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U n t er r i ch t spl a n
M ul t ip l ic at io n: M ul t ip l e s o f 10 b y
1-Dig it Numb e rs
Altersgruppe: 3 r d Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .5 , 3 .6
Virginia - Mathematics Standards of Learning (2016): 3 .4 .a, 3 .4 .b,
3 .4 .c , 4 .4 .b, 4 .4 .c
Fairfax County Public Schools Program of Studies: 3 .5 .a.1, 3 .5 .a.2,
3 .6.a.3 , 3 .6.a.4 , 3 .6.a.6
Online-Ressourcen: B i r ds i n H and
St udent s
pract ice
Class
discussion
Mat h
Worksheet
Pract ice
Closing
Opening
T eacher
present s
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M at h Obj e c t i v e s
E x pe r i e nc e visualizations for products of 1-digit numbers
and multiples of 10
P r ac t i c e using repeated addition to write expressions with
multiplication
L e ar n to extend principles of multiplying by 10 to factors that
are multiples of 10
De v e l o p strategies for finding products that involve multiples
of 10
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Ope ni ng | 15 min
As a quick lead-in to multiplying by a multiple of 10, remind your students
about multiplying by just 10. Write a few products, such as those below, on
the board. Ask your students for the results.
5 x 10
10 x 7
8 x 10
A sk: What happens each time?
Your students should remember or be able to see that a 0 is
added to each 1-digit number (e.g., 5 becomes 50).
A sk: Why does this happen? Or how do we know this is correct?
The goal here is simply to remind your students about place
value.
Ideally, your students will mention, for example, that 50 means
five 10s (and zero 1s), while 5 x 10 also means five 10s.
Then project or show some base blocks (1s only), such that there are several
groups, each with the same number of blocks. An example is shown below.
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A sk: How many blocks are shown?
Some students may attempt to simply count the blocks. With so
few blocks, this is not unreasonable. However, seek out other
strategies and try to delve into how your students arrived at their
results.
The blocks above are clearly grouped into 4s. As such, a
reasonable conclusion is to find the sum: 4 + 4 + 4 + 4 + 4.
A sk: Is there another way we can think about finding the total?
From previous work with repeated addition, you should be able to
nudge your students toward the fact that 4 + 4 + 4 + 4 + 4 = 5 x 4.
Of course, the result is 20, but the process of leading to
multiplication is important for the rest of the lesson.
Now show some base blocks, but only use 10s this time. Again, the blocks
should be in obvious groups, as before. For the first example, use the same
number of 10s as 1s from before.
A sk: How many blocks are in each group this time?
Finding this should be easy, but you can relate it to the beginning
of the lesson, if necessary.
i.e., four 10s makes 40, or 4 x 10 = 40.
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A sk: How many blocks are shown in total?
Without much help, your students can probably find the sum: 40 +
40 + 40 + 40 + 40.
Once again, try to lead them toward the conclusion that 40 + 40 +
40 + 40 + 40 = 5 x 40.
From here, there are a multitude of possible routes for finding the actual
product. Your students may already know from the sum that the total is 200.
However, it is critical to connect the p r o d u c t with the total, as
multiplication is the emphasis of this lesson.
Several strategies point to the relationship between the first example and the
second. 5 x 4 yielded 20, or two 10s. Replacing each 1s block with a 10s block
increases the total by a factor of 10. Thus, 5 x 40 can be thought of as 5 x 4 x
10, or as the previous product times 10: 20 x 10. In both cases, we have 10 as
a factor, which was covered in previous lessons and at the beginning of this
lesson.
Another thought is that if 5 x 4 gives a total of two 10s, then 5 x 40 should
also yield two of something. Since one factor (4) increased tenfold (to 40),
then instead of two 10s, there should be two 100s. This can be verified
visually using the base blocks. The relationship between 5 x 4 and 5 x 40 can
be strengthened by showing how 5 x 4 creates two 10s as well.
These are simply a few possible strategies that include some discussion
about why the result is 200. Spend some time fielding various responses
from your students, helping them to flesh out the reasoning behind why a
strategy works (or does not work).
Try one or two more examples involving the product of a 1-digit number and a
multiple of 10, as shown using blocks. If your students are still struggling
with some of the ideas, the episode for this lesson will provide new
opportunities for comprehension.
T e ac he r pr e se nt s M at h game : B i r ds i n H and - M ul t i pl y
T e ns | 10 min
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Present Matific ’s episode B ir d s in H a n d - M u lt ip ly T e n s to the class,
using the projector.
The goal of this episode is to use visuals to aid in finding products that
involve a 1-digit number and a multiple of 10. Each screen shows a collection
of birdhouses, where each birdhouse has 10 birds, and each of several poles
has the same number of birdhouses. The poles are meant to represent the 1digit number, while the total number of birds associated with each pole is the
multiple of 10. In the example below, there are 3 poles, each with 30 total
birds (3 birdhouses of 10 birds).
