1. Engage NY Math Module 3
Lesson 5: Subtract fractions with unlike units using the strategy of creating equivalent fractions.

2. SPRINT Subtract. Give each answer in simplest form. 4 - 𝟏 𝟐 =
4 - 𝟏 𝟐 =
3 - 𝟏 𝟐 =
2 - 𝟏 𝟐 =
1 − 𝟏 𝟐 =
1 - 𝟏 𝟑 =
2 - 𝟏 𝟑 =
4 - 𝟏 𝟑 =
4 - 𝟐 𝟑 =
2 - 𝟐 𝟑 =
2 - 𝟏 𝟒 =
2 - 𝟑 𝟒 =
3 - 𝟑 𝟒 =
3 - 𝟏 𝟒 =
4 - 𝟑 𝟒 =
2 - 𝟏 𝟏𝟎 =
3 - 𝟗 𝟏𝟎 =
2 - 𝟕 𝟏𝟎 =
4 - 𝟑 𝟏𝟎 =
3 - 𝟏 𝟓 =
3 - 𝟐 𝟓 =
3 - 𝟒 𝟓 =
3 - 𝟑 𝟓 =
2 - 𝟖 𝟏𝟐 =
3 - 𝟐 𝟔 =
4 - 𝟐 𝟏𝟐 =
2 - 𝟗 𝟏𝟐 =
4 - 𝟐 𝟖 =
3 - 𝟓 𝟏𝟎 =
3 - 𝟕 𝟏𝟎 =
4 - 𝟑 𝟕 =
4 - 𝟒 𝟕 =
2 - 𝟕 𝟖 =

3. Application Problem:
Use the RDW (read, draw, write) process to solve the following problem.
A farmer uses of his field to plant corn, of his field to plant beans, and the rest to plant wheat. What fraction of his crop is used for wheat?

4. Concept Development 3 boys - 1 girl =
Talk with your tablemates about the answer to this problem.
3 boys – 1 girl, you can’t do it. You don’t have any girls.
We need to rename the units as students.
3 students – 1 student = 2 students
1 half – 1 third =
How is this problem the same as the one before?
The units are not the same. We have to change the units before we can say an answer.

5. Concept Development – Problem 1:
We’ll need to change both units. =
We can draw one rectangle, partition it into 2 equal units. Then we’ll write 1 half below one part to make it easier to see what 1 half is after I change the units.
We can make thirds with horizontal lines and write 1 next to it. (We make the new units by drawing thirds horizontally.)
How many new units do we have?
6 units
1 half is how many sixths?
1 half is 3 sixths
1 third is how many sixths?
1 third is 2 sixths
Say the subtraction sentence and answer with like units.
= = (3 sixths – 2 sixths = 1 sixth)
With unlike units: 1 half – 1 third = 1 sixth

6. Concept Development – Problem 2:
1 3 − 1 4
Subtract ¼ from and then talk to your table about your process.
To create like units we can do exactly as we did when adding or when subtracting ½ , make smaller units.
First draw parts vertically just like when we create a bar diagram. Then partition horizontally.
The only thing we have to remember is that we are subtracting the units, not adding.
Let’s draw a diagram to help solve this problem.
What is our smaller unit?
Twelfths
1 third is?
4 twelfths
1 fourth is?
3 twelfths − = − 3 12
Say the subtraction sentence and answer with like & unlike units.
4 twelfths – 3 twelfths = 1 third – 1 fourth = 1 twelfth

7. Concept Development – Problem 3:
1 2 − 1 5
Solve this problem in your math notebook. When you finish, check your work with a tablemate.
1 2 − = − = 3 10
What do you notice about all three of our first problems?
All the fractions have a numerator of 1.
Fractions with a numerator of 1 are called unit fractions and are generally easier to manipulate. Let’s try this next problem subtracting from a non-unit fraction.

8. Concept Development – Problems 4-6:
Solve the following problems in your journal. Draw a picture using a rectangular fraction model. When you are finished, check your work with your tablemates.
2 3 − 1 4 =
1 2 − 2 7 =
4 5 − 2 3 =

9. Exit Ticket

10. Problem Set
1. For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer. a) 𝟏 𝟑 − 𝟏 𝟒 = b) 𝟐 𝟑 − 𝟏 𝟐 = c) 𝟓 𝟔 − 𝟏 𝟒 = d) 𝟐 𝟑 − 𝟏 𝟕 = e) 𝟑 𝟒 − 𝟑 𝟖 = f) 𝟑 𝟒 − 𝟐 𝟕 =

11. Problem Set
Solve the following problems. Draw a picture and/or write the number sentence that proves the answer. Simplify your answer.
Mr. Penman had 𝟐 𝟑 liter of salt water. He used 𝟏 𝟓 liter for an experiment. How much salt water does Mr. Penman have left?
Sandra says that 𝟒 𝟕 - 𝟏 𝟑 = 𝟑 𝟒 because all you have to do is subtract the numerators and subtract the denominators. Convince Sandra that she is wrong. You may have to draw a rectangular fraction model to help.

12. HOMEWORK TASK
Assign Homework Task. Due Date: ______________

13. Homework Task
1. The picture shows ¾ of the square shaded. Use the picture to show how to create equal fractions with the units that would allow you to subtract 1/3, and then find the difference.
𝟑 𝟒 − 𝟏 𝟑 =
2. Find the difference. Use a rectangular fraction model to show how to convert to fractions with common denominators.
a) 𝟓 𝟔 − 𝟏 𝟑 =
b) 𝟐 𝟑 − 𝟏 𝟐 =
c) 𝟓 𝟔 − 𝟏 𝟒 =
d) 𝟒 𝟓 − 𝟏 𝟐 =
e) 𝟐 𝟑 − 𝟐 𝟓 =
f) 𝟓 𝟕 − 𝟐 𝟑 =

14. Homework Task
Robin used 𝟏 𝟒 pound of butter to make a cake. Afterward she had 𝟓 𝟖 of a pound left. How much butter did she have at first?
Katrina needs 𝟑 𝟓 kilogram of flour for a recipe. Her mother has 𝟑 𝟕 kilogram in her pantry. Is this enough flour to make the recipe? If not, how much more will she need?