Module 3 – Lesson 2Objective – Make equivalent fractions with sums of fractions with like denominators.

½ or (What fraction piece is this?)◦ 1 piece out of 2. It is half of an object.

How do you say ½ ?◦ One half

½ equals how many fourths? (?/4)◦ ½ = 2 fourths (2/4)

½ = ?/6 ◦ Three sixths (3/6)

1/3 = ?/6◦ Two sixths (2/6)

2/3 = ?/12◦ Eight Twelfths (8/12)

3/5 = ?/25◦ Fifteen Twenty-fifths (15/25)

Fluency Practice – Equivalent Fractions

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½ = 2/ ?◦ Two Fourths (2/4)

1/5 = 2/?◦ Two Tenths (2/10)

2/5 = 8/?◦ Eight Twentieths (8/20)

¾ = 9/?◦ Nine Twelfths (9/12)

4/5 = 16/?◦ Sixteen Twentieths (16/20)

3/9 = 6/?◦ Six Eighteenths (6/18)

1/7 = 2/?◦ Two Fourteenths (2/14)

Fluency Practice – Equivalent Fractions

½ = ?/4 1/5 = 2/? 2/5 = ?/10

4/10 = ?/5 6/9 = ?/3 9/12 = ?/4

5/6 = 45/? 45/81 = ?/9 1/6 = ?/12

35/63 = 5/? 5/8 = ?/64 5/8 = 40/?

1/3 = ?/9 ¼ = ?/12 3/7 = ?/21

8/12 = 2/? 12/16 = 3/? 5/6 = ?/42

6/7 = ?/56 4/5 = 28/? 4/5 = ?/35

Sprint – Find the missing numerator or denominator

Mr. Hopkins has a 1 meter wire he is using to make clocks. Each fourth meter is marked off with 5 smaller equal lengths. If Mr. Hopkins bends the wire at ¾ meter, what fraction of the marks is that?

Application Problem

1 meter

1/4

5 units

bent

Bent after 3 units3 x 5 units = 15 units15/20 = 3/4

Mr. Hopkins bent the wire at ¾ m or at 15/20 of the meter.

0/4 4/4

1 mark is 1/20 m.¾ m is the same as 15/20 m.

1/3 + 1/3 Using a number line, mark the end points as zero

and 1. Between zero and 1 estimate to make three parts of equal length and label them with their fractional value.

Now show 1/3 plus 1/3 on your number line using arrows designating lengths.

What did you get as your answer?◦ 2/3 (two thirds)

Concept Development – Problem 1

Express this as a multiplication equation and as an addition sentence.◦ 1/3 + 1/3 = 2 x 1/3 = 2/3

Following the same pattern of adding unit fractions by joining lengths, show 3 fourths (3/4) on a number line.

¼ + ¼ + ¼ = 3 x ¼ = ¾

Concept Development – Problem 1

3/8 + 3/8 + 1/8 (3 eighths + 3 eighths + 1 eighths)

On a number line, again mark the end points as zero and one. Between zero and one, estimate to make 8 parts of equal length. This time only label what is necessary to show 3 eights.

The answer is?◦ 7 eighths (7/8)

Concept Development – Problem 2

3/8 6/8 7/8

3/8 6/8 7/8 Write a math equation to represent the

problem you just demonstrated.◦ 2 x 3/8 + 1/8 = 7/8

Concept Development – Problem 2

6/2 = 2/2 + 2/2 + 2/2 = 1 + 1 + 1 = ? On a number line, mark the end points as 0

halves and 6 halves below the number line. Estimate to make 6 parts of equal length. This time only label 2 halves.

Record the whole number equivalents above on your number line.

Then represent 3 x 2 halves on your number line.

Concept Development – Problem 3

6/20/2 2/2 4/2

21 3

What is the answer?◦ 6 halves or 3

What is the unit of 3?◦ 3 ones

Express this as an addition equation and as an multiplication equation.◦ 6/2 = 2/2 + 2/2 + 2/2 = 3 x 2/2 = 3

Concept Development – Problem 3

6/20/2 2/2 4/2

21 3 Think:6/2 = 2/2 + 2/2 + 2/2 = 3 x 2/2 = 3 x 1 = 3

8 fifths = 5/5 + 3/5 = ? Use a number line. Mark the end points as

0 fifths and 10 fifths below it. Estimate and five a value to the halfway point.

