequence.

? Is the sequence increasing or decreasing from one term to the next? Explain.

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Rule: ________

STEP 3 Extend the sequence to solve the problem.

31_2_, 45_6_, 61_6_, 71_2_, _ , _ So, Mr. Patrick will use _ ounces of chili powder in the sixth batch.

Chapter 6 395

Example Find the unknown terms in the sequence.

_ _ _ 13_4_, 1_19_6_ , 13_8_ , 1_13_6_ ,

,

,

,

_7__ 16

,

1__ 4

STEP 1 Write the terms in the sequence as equivalent fractions with a common denominator.

_ , _ , _ , _ , _ ? , _ ? , _ ? ,_ , _

STEP 2 Write a rule describing the pattern in the sequence. ? What operation can be used to describe a sequence that increases?

__

? What operation can be used to describe a sequence that decreases?

__

Rule: _____

STEP 3 Use your rule to find the unknown terms. Then complete the sequence above.

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MATHEMATICAL PRACTICES 1

Analyze How do you know whether your rule for a sequence would involve addition or subtraction?

Try This!

A Write a rule for the sequence. Then find the unknown term.

_ 1_11_2_, 5_6_,

,

1_3_,

_1__ 12

Rule: _____

B Write the first four terms of the sequence.

Rule:

start

at

1_4,

add

3 _

8

_ , _ , _ , _

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396

Name

SShhaarree aanndd SShhooww

MATH

BOARD

Write a rule for the sequence.

1. 1_4, 1_2, 3_4, ...

Think: Is the sequence increasing or decreasing?

Rule: __

2. 1_9, 1_3, 5_9, ...

Rule: __

Write a rule for the sequence. Then, find the unknown term.

3.

_130_,

2_5,

__

,

3_5,

_7_ 10

4. 102_3, 91_118_, 85_9, __ , 64_9

Rule: __

Rule: __

OOnn YYoouurr OOwwnn

Write the first four terms of the sequence.

5.

Rule:

start

at

53_4,

subtract

5 _

8

_ , _ , _ , _

7. Rule: start at 21_3, add 21_4

_ , _ , _ , _

6.

Rule:

start

at

3_8,

add

_3_

16

_,_,_,_

8.

Rule:

start

at

8_9,

subtract

_1_

18

_ , _ , _ , _

9.

MATHEMATICAL PRACTICE

7

Look for a Pattern Vicki started jogging. The first time she ran, she

ran

_3_

16

mile.

The

second

time,

she

ran

3 _

8

mile,

and

the

third

time,

she

ran

_9_

16

mile.

If

she

continued this pattern, when was the first time she ran more than 1 mile? Explain.

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10.

DEEPER Mr. Conners drove 781_3 miles on Monday, 77_112_ miles on Tuesday, and

755_6 miles on Wednesday. If he continues this pattern on Thursday and Friday, how

many fewer miles will he drive on Friday than on Tuesday?

Chapter 6 ? Lesson 8 397

MATHEMATICAL PRACTICES ANALYZEt-00,'034536$563&t13&$*4*0/

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11.

When

Bill

bought

a

marigold

plant,

it

was

1 _

4

inch

tall.

After

the

first

week,

it

measured

1

_1_

12

inches

tall.

After

the

second

week,

it

was

11_112_

inches.

After

week

3,

it

was

2

3 _

4

inches

tall.

Assuming

the

growth

of

the

plant

was

constant, what was the height of the plant at the end of week 4?

12.

SMARTER What if Bill's plant grew at the same

rate but was 11_2 inches when he bought it? How tall

would the plant be after 3 weeks?

13.

SMARTER Kendra hiked each day for a week. The first day

she

hiked

1 _

8

mile,

the

second

day

she

hiked

3 _

8

mile,

and

the

third

day

she

hiked

5 _

8

mile.

What is the rule for the distance Kendra hikes each day? Show how you can check your answer.

If the pattern continues, how many miles will Kendra hike on day 7? Explain how you found your answer.

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398

Name

Patterns with Fractions

Practice and Homework

Lesson 6.8

COMMON CORE STANDARD--5.NF.A.1 Use equivalent fractions as a strategy to add and subtract fractions.

Write a rule for the sequence. Then, find the unknown term.

1.

1_,

2

2_3,

5__ , _ 6

1,

11_

6

2. 13_, 13_, 21_,

, 27_

8 4 8_ 8

Think: The pattern is increasing. Add 1__ to find

6

the next term.

Rule: ____

Rule: ____

3.

1_9_,

10

1_7_,

10

_,

1_3_,

10

1_1_

10

4.

2_5_,

12

21_,

6

1_1_1,

12

_,

1_5_

12

Rule: ____

Write the first four terms of the sequence.

5.

Rule:

start

at

1 _

2

,

add

1 _

3

Rule: ____

6.

Rule:

start

at

31_8,

subtract

3 _

4

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PPrroobblleemm SSoollvviinngg

7.

Jarett's

puppy

weighed

3

3 _

4

ounces

at

birth.

At one week old, the puppy weighed 51_8 ounces. At two weeks old, the puppy weighed 61_2 ounces.

If the weight gain continues in this pattern, how

much will the puppy weigh at three weeks old?

8. A baker started out with 12 cups of flour. She had

9

1 _

4

cups

of

flour

left

after

the

first

batch

of

batter

she made. She had 61_2 cups of flour left after the

second batch of batter she made. If she makes

two more batches of batter, how many cups of

flour will be left?

_______

_______

9. WRITE Math Make up your own sequence of 5 fractions or mixed

numbers. Offer the sequence to another student to try and find the next fraction in the sequence.

Chapter 6 399

Lesson Check (5.NF.A.1)

1. What is a rule for the sequence?

5_6, 11_2, 21_6, 25_6, ...

2.

Jaime

biked

51_4

miles

on

Monday,

6

7 _

8

miles

on

Tuesday,

and

8

1 _

2

miles

on

Wednesday.

If

he

continues the pattern, how many miles will he

bike on Friday?

Spiral Review (5.OA.A.2, 5.NBT.B.5, 5.NTB.B.7)

3. Jaylyn rode her bicycle in a bike-a-thon. She rode 33.48 miles in 2.7 hours. If she rode at the same speed, what was her speed in miles per hour?

4. One week a company filled 546 boxes with widgets. Each box held 38 widgets. How many widgets did the company pack in boxes that week?

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5. Write an expression that represents the statement "Add 9 and 3, then multiply by 6."

6. Mason took 9.4 minutes to complete the first challenge in the Champs Challenge. He completed the second challenge 2.65 minutes faster than the first challenge. How long did it take Mason to complete the second challenge?

400

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