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U n t er r i ch t spl a n
Co nve rt ing Co mmo n F rac t io ns To
De c imal s
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 4 .3 d
Virginia - Mathematics Standards of Learning (2016): 5 .2.a, 5 .2.b
Fairfax County Public Schools Program of Studies: 4 .3 .d.1
Online-Ressourcen: F r ac t i o n t o De c i mal
Class
discussion
Mat h
Worksheet
Pract ice
Opening
T eacher
present s
St udent s
pract ice
8
10
12
7
6
2
min
min
min
min
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e converting fractions to decimals.
P r ac t i c e expanding and simplifying fractions.
L e ar n that there may be multiple representations of the same
fraction.
De v e l o p algebraic skills.
Ope ni ng | 8 min
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Draw the following table:
Divide the class into pairs. Ask students to copy the table into their
notebooks and fill in each cell, indicating if the number in the left column is a
factor of 10, 100 or 1,000.
A sk : Which numbers are factors of 10?
The numbers 2 and 5 are factors of 10.
A sk : Which numbers are factors of 100?
The numbers 2, 4 and 5 are factors of 100.
A sk : Which numbers are factors of 1,000?
The numbers 2, 4, 5 and 8 are factors of 1,000.
A sk : Is a number that is a factor of 10, also a factor of 100? If so,
why?
Yes, a number that is a factor of 10 is also a factor of 100 (and
also a factor of 1,000). Additionally, 10 itself is a factor of 100,
so if a number is a factor of 10 it is a factor of 100, simply by
multiplying the multiplication by 10 (for example, 5 is a factor of
10 by multiplying it by 2. If we multiply the expression 2×5 by 10
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we get 100. 5×2×10 = 100, 5×20 = 100).
A sk : Is a number that is a factor of 100, also a factor of 10?
No. For example, the number 4 is a factor of 100, but it is not a
factor of 10.
A sk : What is a decimal?
A “Decimal” is a fraction that is represented in base ten, as a
fraction whose denominator is a power of 10.
S ay : That’s why, in order to represent fractions as decimals, we
should know the factors of the powers of 10.
Draw the following sketch on the board: _ _ _ , _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _
___
S ay : The names of the places from left to right are - thousands,
hundreds, tens, ones, tenths, hundredths, thousandths.
Write on the lines a decimal, and emphasize what each digit represents.
T e ac he r pr e se nt s M at h game : F r ac t i o n t o De c i mal - | 10
min
Present Matific ’s episode F r a c t io n t o De c im a l - to the class, using the
projector, on the Preset mode.
This episode practices the conversion of fractions into a decimal
representation. The task is to write a given fraction as a decimal. You have at
your disposal a tool that either simplifies a fraction, expands it by a factor of
2, or expands it by a factor of 5. You can use this tool repeatedly to obtain a
fraction whose denominator is a power of ten. This particular variant
focuses on fractions that occur commonly, such as 0.1, 0.5, 0.25 and 0.125.
E x a m p le :
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S ay : In this game we are given a fraction and should write it as a
decimal. We have at our disposal a tool that expands a fraction by a
factor of 2, expands it by a factor of 5, or simplifies it.
A sk : What is expanding a fraction by a factor of 2?
When we expand a fraction by a factor of 2 we multiply the
numerator and the denominator by 2.
A sk : What is expanding a fraction by a factor of 5?
When we expand a fraction by a factor of 5, we multiply the
numerator and the denominator by 5.
A sk : What is simplifying a fraction?
If there is a number that is a factor of the numerator and the
denominator (meaning we can divide the numerator and the
denominator by that number), simplifying is to divide the
numerator and the denominator by the same number.
S ay : We can use these buttons in order to create a fractions equal
to the original fraction . Our goal is to create a fraction whose
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denominator is 10, 100 or 1,000 so that we could convert the
fraction we got, into a decimal.
A sk : What button should we click in order to convert the fraction
to a fraction
with a denominator that is a multiple of 10?
