Module 3 – Lesson 12
Objective: Subtract fractions greater
than or equal to 1.
Sprint – Subtracting Fractions with
Unlike Units Sprint
•
•
•
•
•
•
•
•
•
3 1
– =
4 4
1 1
– =
2 4
3 1
– =
4 8
4
3
– =
10 10
2
1
– =
5 10
4
1
– =
5 10
4
5
– =
5 15
1
5
– =
2 12
10 5
- =
12 12
1
3
– =
3 12
5
5
– =
6 12
10
6
– =
12 12
3
2
– =
4 12
3
5
– =
4 16
2
5
– =
3 15
3 1
– =
4 2
1 1
– =
4 8
3 3
– =
4 8
Application Problem #1
1
2
• Max’s reading assignment was to read 15 pages.
1
3
After reading 4 pages, he took a break. How many
more pages does he need to read to finish his
assignment?
1
4
3
pages
?
1
2
15 pages
1
11
6
1
1
15 - 4 pages =
2
3
1
1
15 - 4 pages =
2
3
1 3
1 2
15 ( * ) – 4 ( *
2 3
3 2
3
2
1
15 – 4 = 11
6
6
6
Max still needs to read
pages to finish his assignment.
)=
Application Problem #2
• Sam and Nathan are training for a race. Monday,
3
1
Sam ran 2 miles, and Nathan ran 2 miles. How
4
3
much farther did Sam run than Nathan?
3
1
4
3
3 3
1 4
( * )–2( * )
4 3
3 4
9
4
5
–2 =
12
12 12
2 –2 =
3
4
Sam = 2 miles
1
3
Nathan = 2 miles
?
2
2
=
5
12
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
2
–1 –
1
5
1
5
and 1 –
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
1
from 1 and the other taking half from 1 and .
5
0
1
1 1/2
2
1 ½ - 1/5
0
1 1 1/5
1 1/5 - 1/2
2
Concept Development – Problem 1
• Method 1
1
5
1 –
1
2
1+
1–
1 1
= 1
2 2 +
1
5
1
2 5
1 5
1 2
( * )+( * )
2 5
5 2
5
2
7
+ =
10 10 10
Method 2
1 1
1 –
5 2
6 1
= –
5 2
6 2
1 5
=( * )–( * )
5 2
2 2
12
5
= –
10 10
7
=
10
Concept Development – Problem 2
3
4
• 1 –
6
7
• Method 1
3 6
1 –
4
Method 2
7
1 + 3/4
1 – 6/7 = 1/7 0 1 1/7 + 1
/
1/7 + 3/4
7 3/4
(1/7 * 4/4) + (3/4 * 7/7)
4/28 + 21/28 = 25/28
3
2
6
1 –
4 7
= 7/4 – 6/7
= (7/4 * 7/7) – (6/7 * 4/4)
=49/28 – 24/28
= 25/28
1 3/4 - 6/7
0
1
2
Concept Development – Problem 3
1
4
• 3 –2
1
2
• Method 1
Method 2
3 1/4 – 2 1/2
3+
2 1/2
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
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
Concept Development – Problem 4
1
2
• 4 –3
2
3
Method 1
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
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
End of Lesson Activities
•
•
•
•
Student Debrief
Problem Set
Exit Ticket
Homework
Exit Ticket #12
• Solve the problems.
1
2
3
4
1) 5 – 1
2) 8 – 5
1
3
5
6
Problem Set
• 1) Subtract
– a) 3 1/5 – 2 ¼
– d) 7 2/5 – 5 2/3
– g) 17 2/3 – 5 5/6
b) 4 2/5 – 3 3/4
e) 4 2/7 – 3 1/3
h) 18 1/3 – 3 3/8
c) 7 1/5 – 4 1/3
f) 9 2/3 – 2 6/7
• 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
– d) 6 3/5 – 4 3/4
– g) 18 3/4 – 5 7/8
b) 3 2/3 – 2 3/4
e) 5 2/7 – 4 1/3
h) 17 1/5 – 2 5/8
c) 6 1/5 – 4 1/4
f) 8 2/3 – 3 5/7
• 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?