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U n t er r i ch t spl a n
Es t imat e M ul t ip l ic at io n wit h
De c imal s – Two De c imal Pl ac e s
Altersgruppe: 5 t h Gr ade , 6t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 5 .5 a, 6.7
Virginia - Mathematics Standards of Learning (2016): 5 .5 .a, 6.5 .a
Fairfax County Public Schools Program of Studies: 5 .5 .a.1, 5 .5 .a.2,
5 .5 .a.3 , 5 .5 .a.5 , 6.7 .a.1, 6.7 .a.2
Online-Ressourcen: A B al l par k E st i mat e
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
7
13
12
10
3
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 : estimation problems.
P r ac t i c e : multiplication with decimals.
L e ar n: that there are different degrees of accuracy in
estimation.
De v e l o p: the concept of estimation.
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Ope ni ng | 7 min
Display the following problems:
4 × 5.36 =
5 × 6.87 =
A sk : Without solving the problem, estimate the product of 4 × 5.36.
How did you determine your estimate?
A possible response: The product is approximately 20, arrived at
by considering 5.36 is close to 5, therefore 4 x 5 is 20. The
estimation concludes 4 x 5.36 will be greater than 20.
Now, ask students to be more specific: How could we get a closer
estimate for the product of 4 × 5.36? What will be the upper limit
of the estimation?
A possible response: 5.36 is close to 5.5, consider four times 5.5
is 22 so the upper limit of the product is 22. Therefore, in order
to arrive at a more exact estimation, one should round the factors
more accurately.
A sk : What is your estimate for the product of 5 and 6.87? How did
you arrive at that estimate? What will be the upper and lower limits
of the product?
A possible response: The product is close to 35, considering 6.87
is close to 7. Therefore, five times 7 is 35, so 5 times 6.87 is
less than 35.
Explain that in the process of estimating, one should give a range by saying
that the answer is greater or less than a particular estimate. The closer the
estimate is to the exact answer, or the narrower the range, the better the
estimate.
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T e ac he r pr e se nt s M at h game : A B al l par k E st i mat e M ul t i pl i c at i o n: T w o De c i mal P l ac e s | 13 min
Using the Preset mode, on a projector, present Matific ’s episode A B a llp a r k
E s t im a t e - M u lt ip lic a t io n : T w o De c im a l Pla c e s to the class.
This episode provides students an opportunity to practice estimation of
products of whole numbers and decimals, within two decimal places.
Estimate the product by marking a range on a number line. The narrower the
range, the higher the score.
E x a m p le :
S ay: Please read the instructions at the bottom of the screen.
Students can read the instructions.
A sk: Let’s estimate the product of 8.44 × 3. State a lower limit for
the product. The answer must be greater than what number? How do
you know?
A possible response: The product must be greater than 24. Eight
is close to, and less than, 8.44. Three times 8 is 24 so the product
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is greater than 24.
S ay: Let’s find an upper limit for this product. The answer must be
less than what number? How do you know?
A possible response: The product must be less than 27. Nine is
close to, and greater than, 8.44. Three times 9 is 27 so the
product is less than 27. The estimate is between 24 and 27.
Now we mark our estimate on the number line.
E x a m p le :
S ay : After we mark our estimate we can see how accurate it was.
A sk : Who knows how our estimate can become more accurate?
In order for an estimate to be more accurate we have to narrow
its limits. Consider 8.44 is closer to 8.5 than to 9. Three times
8.5 is 25.5, so the upper limit is 25.5.
Now we mark our estimate on the number line.
E x a m p le :
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S ay : Let’s see the next question.
E x a m p le :
S ay: Please read the instructions at the bottom of the screen.
Students can read the instructions.
S ay: Let’s estimate the product of 7.92 × 4.8, trying to be as
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accurate as we can.
A possible response: First we will round off each factor
separately. Representing, 8 is close to, and greater than, 7.92 and
5 is close to and greater than 4.8. So, eight times 5 is 40,
therefore the product is close to, but less than, 40.
S t ude nt s pr ac t i c e M at h game : A B al l par k E st i mat e M ul t i pl i c at i o n: T w o De c i mal P l ac e s | 12 min
Have students play A B a llp a r k E s t im a t e - M u lt ip lic a t io n : T w o
De c im a l Pla c e s on their personal devices.
Circulate answering questions.
Ask students, especially the stronger ones, not to settle for less than
excellent accuracy.
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M at h P r ac t i c e : E st i mat i ng M ul t i pl i c at i o n W o r kshe e t | 10
min
Discuss any problems students faced while working on their own.
Ask the class for responses relating to how they dealt with any common
issues encountered by their classmates.
Display the following problems:
4 × 5.12 =
3.33 × 4.9 =
6.15 × 4.04 =
Have students work in pairs. Ask them to arrange the products from the
lowest to the highest.
After the pairs have worked together for a few minutes, share answers with
the class.
A sk : What is your estimate for every product? How did you reach
that estimate?
The product of 4 × 5.12 is close to, but greater than, 20.
The product of 3.33 × 4.9 is approximately 16.
The product of 6.15 × 4.04 is close to, but greater than, 24. Next, 6
is close to, but less than, 6.15 and 4 is close to, but less than, 4.04,
representing 6 × 4 is 24. So the product is just over 24.
The product of 3.33 × 4.9 is the lowest, the product of 4 × 5.12 is next, and
the product of 6.15 × 4.04 is the highest.
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C l o si ng | 3 min
S ay : State each step needed to decide which value is lower: 5 ×
7.98 or 13.5 × 3.
7.98 is close to 8. Five times 8 is 40, so the product is less than
40.
13.5 is close to 13. Three times 13 is 39, so the product is more
than 39.
Now, we can’t tell which is lower, so we need to narrow the limits
in order for the estimate to be more accurate.
13.5 × 3 is 40.5. Therefore, 5 × 7.98 is lower than 13.5 × 3.
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