What will be the value of the halfway point?◦ 5 fifths.

Now make 10 parts of equal length from 0 fifths to 10 fifths, with the middle being 5 fifths.

Concept Development – Problem 4

0/5 10/5

0/5 10/55/5

Record the whole number equivalents above the line.

Label 8 fifths (8/5) on the number line and show the sum of 5/5 and 3/5 on the number line.

Express this as an addition equation in two ways: as the sum of fifths and as the sum of a whole number and fifths.

Concept Development – Problem 4

0/5 10/55/5

0 1 2

0/5 10/55/5

0 1 2

8/5

5/5 + 3/5 = 8/5 or 5/5 + 3/5 = 1 3/5 or 1 + 3/5 = 1 3/5

What is another way to express 1 plus 3 fifths is?◦ 1 and 3 fifths.

8 fifths is between what 2 whole numbers?◦ 1 and 2

Concept Development – Problem 4

0/5 10/55/5

0 1 2

8/5

7/3 = 6/3 + 1/3 = 2 x 3/3 + 1/3 = ? Use a number line. Mark the end points as

0 thirds and 9 thirds below the number line. Divide the whole length into three equal smaller lengths and mark their values using thirds. (Compare with a table mate after completing your number line.)

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What are the values of those points?◦ 0/3, 3/3, 6/3, 9/3 or 0, 1, 2, 3

Concept Development – Problem 5

0/3 3/3 9/36/3

Mark the whole numbers above the number line.

Divide each of those whole number lengths into 3 smaller lengths. Mark the number 7 thirds.

Show 7 thirds as two units of 3 thirds and one more third on your number line and in an equation. (Compare with a tablemate after you have completed the step.)◦ (2 x 3/3) + 1/3 = 6/3 + 1/3 = 2 + 1/3 = 2 1/3 (7/3)

Concept Development – Problem 5

0/3 3/3 9/36/3

0 1 32

0/3 3/3 9/36/3

0 1 32

7/3

0/3 3/3 9/36/3

0 1 32

7/3

Debrief Problem Set Exit Ticket Homework

End of Lesson Activities

1. Show each expression on a number line. Solve.◦ a) 2/5 + 1/5 b) 1/3 + 1/3 + 1/3◦ c) 3/10 + 3/10 + 3/10 d) 2 x ¾ + ¼

2. Express each fraction as the sum of two or three equal fractional parts. Rewrite as a multiplication equation. Show letter a) on a number line.◦ a) 6/7 b) 9/2 c) 12/10 d) 27/5

Express each of the following as the sum of a whole number and a fraction. Show c) and d) on a number lines.◦ a) 9/7 b) 9/2 c) 32/7 d) 24/9

Marisela cut four equivalent lengths of ribbon. Each was 5 eights of a yard long. How many yards of fabric did she cut? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.

Problem Set

1) Show each expression on a number line. Solve.◦ a) 5/5 + 2/5 b) 6/3 + 2/3

Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. Show letter b) on a number line.◦ a) 6/9 b) 15/4

Exit Ticket

1. Show each expression on a number line. Solve.◦ a) 4/9 + 1/9 b) ¼ + ¼ + ¼ + ¼ ◦ c) 2/7 + 2/7 + 2/7 d) 2 x 3/5 + 1/5

2. Express each fraction as the sum of two or three equal fractional parts. Rewrite as a multiplication equation. Show letter a) on a number line.◦ a) 6/11 b) 9/4 c) 12/8 d) 27/10

3. Express each of the following as the sum of a whole number and a fraction. Show c) and d) on a number lines.◦ a) 9/5 b) 7/2 c) 25/7 d) 21/9

Natalie sawed five boards of equal length to make a stool. Each was 9 tenths of a meter long. How many meters of board did she saw? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.

Homework

Terminology and review of what a fraction is.◦ http://www.slideshare.net/lauracstelling/fractions-

powerpoint-1◦ http://www.slideshare.net/SnehalBhargava/fractio

ns-11546923◦ http://www.slideshare.net/htaylor2010/understand

ing-fractions (a little with ordering fractions)

◦ http://www.slideshare.net/kkerr/fraction-overview (adding, subtracting, multiplying, and dividing fractions)

◦ http://www.slideshare.net/mstfdemirdag/fractions-8693215

Fraction