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U n t er r i ch t spl a n
R o und De c imal s
Altersgruppe: 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 4 .3 b, 4 .3 c ,
5 .1
Virginia - Mathematics Standards of Learning (2016): 4 .3 .b, 5 .1
Fairfax County Public Schools Program of Studies: 4 .3 .b.1, 4 .3 .c .1,
4 .3 .c .2, 5 .1.a.1
Online-Ressourcen: W e i ghi ng M at t e r s
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
13
10
12
10
min
min
min
min
M at h Obj e c t i v e s
E x pe r i e nc e a visual model of one, one tenth, and one
hundredth
P r ac t i c e using a balance scale
L e ar n to round decimals
De v e l o p a better understanding of place value
Ope ni ng | 13 min
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Display the following number line on the board:
S ay : I will draw a sign on the number line and each time we’re going
to determine whole number the sign is closest to.
Place the ‘x’ above the number 0.2.
A sk : Which whole number is closest to the ‘x’?
The closest whole number to 0.2 is 0.
Place the ‘x’ above the number 0.6.
A sk : Which whole number is closest to the ‘x’?
The closest whole number to 0.6 is 1.
Place the ‘x’ above the number 1.5.
A sk : Which whole number is closest to the ‘x’?
The distance of 1.5 from 1 and from 2 is the same, so there is not
one closest whole number to 1.5.
Continue asking questions of this nature until you are confident that the
students can easily identify the closest whole number.
Display the following number line on the board:
S ay : Now I will draw a sign on this new number line and this time
we’re going to determine to which t e nt h the sign is closer.
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Add the 0.22 tick and place the ‘x’ above it.
A sk : Which tenth is closest to the ‘x’?
The closest tenth to 0.22 is 0.2.
A sk : Which tenth is closest to 0.79?
The closest tenth to 0.79 is 0.8.
Continue asking questions of this nature until you are confident that the
students can easily identify the closest tenth.
S ay: In mathematics, rather than asking which whole number is the
closest, we ask which whole number we should r o und o f f to.
When we round off to 2, we mean that the closest whole number is
2. When we round off to 1, we mean that the closest whole number
is 1.
A sk : State a number that rounds off to the nearest tenth to 2.6.
A possible response: 2.61 rounds off to 2.6.
A sk : State a number that rounds off to 9, the nearest whole number.
A possible response: 8.7 rounds off to 9.
A sk : To which whole number should we round off 1.5?
Although the distances of 1.5 from 1 and from 2 are the same, so
there is no closest whole number to 1.5, but the common
convention is to round off to the larger number, 2 in this case.
S ay : Because we are using base 10 number system, there are 10
optional digits in every place value. So 5 digits (0, 1, 2, 3, 4) round
down and 5 digits (5, 6, 7, 8, 9) round up.
A sk : What is the largest decimal that rounds off to 3, with two
decimal digits?
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The largest decimal (with two decimal digits) that rounds off to
3 is 3.49, because the next number (with two decimal digits) is
3.50 which rounds off to 4, according to the convention.
A sk : What is the smallest decimal that rounds off to 5, with two
decimal digits?
The smallest decimal (with two decimal digits) that rounds off to
5 is 4.50, because 4.49 rounds down to 4, and according to the
convention 4.50 round up to 5.
A sk : What is the largest decimal (with two decimal digits) that
rounds off to the nearest tenth to 7.4?
The largest decimal (with two decimal digits) that rounds to 7.4
is 7.44, because the next decimal with two decimal digits is 7.45,
which rounds off to 7.50.
A sk : What is the smallest decimal (with two decimal digits) that
rounds off to the nearest tenth to 9.1?
The smallest decimal (with two decimal digits) that rounds off to
9.1 is 9.05 .
A sk : What does "round off 2.7 to the nearest whole" mean?
It is asking if 2.7 is closer to 2 or 3.
A sk : Round off 15.81 to the nearest tenth. What do we get?
To the nearest tenth, 15.81 rounds off to 15.8.
A sk : Round off 15.81 to the nearest whole. What do we get?
To the nearest whole, 15.81 rounds off to 16.
A sk: Round off 15.81 to the nearest ten (that is asking which is
closer, 10 or 20?). What do we get?
To the nearest ten, 15.81 rounds off to 20.
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S ay: Round off 15.81 to the nearest hundred. What do we get?
To the nearest hundred, 15.81 rounds off to 0.
