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

2. Fluency Practice – Equivalent Fractions1
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) 2

3. Fluency Practice – Equivalent Fractions
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)

4. Sprint – Find the missing numerator or denominator
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

5. Application Problem
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?
1 meter
1/4
5 units
bent
Bent after 3 units
3 x 5 units = 15 units
15/20 = 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.

6. Concept Development – Problem 1
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)

7. 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

8. Concept Development – Problem 2
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)
3/8
6/8
7/8

9. Concept Development – Problem 2
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

10. Concept Development – Problem 3
6/2 = 2/2 + 2/2 + 2/2 = = ?
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.
6/2
0/2
2/2
4/2 2 1 3

11. Concept Development – Problem 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
Think:
6/2 = 2/2 + 2/2 + 2/2
= 3 x 2/2
= 3 x 1
= 3
6/2
0/2
2/2
4/2 2 1 3

12. Concept Development – Problem 4
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.
0/5
10/5
0/5
10/5
5/5

13. Concept Development – Problem 4
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.
0/5
10/5
5/5 1 2
0/5
10/5
5/5 1 2
8/5

14. Concept Development – Problem 4
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
0/5
10/5
5/5 1 2
8/5

15. Concept Development – Problem 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.) 3
What are the values of those points?
0/3, 3/3, 6/3, 9/3 or 0, 1, 2, 3
0/3
3/3
9/3
6/3

16. Concept Development – Problem 5
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)
0/3
3/3
9/3
6/3 1 3 2
0/3
3/3
9/3
6/3 1 3 2
7/3
0/3
3/3
9/3
6/3 1 3 2
7/3

17. End of Lesson Activities
Debrief
Problem Set
Exit Ticket
Homework

18. Problem Set 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.

19. Exit Ticket 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

20. Homework 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.

21. Fraction Terminology and review of what a fraction is.1
fractions (a little with ordering fractions)
(adding, subtracting, multiplying, and dividing fractions)