1
U n t er r i ch t spl a n
Sub t rac t M ixe d Numb e rs (Like
De no minat o rs )
Altersgruppe: 4 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 4 .5 b, 5 .6
Virginia - Mathematics Standards of Learning (2016): 4 .5 .b, 4 .5 .c ,
5 .6.a
Fairfax County Public Schools Program of Studies: 4 .5 .b.6, 5 .6.a.1,
5 .6.a.2, 5 .6.a.3 , 5 .6.a.4
Online-Ressourcen: S ay C he e se
Opening
T eacher
present s
St udent s
pract ice
Mat h game
5
12
12
14
4
min
min
min
min
min
Class
discussion
Closing
M at h Obj e c t i v e s
E x pe r i e nc e a visual model for subtracting mixed numbers
P r ac t i c e borrowing
L e ar n to subtract mixed numbers with like denominators
De v e l o p arithmetic skills
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Ope ni ng | 5 min
Display the following problem. Have the students solve it in their
notebooks.
When the students are done, ask: What is the first step?
The first step is to subtract in the ones place. We subtract 1 from
4 to get 3.
Display the following:
A sk : What is the next step?
We subtract in the tens place. We subtract 7 from 2. But 7 is too
large. We need to borrow from the 3 in the hundreds place to
make the 2 in the tens place into 12.
Display the following:
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A sk : What is the final step?
We subtract in the hundreds place. We subtract 1 from 2 to get 1.
Display the following:
S ay : Today we are going to look at subtraction of mixed numbers.
We may need to borrow in these problems, too.
T e ac he r pr e se nt s M at h game : S ay C he e se - S ubt r ac t
M i x e d N umbe r s | 12 min
Using Presentation Mode, present Matific ’s episode S ay C he e se
- S ubt r ac t M i x e d N umbe r s to the class, using the projector.
The goal of the episode is to subtract mixed numbers with like denominators.
E x a m p le :
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A sk : What problem are we trying to solve?
The question asks us to subtract
from
.
A sk : How does the image of the bread and cheese help us?
The bread and cheese show us the mi nue nd . They represent
There are slices of bread completely covered with cheese,
representing the 3. Then another slice of bread has
covered with cheese. Together, that makes
.
of it
.
A sk : How do we represent the subtraction in this situation?
We feed the monster in the corner
subtraction.
of cheese to show the
S ay : We don’t have 5 strips of cheese of size on the bread with
which to feed the monster. How can we get 5 strips of cheese this
size?
We can exchange 1 whole slice of cheese for 6 strips of size
each.
Move 1 whole slice of cheese off of the bread. Use the arrows (
or ) to change the cheese strips into sixths. Place 6 strips of
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cheese of size
each onto the empty slice of bread.
S ay : Now we have enough strips to do the subtraction. What should
we do next?
We should feed the monster 5 strips of cheese of size
each to
represent subtracting .
Move 5 strips of cheese of size
each to the monster’s mouth.
A sk : What is the answer to the problem?
Enter the students’ answer by clicking on the
.
If the answer is correct, the episode will proceed to the next problem.
If the answer is correct but not in lowest terms, a message stating this will
appear. Click on the to proceed.
If the answer is incorrect, the problem will wiggle.
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S t ude nt s pr ac t i c e M at h game : S ay C he e se - S ubt r ac t
M i x e d N umbe r s | 12 min
Have the students play S ay C he e se - S ubt r ac t M i x e d
N umbe r s on their personal devices. Circulate, answering
questions as necessary.
C l ass di sc ussi o n | 14 min
Display the following problem:
A sk a student to come to the board to make a diagram that
represents
.
Possible answer:
A sk : How do we represent subtracting
We can erase 1 whole rectangle and
?
of the other rectangle.
A sk : What is the answer to the problem?
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The answer is
, which simplifies to
.
A sk : How could we see that the answer is
problem, without drawing a diagram?
directly from the
We can subtract each part separately – the whole number part
and the fraction part of the mixed number. First, we subtract the
whole numbers (3 minus 1) to get 2. Then, we subtract the
fractions ( minus ) to get . We pair the whole number with the
fraction to get
S ay : The problem
We can’t subtract
, which simplifies to
minus
.
is not as easy to solve. Why not?
from . We need to borrow.
S ay : First, let’s draw a diagram representing the minuend.
A sk a student to come to the board to make a diagram that
represents
.
Possible answer:
A sk : What do we do to the diagram to be able to subtract
?
We need to partition one of the colored rectangles into fifths:
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A sk : How would we rewrite
rectangles into fifths?
We rewrite it as
.
A sk : How do you know that
We know that
to show that we just cut one of the
is equivalent to
is equal to 2 plus
?
. So we can change
into
an i mpr o pe r f r ac t i o n and get . We keep the 2 the same. So
we have
. So
is equivalent to
.
Display the following:
A sk a student to come to the board to erase
from the diagram.
Possible answer:
A sk : What is the answer to the subtraction problem?
The answer is
.
A sk : How can we see the answer ( ) directly from the subtraction
problem, without using the diagram?
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Once we rewrite
as
, the problem is easy. We subtract the
whole numbers (1 from 2) to get 1. Then we subtract the
fractions ( from ) to get
. We pair both numbers to get
.
A sk the students to solve the following problems, without drawing
models:
Review solutions to the four problems. Discuss any questions the
students may have.
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C l o si ng | 4 min
Display the following incorrect work for the problem
.
A sk : What mistake was made here?
When the person borrowed from the 4, he put a 1 in front of the
numerator, making it 11. It is not 11. When we subtract whole
numbers and borrow, we write a 1 because we are borrowing 10
from the place to the left. Here, however, we are not borrowing
10. We are only borrowing 1. We need to change the numerator to
indicate that we borrowed 1.
A sk : How could we correct the mistake?
The numerator of the top fraction should be 6. We borrowed 1
from the 4. So we borrowed . Adding
to the
there makes .
A sk : What is the correct answer to the problem?
The correct answer to the problem is
.
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that was already