Objective: Subtract fractions greater than or equal to 1. Module 3 – Lesson 12 Objective: Subtract fractions greater than or equal to 1.

Sprint – Subtracting Fractions with Unlike Units Sprint 3 4 – 1 4 = 1 3 – 3 12 = 1 2 – 1 4 = 5 6 – 5 12 = 3 4 – 1 8 = 10 12 – 6 12 = 4 10 – 3 10 = 3 4 – 2 12 = 2 5 – 1 10 = 3 4 – 5 16 = 4 5 – 1 10 = 2 3 – 5 15 = 4 5 – 5 15 = 3 4 – 1 2 = 1 2 – 5 12 = 1 4 – 1 8 = 10 12 - 5 12 = 3 4 – 3 8 =

Application Problem #1 Max’s reading assignment was to read 15 1 2 pages. After reading 4 1 3 pages, he took a break. How many more pages does he need to read to finish his assignment? 4 1 3 pages 15 1 2 - 4 1 3 pages = ? 15 1 2 - 4 1 3 pages = 15 ( 1 2 * 3 3 ) – 4 ( 1 3 * 2 2 )= 15 3 6 – 4 2 6 = 11 1 6 15 1 2 pages Max still needs to read 11 1 6 pages to finish his assignment.

Application Problem #2 Sam and Nathan are training for a race. Monday, Sam ran 2 3 4 miles, and Nathan ran 2 1 3 miles. How much farther did Sam run than Nathan? 2 3 4 – 2 1 3 = 2 ( 3 4 * 3 3 ) – 2 ( 1 3 * 4 4 ) = 2 9 12 – 2 4 12 = 5 12 Sam = 2 3 4 miles Nathan = 2 1 3 miles ? Sam ran 5 12 of a mile farther than Nathan.

Concept Development – Problem 1 Look at the following problems for a fe minutes before we discuss. 1 1 2 – 1 5 and 1 1 5 – 1 2 What do you notice? They are the same except the half and the fifth are switched around. Sketch a number line number line to show each. How are they different? Find like units by multiplying. Show 2 methods for writing the equation. Show one way taking the half from 1 and the other taking half from 1 and 1 5 . 2 1 1 1/2 1 ½ - 1/5 2 1 1 1/5 1 1/5 - 1/2

Concept Development – Problem 1 Method 1 Method 2 1 1 5 – 1 2 1 1 5 – 1 2 = 6 5 – 1 2 = ( 6 5 * 2 2 ) – ( 1 2 * 5 2 ) = 12 10 – 5 10 = 7 10 1 + 1 5 1 – 1 2 = 1 2 1 2 + 1 5 ( 1 2 * 5 5 ) + ( 1 5 * 2 2 ) 5 10 + 2 10 = 7 10

Concept Development – Problem 2 1 3 4 – 6 7 Method 1 Method 2 1 3 4 – 6 7 1 3 4 – 6 7 = 7/4 – 6/7 = (7/4 * 7/7) – (6/7 * 4/4) =49/28 – 24/28 = 25/28 1 + 3/4 1 – 6/7 = 1/7 1/7 2 1/7 + 3/4 1 1/7 + 3/4 (1/7 * 4/4) + (3/4 * 7/7) 4/28 + 21/28 = 25/28 1 3/4 - 6/7 2 1

Concept Development – Problem 3 3 1 4 – 2 1 2 Method 1 Method 2 3 1/4 – 2 1/2 3 1/4 – 2 1/2 3 (1/4 * 2/2) – 2 (1/2 * 4/4) 3 2/8 – 2 4/8 3 10/8 – 2 4/8 6/8 = 3/4 3 + 2 1/2 2 3 – 2 1/2 = 1/2 1/2 + 1/4 (1/2 * 4/4) + (1/4 * 2/2) 4/8 + 2/8 = 6/8 = 3/4

Concept Development – Problem 4 4 1 2 – 3 2 3 Method 1 Method 2 4 1/2 – 3 2/3 = 9/2 – 11/3 = (9/2 * 3/3) – (11/3 * 2/2) = 27/6 – 22/6 = 5/6 4 1/2 – 3 2/3 4 + 1/2 4 – 3 2/3 = 1/3 1/3 + 1/2 (1/3 * 2/2) + (1/2* 3/3) 2/6 + 3/6 5/6

End of Lesson Activities Student Debrief Problem Set Exit Ticket Homework

Exit Ticket #12 Solve the problems. 5 1 2 – 1 1 3 2) 8 3 4 – 5 5 6

Problem Set 1) Subtract a) 3 1/5 – 2 ¼ b) 4 2/5 – 3 3/4 c) 7 1/5 – 4 1/3 d) 7 2/5 – 5 2/3 e) 4 2/7 – 3 1/3 f) 9 2/3 – 2 6/7 g) 17 2/3 – 5 5/6 h) 18 1/3 – 3 3/8 2) Toby wrote the following: 7 1/4 – 3 3/4 = 4 2/4 = 4 ½. Is Toby’s calculation correct? Draw a diagram to support your answer. 3) Mr. Neville Iceguy mixed up 12 3/5 gallons of chili for a party. If 7 ¼ gallons of chili was mild, and the rest was extra spicy, how much extra spicy chili did Mr. N. Iceguy make? 4) Jazmyne determined to spent 6 1/2 hours studying over the weekend. She spent 1 1/4 hours studying on Friday evening and 2 2/3 hours on Saturday. How much longer does she need to spend studying on Sunday in order to reach her goal?

Homework 1)Subtract a) 3 1/4 – 2 1/3 b) 3 2/3 – 2 3/4 c) 6 1/5 – 4 1/4 d) 6 3/5 – 4 3/4 e) 5 2/7 – 4 1/3 f) 8 2/3 – 3 5/7 g) 18 3/4 – 5 7/8 h) 17 1/5 – 2 5/8 2) Tony wrote the following: 7 1/4 – 3 3/4 = 4 1/4 – 3/4. Is Tony’s statement correct? Draw a diagram to support your answer. 3)Ms. Sanger blended 8 3/4 gallons of iced tea with some lemonade for a picnic. If there were 13 2/5 gallons in the mixture, how many gallons of lemonade did she use? 4) A carpenter has a 10 ½ foot wood plank He cuts off 4 ¼ feet to replace the slat of a deck and 3 2/3 feet to repair a banister. He uses the rest of the plank to fix a stair. How many feet of wood does the carpenter use to fix the stair?