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

2. Sprint – Subtracting Fractions with Unlike Units Sprint
3 4 – = – =
1 2 – = – =
3 4 – = – =
4 10 – = – =
2 5 – = – =
4 5 – = – =
4 5 – = – =
1 2 – = – =
= – =

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

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

5. Concept Development – Problem 1
Look at the following problems for a fe minutes before we discuss.
– and – 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 2 1
1 1/2
1 ½ - 1/5 2 1
1 1/5
1 1/5 - 1/2

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

7. Concept Development – Problem 2
– 6 7
Method 1 Method 2
– 6 7
– 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 = 25/28
1 3/4 - 6/7 2 1

8. Concept Development – Problem 3–
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

9. Concept Development – Problem 4–
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

10. End of Lesson Activities
Student Debrief
Problem Set
Exit Ticket
Homework

11. Exit Ticket #12
Solve the problems. –
2) –

12. 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?

13. 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?