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U n t er r i ch t spl a n
Co nve rt ing F rac t io ns t o De c imal s
- 3 De c imal Pl ac e s
Altersgruppe:
Online-Ressourcen: F r ac t i o n t o De c i mal
Opening
T eacher
present s
St udent s
play
Ext ension
6
10
12
15
4
min
min
min
min
min
Closing
ZIE L E :
E x pe r i e nc e multiple representations of numbers
P r ac t i c e finding equivalent fractions
L e ar n to convert fractions to decimals
De v e l o p critical thinking skills
Ope ni ng | 6 min
Have the students work in pairs. Display the following table:
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A sk the students to copy the table. They should make check marks
when the number in the left column is a factor of 10, 100, or 1000.
When the students have filled in their tables, share.
A sk: Which numbers are factors of 10?
The numbers two and five are factors of 10.
A sk: Which numbers are factors of 100?
The numbers two, four, and five are factors of 100.
A sk: Which numbers are factors of 1000?
The numbers two, four, five, and eight are factors of 1000.
S ay: So two, four, five, and eight are factors of 1000, but six is
not. All of these numbers are even. How is six different from two,
four, and eight?
Six has a factor of three. Two, four, and eight are all powers of
two.
A sk: Can we use the fact that six is a multiple of three to explain
why six is not a factor of 1000?
Three is not a factor of 1000. So no multiple of three can be a
factor of 1000.
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T e ac he r pr e se nt s F r ac t i o n t o De c i mal – 3 De c i mal
P l ac e s | 10 min
Present Matific ’s episode F r ac t i o n t o De c i mal – 3 De c i mal
P l ac e s to the class, using the projector.
The goal of the episode is to convert fractions to decimals.
E x a m p le :
S ay: Read the instruction.
Students should read the instruction at the bottom of the screen.
S ay: There are three buttons in the episode, “Expand by 2”, “Expand
by 5”, and “Simplify”. We can use these buttons to make equivalent
fractions to the fraction we are given. Our goal is to have the
denominator be 10, 100, or 1000, so that we can then easily convert
to a decimal. Which button should we click on first in order to
change our fraction’s denominator to a power of 10?
Click on the button that the students suggest.
A sk: Does our fraction have a denominator of 10, 100, or 1000 yet?
Students should respond based on the episode.
Continue to ask the students for guidance as to what steps to take
to arrive at a denominator that is a power of 10.
Once the denominator is 10, 100, or 1000, ask the students how to
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write it as a decimal.
Enter their decimal by clicking on the
.
If the answer is correct, the episode will proceed to the next fraction.
If the answer is incorrect, the instruction will wiggle.
The episode will present a total of six fractions to convert to
decimals.
S t ude nt s pl ay F r ac t i o n t o De c i mal – 3 De c i mal P l ac e s |
12 min
Have the students play F r ac t i o n t o De c i mal – 3 De c i mal
P l ac e s on their personal devices. Circulate, answering questions
as necessary.
E x t e nsi o n | 15 min
S ay: We know that
0.25. Since seven is not a factor of 100,
we cannot use the exact same process for . However, we can
approximate. Seven is a factor of 98, which is close to 100. What
numerator makes this statement true:
?
The missing numerator is 14.
S ay: Yes, so
, which is close to . So is close to 0.14. Let’s
get a better approximation. If I think of a number close to 1000 that
is a multiple of seven, I get 1001. Now I can ask myself:
What number belongs in the numerator?
The missing numerator is 143.
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S ay: So
, which is close to
So is close to 0.143. 0.143
is a better approximation of than 0.14. Now you are going to
repeat these steps with other fractions to come up with decimal
approximations for
and .
Distribute the following:
A. Find an approximate decimal representation of .
1. Find a multiple of 3 that is close to 100.
2. Set up equivalent fractions, with the answer to #1 as the new
denominator:
3. Calculate the numerator from #2.
4. Since the denominator is close to 100, we can use this as an
approximation for
5. Re-write the fraction from #4 as a decimal.
6. Repeat steps #1 through 5, except this time use a multiple close to
1000.
B. Find an approximate decimal representation of .
1. Find a multiple of 6 that is close to 100.
2. Set up equivalent fractions, with the answer to #1 as the new
denominator:
3. Calculate the numerator from #2.
4. Since the denominator is close to 100, we can use this as an
approximation for
5. Re-write the fraction from #4 as a decimal.
6. Repeat steps #1 through 5, except this time use a multiple close to
1000.
C. Find an approximate decimal representation of .
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1. Find a multiple of 9 that is close to 100.
2. Set up equivalent fractions, with the answer to #1 as the newv
denominator:
3. Calculate the numerator from #2.
4. Since the denominator is close to 100, we can use this as an
approximation for
5. Re-write the fraction from #4 as a decimal.
6. Repeat steps #1 through 5, except this time use a multiple close to
1000.
If there is time, students can find decimal approximations for other
fractions, such as
and .
Review solutions. Answers may vary, depending on what
denominator students chose to be close to 100 or 1000. For
example, when looking for a multiple of seven that is close to 1000,
we might think of 994 or 1001. So then we have two different
problems:
and
. The first problem becomes
and
the second problem becomes
. So one approximation could
be 0.142 while another is 0.143. You may wish to further the
discussion by asking which approximation is more accurate, 0.142
or 0.143.
Discuss any questions the students may have.
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C l o si ng | 4 min
A sk: What steps can we take to convert to a decimal?
We can make equivalent fractions. We want to write as a
fraction with 1000 in the denominator. So we set
and solve
for the numerator. The numerator is 125. So
.
A sk: If we know that is 0.125, then how could we convert
decimal?
to a
Responses may vary. Two possible responses:
. We could solve for the numerator (375) and then re-write as
a decimal (0.375).
is 0.125, then is three times as big. So three times 0.125 is
0.375.
A sk: So if we know that
is twice , so if is
is
, then what is as a decimal?
, then is double that, or
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