We should click on “expand by 5”. The numerator will multiply by
5 and will be “5,” and the denominator will multiply by 5 and will
be “10”.
Click on “expand by 5”.
E x a m p le :
A sk : How can we write the fraction
as decimal? Why?
0.5. The digit left to the decimal point represents the number of
ones, and in the fraction
there are no “one’s.” The digit right of
the decimal point represents the number of tenths, and in the
fraction
there are 5 tenths.
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Present the next question.
E x a m p le :
A sk : On what button should we click in order to convert the
fraction to a fraction
with a denominator that is a multiple of 10?
We should click on “expand by 2”. The numerator will multiply by 2
and will be “2” and the denominator will multiply by 2 and will be
“10”.
Click on “expand by 2”.
E x a m p le :
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A sk : How can we write the fraction
as decimal? Why?
0.2. The digit left of the decimal point represents the number of
ones, and in the fraction
there are no “ones.” The digit to the
right of the decimal point represents the number of tenths, and in
the fraction
there are 2 tenths.
Present the next question.
E x a m p le :
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A sk: Is 4 a factor of 10?
No.
A sk : Is 4 a factor of 100?
Yes.
A sk : What number multiplying by 4 is 100?
25.
A sk : On what button should we click in order to convert the
fraction
to a fraction with a denominator 100?
We should click on “expand by 5” twice, because we need to
multiply the denominator by 25, i.e multiplying by 5 and again by 5.
Click on “expand by 5” twice.
E x a m p le :
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A sk : How can we write the fraction
as a decimal? Why?
0.25. The digit left of the decimal point represents the number of
ones, and in the fraction
there are no “one’s”. The digit to the
right of the decimal point represents the number of tenths, and in
the fraction
there are 2 tenths. The digit to the right of the
tenths is the hundredths and in the fraction
hundredths.
there are 5
S t ude nt s pr ac t i c e M at h game : F r ac t i o n t o De c i mal - | 12
min
Have students play F r a c t io n t o De c im a l - on their personal devices.
Advanced students can play F r a c t io n t o De c im a l - 2 De c im a l Pla c e s .
Circulate among them answering questions.
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C l ass di sc ussi o n | 7 min
Write on the board the decimal 0.37.
A sk : What represents the digit 0?
The digit 0 represents the number of ones.
A sk : What represents the digit 3?
The digit 3 represents the number of tenths.
A sk : What represents the digit 7?
The digit 7 represents the number of hundredths.
S ay : Let’s demonstrate the meaning of the digits 3 and 7 in this
decimal.
Write on the board:
S ay : We start with 3 tenths plus 7 hundredths. After we expanded
the fraction
by 10, we add the fractions and get 37 hundredths.
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M at h W o r kshe e t P r ac t i c e : E q ui v al e nt F r ac t i o ns - T e nt hs
and H undr e dt hs | 6 min
Have students work on the following worksheets:
1. E q u iv a le n t F r a c t io n s - T e n t h s a n d H u n d r e d t h s .
2. F r a c t io n s a n d De c im a ls - T e n t h s a n d H u n d r e d t h s .
Circulate among them answering questions.
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C l o si ng | 2 min
Draw the following on the board: _ _ _ , _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _
A sk : What is the name of each place, from left to right?
Thousands, hundreds, tens, ones, tenths, hundredths, thousandths.
A sk : How would we convert the fraction
to a decimal?
We expand the fraction by 25. Multiply the numerator and the
denominator by 25.
Write on the board: 3 × 25 = 75, 4 × 25 = 100
Then, we look at the fraction answer,
. According to that
fraction we would write the appropriate decimal: 0.75. The digit
left to the decimal point represents the number of ones, and in the
fraction
there are no “ones.” The digit to the right of the
decimal point represents the number of tenths, and in the fraction
there are 7 tenths. The digit to the right of the tenths is the
hundredths and in the fraction
there are 5 hundredths.
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