T e ac he r pr e se nt s M at h game : W e i ghi ng M at t e r s - R o und
De c i mal s | 10 min
Present Matific ’s episode W e ig h in g M a t t e r s - R o u n d De c im a ls to the
class, using the projector.
This episode allows students to practice the rounding off of decimals in the
context of weight measurements. Find the weight of a cubic-cm of a certain
material using a balance scale and weights of 1gr, 0.1gr and 0.01gr, and round
off the answer as requested.
E x a m p le :
S ay: Please read the instructions at the bottom of the screen.
S ay: First we are being asked how much a cubic cm of chalk
weighs. In order to answer this question we need to place the chalk
on one side of the scale and then place weights on the other side of
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the scale until the scale is balanced.
Place the chalk on the left side of the scale.
A sk : What weight should we place first on the left side – the 1g,
0.1g or 0.01g?
We should first place the 1g weight in order to estimate whether
the chalk weighs more or less than 1g. If we place the 0.1g or the
0.01g first, we might need to add several more weights later on,
and the fewer the weights, the easier the problem becomes.
Place the 1g weight on the right side of the scale.
A sk : What can we tell about the weight of the chalk? How do you
know?
We can see that the chalk weighs more than 1g since the scale is
still tilted to the left.
Place another 1g weight on the right side of the scale.
A sk : What can we tell about the weight of the chalk now? How do
you know?
We can see that the chalk weighs more than 2g since the scale is
still tilted to the left.
Place another 1g weight on the right side of the scale.
A sk : What can we tell about the weight of the chalk now? How do
you know?
We can see that the chalk weighs less than 3g since the scale is
now tilted to the right.
Remove the 1g weight and place 0.1g weight on the right side of the scale.
A sk : What can we tell about the weight of the chalk now? How do
you know?
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We can see that the chalk weighs more than 2.1g since the scale
is still tilted to the left.
Repeat this until there are 2 weights of 1g and 3 weights of 0.1g on the right
side of the scale.
A sk : What can we tell about the weight of the chalk now? How do
you know?
We can see that the chalk weighs exactly 2.3g since the scale is
balanced and there are 2 weights of 1g and 3 weights of 0.1g on
the right side of the scale.
S ay : Now we are being asked to round off the answer to the nearest
gram.
A sk : is 2.3 closer to 2 or 3?
2.3 is closer to 2, therefore 2.3g rounded off to the nearest gram
is 2g.
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S t ude nt s pr ac t i c e M at h game : W e i ghi ng M at t e r s - R o und
De c i mal s | 12 min
Have students play W e ig h in g M a t t e r s - R o u n d De c im a ls on their
personal devices.
Circulate among them answering their questions.
C l ass di sc ussi o n | 10 min
Discuss any problems the students faced while working individually.
Ask the class for responses as to how they dealt with any issues their
classmates brought up.
Display the following problems. Have students solve the equations, and then
round off the solution to the nearest ten, the nearest whole and the nearest
tenth:
1. 4.21 + 3.2 =
2. 6.01 + 0.90 =
3. 12.14 + 7.2 =
4. 0.08 + 30.5 =
5. 22 + 1.91 =
6. 0.2 + 2.02 + 0.22 =
Have the students work in their notebooks.
When the students have finished working, review the solutions.
Discuss any questions they may have.
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1. 4.21 + 3.2 = 7.41
To the nearest ten, 7.41 rounds to 10.
To the nearest whole, 7.41 rounds to 7.
To the nearest tenth, 7.41 rounds to 7.4.
2. 6.01 + 0.90 = 6.91
To the nearest ten, 6.91 rounds to 10.
To the nearest whole, 6.91 rounds to 7.
To the nearest tenth, 6.91 rounds to 6.9.
3. 12.14 + 7.2 = 19.34
To the nearest ten, 19.34 rounds to 20.
To the nearest whole, 19.34 rounds to 19.
To the nearest tenth, 19.34 rounds to 19.3.
4. 0.08 + 30.5 = 30.58
To the nearest ten, 30.58 rounds to 30.
To the nearest whole, 30.58 rounds to 31.
To the nearest tenth, 30.58 rounds to 30.6.
5. 22 + 1.91 = 23.91
To the nearest ten, 23.91 rounds to 20.
To the nearest whole, 23.91 rounds to 24.
To the nearest tenth, 23.91 rounds to 23.9.
6. 0.2 + 2.02 + 0.22 = 2.44
To the nearest ten, 2.44 rounds to 0.
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To the nearest whole, 2.44 rounds to 2.
To the nearest tenth, 2.44 rounds to 2.4.
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