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

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 =

Application Problem: Use the RDW (read, draw, write) process to solve the following problem. A farmer uses 3 4 of his field to plant corn, 1 6 of his field to plant beans, and the rest to plant wheat. What fraction of his crop is used for wheat?

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.

Concept Development – Problem 1: We’ll need to change both units. 1 2 - 1 3 = 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. 1 2 - 1 3 = 3 6 - 2 6 = 1 6 (3 sixths – 2 sixths = 1 sixth) With unlike units: 1 half – 1 third = 1 sixth

Concept Development – Problem 2: 1 3 − 1 4 Subtract ¼ from 1 3 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 - 1 3 , 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 1 3 − 1 4 = 4 12 − 3 12 Say the subtraction sentence and answer with like & unlike units. 4 twelfths – 3 twelfths = 1 third – 1 fourth = 1 twelfth

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 − 1 5 = 5 10 − 2 10 = 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.

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 =

Exit Ticket

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 =

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.

HOMEWORK TASK Assign Homework Task. Due Date: ______________

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 =

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?