treasures, ch. 2, lesson 1

Treasures from the Attic

Chapter 2: Addition & Subtraction with Fractions

M3

Sew What

Lesson 1Mrs. Matthews/CES

Objectives

Extend your understanding of the concepts of addition and subtraction to include

fractions.

Estimate to compare combinations of fractions to benchmarks like 1/2 and 1.

Develop a variety of concrete methods and written algorithms for adding proper

fractions with like and unlike denominators.

Find a variety of fractions that combine to make 1 whole.

Materials

Folded fraction strips from the first chapter.

Rectangular fraction pieces or other area models for fractions.

Initiate

Sew What

In the trunk in the attic, Tori and Jordan found some records from the Rabbit Hutch

General Store about a number of purchases of cloth made by Mr. Diwoky, the town

tailor. Because he was always making suits and dresses for the people in town, he

bought cloth and other material from the store every week. Every time he bought

material, their great-great-grandma first estimated the total amount that he was buying.

The following are some of the amounts of material that Mr. Diwoky bought in February.

 If you think that the total amount is more than 1 yard,

 put your thumb up.

 If it is less than 1 yard, put your thumb down.

 If it is exactly equal to 1 yard, put your thumb sideways.

Be sure to explain your reasoning.

More that 1

Less than 1

Equal to 1

Challenge!

1/4 yard, 1/3 yard and 1/6 yard

1/2 yard, 1/3 yard and 1/4 yard

1/3 yard, 1/8 yard, 1/4 yard and 1/6 yard

Can you suggest your own challenge & write it below?

Benchmark = 1/2

Explain your reasoning.

Benchmark = 2

Explain your reasoning.

Investigate

Sew What

Complete "Is This 1?"

on page 33

of your

Student Mathematician's Journal.

Use drawings and other means to explain the reasoning for your answers.

Less than 1 Equal to 1 greater than 1

Is This 1?, p. 33

2/3 + 1/2


Is This 1?, p. 33

3/4 + 1/3


Is This 1?, p. 33

5/8 + 1/4


Is This 1?, p. 33

1/3 + 1/2 + 1/4


Is This 1?, p. 33

2/8 + 1/2 + 1/4

Tori and Jordan's Great-great-grandma Milotz had to not only estimate but determine

the exact amounts of cloth that Mr. Diwoky bought so she could charge him the

correct amount.

One day, Mr. Diwoky came in and needed exactly 1 yard of cloth. Grandma had

several remnants of cloth (pieces left over when most of the cloth has already been

sold.) .

Grandma had one remnant of each of the following sizes:

1/2 yard

2/3 yard

3/4 yard

1/8 yard

1/4 yard

3/8 yard

She asked Mr. Diwoky to choose any number of pieces so the total would be exactly 1 yard. What

combinations might he choose?

Complete "Make 1"

on page 35

of your

Student Mathematician's Journal.

Use drawings and other means to explain the reasoning for your answers.

1. Mrs. Militz had the following remnants of cloth. Mr. Diwoky needs to buy exactly 1

yard of cloth. List all the different ways that he might buy exactly 1 yard using two

remnants.

1/8 yard (four pieces available)

1/6 yard (three pieces available)

1/4 yard (two pieces available)




5/8 yard (one piece available)





Possible Combinations Using Exactly Two Remnants:

Click on the information button.

Make 1, #2 (page 35)

List three other ways that Mr. Diwoky might have purchased exactly 1 yard of cloth if he

bought three or more pieces. Use diagrams or equations to show that your choices total

exactly 1 yard. You may reuse the remnants with each combination. For example, Mr.

Diwoky used 1/2 twice to make 1 whole when he considered only two remnants.

He can reuse those for other combinations.

Think Deeply Journal, p. 37Mathematician's

Journal

1. Mrs. Militz had the following remnants of cloth. Mr. Diwoky needs to buy exactly 1 yard of cloth.

List all the different ways that he might buy exactly 1 yard using more than two remnants. (You

may reuse the remnants for each combination.)

1/8 yard (four pieces available)

1/6 yard (three pieces available)










Think Deeply Journal, p. 39Mathematician's

Journal

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treasures, ch. 2, lesson 1

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