In order to direct your students toward a certain product, each screen will
ask how many birds are on each pole. As mentioned above, this produces the
multiple of 10 in the product.
The number of poles is not called out explicitly on-screen, so assist your
students with this intermediate step. Consider asking an implicit question,
such as: If we know there are 30 birds on the first pole, how many are on the
second? Prior to multiplication, this may lead your students to finding the
sum: 30 + 30 + 30. Support the progress that led to this result, and even move
on to the next screen without using multiplication, unless a student suggests
it.
For screens with fewer birds or poles, addition may suffice. However, you
should attempt to lead the conversation toward the overall goal of using the
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visuals to model multiplication. Such an example is shown below.
Based on your previous work with repeated addition, your students should be
able to recognize that a sum like 60 + 60 + 60 + 60 is equivalent to the
product 4 x 60. Once the values for the number of birds on each pole and the
total number of birds have been submitted, the equation using multiplication
will be shown.
Even if your students solved the problem using addition, they will get the hint
that multiplication may be more beneficial. Continue to support the
strategies your students attempt, as there are many ways to find the correct
answers here. Additionally, continue to probe deeper into why the product is
what it is (e.g., why 4 x 60 = 240).
S t ude nt s pr ac t i c e M at h game : B i r ds i n H and - M ul t i pl y
T e ns | 8 min
Have the students play B ir d s in H a n d - M u lt ip ly T e n s on their personal
devices. Circulate, answering questions as necessary. Encourage your
students to explain the concepts behind why multiplication works in finding
the total number of birds. Also encourage your students to explain how they
know what the product will be.
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C l ass di sc ussi o n | 6 min
Address any lingering concerns you discovered as your students worked
through the episode. Revisit the relationship between repeated addition and
multiplication as needed.
Ask your students to explain what they have learned so far. It is important
that, while acquiring the ability to find products of 1-digit numbers and
multiples of 10, your students have some sense of the reasoning. While
visuals are useful in the early stages, your students will eventually need to
gain comfort with more numerical strategies.
For example, decomposing the multiple of 10 into a 1-digit number and 10
allows for multiplying two 1-digit numbers first. This strategy was used for 5
x 40, where 40 became 4 x 10, so the overall product became 5 x 4 x 10. This
product is significantly easier to find than the original.
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M at h W o r kshe e t P r ac t i c e : M ul t i pl yi ng T e ns - Up T o 1000
| 8 min
Have your students work on the worksheet M u lt ip ly in g T e n s - Up T o
1 0 0 0 on their personal devices. The goal of this worksheet is to develop
computational skills in multiplying by multiples of 10, as shown below.
By this point, your students should be fairly comfortable with these
calculations, since similar exercises were required in the episode for this
lesson. However, use this time to answer questions one-on-one, clarifying
any points from the lesson that your students are still struggling with. If your
students continue to struggle, encourage them to come up a visual that
corresponds with each expression.
This worksheet does include multiplying a multiple of 10 by 10. Previously in
this lesson, your students had been multiplying a multiple of 10 by a 1-digit
number. This slight extension may seem challenging at first, but you can
connect the concepts through the use of visuals, once again.
C l o si ng | 10 min
On the board, list several products involving 1-digit numbers, as shown below.
3x8
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5x6
9x2
Ask your class to find these products, and write them in on the board. These
do not require any explanation at this point, as fluency is expected.
Then, list a few more products that are variations of the original set, such as
those shown below.
3 x 80
50 x 6
9 x 20
In fielding answers for these, be sure to ask your students why . While some
“rules,” such as tacking on a 0 after multiplying 5 and 6, are ultimately
reasonable, it is vital that your students comprehend why this works. For
example, 6 x 50 can be thought of as 6 x 5 x 10, though this is not trivial
either. You may wish to call out rules such as associativity or commutativity,
provided those have been covered.
Lastly, list one more product, wherein the 0 is in a different place than the
corresponding product in the last set, such as 5 x 60.
A sk: What is the value of this product?
As usual, look for explanations as to why the product is 300.
A sk: Is there some reason 50 x 6 gave us 300, but 5 x 60 did too?
They look very similar!
Be mindful while fielding responses from your students as this
point. While there are many possible explanations, consider tying
in the concepts of birdhouses on poles from this lesson’s
episode with multiplication involving arrays.
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In the visual above, consider each brown box to be like a birdhouse with 10
birds. In this simplified version, it is quite clear that you can still think of this
scenario as an array. You could say that there are 6 poles of 50 birds,
meaning you find 6 x 50. However, the s a m e v is u a l can be thought of as 5
rows of 60 birds, yielding 5 x 60. The power of perspective is key to solving
many mathematical problems, but it can be even more useful when trying to
connect ideas.
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