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U n t er r i ch t spl a n
F rac t io n Ad d it io n Co mp aris o ns
Altersgruppe: 5 t h Gr ade
Texas - TEKS: G4 .3 .N O.E , G5 .3 .N O.H
Riverside USD Scope and Sequence: 5 .N F .2 [5 .3 ]
Oklahoma Academic Standards Mathematics: 5 .N .3 .2, 5 .N .3 .3
Virginia - Mathematics Standards of Learning (2009): 4 .2a, 5 .6,
K .4 b
Common Core: 5 .N F .A .2
Mathematics Florida Standards (MAFS): 5 .N F .1.2
Alaska: 4 .N F .3 a, 4 .N F .3 c , 4 .N F .3 d, 5 .N F .1, 5 .N F .2
Minnesota: 4 .1.2.3 , 5 .1.3 , 5 .1.3 .1
Fairfax County Public Schools Program of Studies: 4 .2.a.5 , 4 .2.a.6,
5 .6.a.2, 5 .6.a.4 , K .4 .b.1
Nebraska Mathematics Standards: M A .5 .1.2.h
South Carolina: 4 .N S F .3 , 4 .N S F .3 a, 4 .N S F .3 c , 5 .N S F .1,
5 .N S F .2
Indiana: 4 .A T .5 , 4 .C .5 , 4 .C .6, 5 .A T .2, 5 .C .4
Georgia Standards of Excellence: M GS E 5 .N F .2
Virginia - Mathematics Standards of Learning (2016): 4 .5 .b, 4 .5 .c ,
5 .6.a, 5 .6.b
Online-Ressourcen: S ay C he e se
Opening
T eacher
present s
St udent s
play
Class
discussion
Closing
5
12
15
10
5
min
min
min
min
min
ZIE L E :
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Experience a visual model for fractions
Practice representing fractions
Learn to compare sums of fractions
Develop a sense of the relative size of fractions
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Ope ni ng | 5 min
Display the following scale:
Write on one side of the scale and on the other.
A sk: Which fraction is heavier (larger)? How do you know?
The larger fraction is . Eight ninths is close to 1, whereas is in
the middle between 0 and 1.
Write on one side of the scale and on the other.
A sk: Which fraction is heavier (larger)? How do you know?
The larger fraction is . Each of these fractions is one piece away
from a whole; needs to be whole and needs to be whole. One
fourth is twice the size of . So is missing a larger piece and is
therefore the smaller fraction.
Write on one side of the scale and
on the other.
A sk: Which fraction is heavier (larger)? How do you know?
The larger fraction is . Seven twelfths is larger than (
is smaller than (
). So
is greater than .
T e ac he r pr e se nt s S ay C he e se | 12 min
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), and
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Present Matific ’s episode S a y C h e e s e - C o m p a r e A d d it iv e
E x p r e s s io n s to the class, using the projector.
The goal of the episode is to compare two additive expressions involving
fractions to determine which is larger.
E x a m p le :
S ay: Please read the instructions.
Students can read the instructions.
S ay: We want to compare the addition problem on the left with the
fraction on the right, to determine which is larger. How do the
pieces of bread and cheese help us?
The two pieces of bread on the left represent the two adde nds .
The piece of bread on the right represents the sum. The amount
of cheese on each slice represents each fraction. We can move
the cheese from the addends onto one piece of bread. Then we
can compare the bread on the left with the bread on the right to
see which is more covered by cheese.
Move the cheese from the addends onto one piece of bread.
A sk the students which symbol is appropriate:
Click on the
,
, or
.
to enter the students’ answer.
If the answer is correct, the episode will proceed to the next problem.
If the answer is incorrect, the problem will wiggle.
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The episode will present a total of six problems. The first three will
contain an addition problem to the left of the and a fraction to
its right. The final three will contain two addition problems,
separated by the .
For the final three problems, the bread and cheese will not be set up.
You can move the bread from the basket and place the cheese on top
of it. To change the size of the cheese strips, click on the arrows ( or
).
S t ude nt s pl ay S ay C he e se | 15 min
Have the students play S ay C he e se - C o mpar e A ddi t i v e
E x pr e ssi o ns on their personal devices. Circulate, answering
questions as necessary.
C l ass di sc ussi o n | 10 min
Display the following situations:
Paul leaves school and walks of a mile to the library. After checking out a
book, he continues home. He walks of a mile home.
Shantel leaves school and walks of a mile to the library. After checking out a
book, she continues home. She walks of a mile home.
A sk: Who walked further altogether? How do you know?
Shantel walked further. If we compare each fraction in Shantel’s
situation to each fraction in Paul’s situation, both times Shantel’s
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fractions are larger. (
and
fractions must be larger.
). So the sum of the larger
Display the following situations:
Chris uses of a cup of sugar in one cookie recipe and of a cup in another.
Maria uses of a cup of sugar in one cookie recipe and of a cup in another.
A sk: Who used more sugar altogether? How do you know?
Chris used more sugar. For each recipe, he used more sugar. (
and
). So altogether his sum is larger.
Display the following situations:
Sara spends of an hour on her math homework and of an hour on her
reading.
Peter spends of an hour on his math homework and of an hour on his
reading.
A sk: Who spent more time on homework altogether? How do you
know?
Peter spent more time. The time they spent on reading was equal
(
), but Peter spent longer on math (
).
Ask students to develop their own word problems that involve
addition of fractions. Have them share with the class. Encourage
the students to create different situations where fractions may
appear (in distances, recipes, time, weights, etc.). Some problems
could be written on the board to show the range of situations.
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C l o si ng | 5 min
Tell the students that they are going to estimate the answer to
some addition problems. Without doing any calculations, they
should examine the problem and determine if the sum is greater
than or less than one. They should give a “thumbs up” sign if the sum
is greater than one or a “thumbs down” sign if the sum is less than
one. All students can participate simultaneously.
State the following problems, one at a time. Check for student
understanding by surveying the students’ hand signals. Discuss any
discrepancies.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
If time allows, lead a discussion of how the students know whether
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an answer is greater than or less than one.
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