Module 3 – Lesson 12

Objective: Subtract fractions greater than or equal to 1.

Sprint – Subtracting Fractions with Unlike Units Sprint

• – = – =• – = – =• – = – =• – = – = • – = – =• – = – =• – = – = • – = – =• - = – =

Application Problem #1

• Max’s reading assignment was to read 15 pages. After reading 4 pages, he took a break. How many more pages does he need to read to finish his assignment?

15 pages

4 pages ?

15 - 4 pages = 15 ( * ) – 4 ( * )=15 – 4 = 11

15 - 4 pages =

Max still needs to read 11 pages to finish his assignment.

Application Problem #2

• Sam and Nathan are training for a race. Monday, Sam ran 2 miles, and Nathan ran 2 miles. How much farther did Sam run than Nathan?

Sam = 2 miles

Nathan = 2 miles

2 – 2 =2 ( * ) – 2 ( * ) =2 – 2 =

?

Sam ran of a mile farther than Nathan.

Concept Development – Problem 1

• Look at the following problems for a fe minutes before we discuss.– 1 – and 1 –

• 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 .

0 21 1 1/2

1 ½ - 1/5 0 21 1 1/5

1 1/5 - 1/2

Concept Development – Problem 1• Method 1 Method 2

1 –

1 + 15

+ ( * ) + ( * ) + =

1 – = – = ( * ) – ( * )= – =

1 – =

Concept Development – Problem 2• 1 –

• Method 1 Method 2

1 –

1 + 3/4

1/7 + 3/4 (1/7 * 4/4) + (3/4 * 7/7)4/28 + 21/28 = 25/28

1 – = 7/4 – 6/7= (7/4 * 7/7) – (6/7 * 4/4)=49/28 – 24/28= 25/28

1 – 6/7 = 1/7 0 1 21/7

1/7 + 3/4

0 1 2

1 3/4 - 6/7

Concept Development – Problem 3• 3 – 2 • Method 1 Method 2

3 1/4 – 2 1/2

3 + 2 1/2

1/2 + 1/4(1/2 * 4/4) + (1/4 * 2/2)4/8 + 2/8 = 6/8 = 3/4

3 1/4 – 2 1/23 (1/4 * 2/2) – 2 (1/2 * 4/4)3 2/8 – 2 4/83 10/8 – 2 4/86/8 = 3/4

3 – 2 1/2 = 1/2 2

Concept Development – Problem 4• 4 – 3 Method 1 Method 2

4 1/2 – 3 2/3

4 + 1/2

1/3 + 1/2(1/3 * 2/2) + (1/2* 3/3)2/6 + 3/6 5/6

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 – 3 2/3 = 1/3

End of Lesson Activities

• Student Debrief• Problem Set• Exit Ticket• Homework

Exit Ticket #12

• Solve the problems.

1) 5 – 1 2) 8 – 5

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?