1
U n t er r i ch t spl a n
M ul t ip l y M ul t i-Dig it b y One -Dig it
Numb e rs
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 4 .16b, 4 .4 a,
4 .4 b, 4 .4 c , 4 .4 d
Virginia - Mathematics Standards of Learning (2016): 4 .4 .a, 4 .4 .d
Fairfax County Public Schools Program of Studies: 4 .16.b.2,
4 .4 .a.1, 4 .4 .b.1, 4 .4 .b.2, 4 .4 .c .1, 4 .4 .c .2, 4 .4 .d.1, 4 .4 .d.3 ,
4 .4 .d.4
Online-Ressourcen: F e e d t he L i o ns
Mat h
Worksheet
Pract ice
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
4
12
14
6
8
3
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 multiplication as repeated addition
P r ac t i c e multiplication facts
L e ar n to multiply multi-digit numbers by one-digit numbers
De v e l o p an application of the Distributive Property
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Ope ni ng | 4 min
S ay: Let’s practice our multiplication facts.
Verbally quiz the students on their one-digit by one-digit
multiplication facts. Try to ask each student at least one question.
Emphasize that they need to memorize their times tables.
T e ac he r pr e se nt s M at h game : F e e d t he L i o ns - M ul t i pl y
w i t ho ut R e gr o upi ng | 12 min
Present Matific ’s episode F e e d t he L i o ns - M ul t i pl y w i t ho ut
R e gr o upi ng to the class, using the projector.
The goal of the episode is to multiply multi-digit numbers by one-digit
numbers.
E x a m p le :
S ay: Please read the instructions.
The instructions say, “Load the truck with animal feed for a week
according to the note. Check the feeding table to see how much
each animal eats.”
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S ay: Please read the note.
Students can respond based on the episode.
Click on the “Feeding Table” to see how much food each animal
eats.
S ay: Let’s start by putting enough food on the truck for just one
animal. How many boxes of each type do we need?
Move the boxes to the truck as the students suggest.
S ay: Now let’s repeat this process until we have enough food for
all the animals we need to feed this week.
Continue to move boxes onto the truck. When all necessary boxes
are on the truck, click
.
If the answer is correct, an equation showing the multiplication will appear.
Click on the to continue.
If the answer is incorrect, the truck and the problem will wiggle.
Place boxes on the truck as required for the second and third
problems.
Say: Let’s look at the food boxes for a minute. The food is packed in
boxes of 1000 pounds, 100 pounds, 10 pounds, and 1 pound. For
each size box, there is a maximum of 9 boxes. Why do you think this
is true?
Since our number system is a base 10 system, the largest digit we
can write in any place is a 9. So here, the largest number of boxes
we can use is 9. Each size box represents one place value.
A sk: What would we do if we already had 9 ten-pound boxes on the
truck and we needed to add another? How do you know?
We would remove all 9 boxes from the truck and replace them
with 1 hundred-pound box. The 9 ten-pound boxes weigh 90
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pounds. If we want to add another ten-pound box, that would
equal a total of 100 pounds. So we could remove all 9 boxes and
replace them with a single hundred-pound box.
The episode will present a total of five problems.
S t ude nt s pr ac t i c e M at h game : F e e d t he L i o ns - M ul t i pl y
w i t ho ut R e gr o upi ng | 14 min
Have the students play F e e d t he L i o ns - M ul t i pl y w i t ho ut
R e gr o upi ng and F e e d t he L i o ns - M ul t i pl y w i t h
R e gr o upi ng on their personal devices. Circulate, answering
questions as necessary.
M at h W o r kshe e t P r ac t i c e : M ul t i pl i c at i o n - 1- Di gi t by 2Di gi t | 6 min
Have the students work on the following worksheets:
M ul t i pl i c at i o n - 1- Di gi t by 2- Di gi t and M ul t i pl i c at i o n 1- Di gi t by 3 - Di gi t . Some students may also be ready to work on
M ul t i pl i c at i o n - 1- Di gi t by 4 - Di gi t . Circulate, answering
questions as necessary.
C l ass di sc ussi o n | 8 min
S ay: Let’s consider that we want to feed 2 animals that each eat
123 pounds of food a week. When we were working as a group, I
suggested thinking of multiplication as repeated addition. So 2
times 123 is equal to 123 plus 123. Every time we added 123
pounds to the truck, we would add 1 hundred-pound box, 2 tenCopyright 2015 www.matific.com
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pound boxes and 3 one-pound boxes. Since we wanted to feed 2
animals, we did this twice.
Display the following:
2 x 123 = 123 + 123 = 246
A sk: How does each digit in the answer compare to the digits in
123?
Each digit is twice the value of the digit in the corresponding
place in 123. In the hundreds place, we went from a 1 to a 2. In the
tens place, we went from a 2 to a 4. In the ones place, we went
from a 3 to a 6.
S ay: So when we multiplied by 2, we could multiply each digit in
123 by 2 to get the answer. Let’s consider another example. What if
we want to multiply 102 by 4? We could add 102 four times.
Display the following:
4 x 102 = 102 + 102 + 102 + 102
A sk: What is the result when we multiply 102 by 4? How does each
digit in the answer compare to the digits in 102?
The answer is 408. Each digit in the answer is four times the
value of the digit in the corresponding place in 102.
S ay: So rather than working out the repeated addition, another way
to solve these problems is to multiply each digit in the multi-digit
number by the one-digit number. Let’s examine this more carefully.
Display the following:
2 x 123 = 2 x (100 + 20 + 3) = (2 x 100) + (2 x 20) + (2 x 3) = 200 + 40 + 6 = 246
4 x 102 = 4 x (100 + 2) = (4 x 100) + (4 x 2) = 400 + 8 = 408
A sk someone to come to the board to solve and show their work
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for multiplying 323 by 3.
3 x 323 = 3 x (300 + 20 + 3) = (3 x 300) + (3 x 20) + (3 x 3) = 900 +
60 + 9 = 969
S ay: What you’ve seen here is an example of the Di st r i but i v e
P r o pe r t y . The Distributive Property says that if you multiply a
number by a sum, the answer is equal to the sum of the products.
You use this all the time without thinking about it with mental math.
If you want to multiply 23 by 8, you can think of 23 as 20 plus 3.
Then you multiply 20 by 8 to get 160 and 3 by 8 to get 24. Finally,
you add 160 and 24 to get 184, which is the answer to 23 times 8.
Let’s look at another one. What is the product of 413 and 2? How
do you know?
The product is 826. We can multiply each digit in 413 by 2. Four
times 2 is 8, 1 times 2 is 2, and 3 times 2 is 6. So the answer is
826.
S ay: Sometimes, it gets a little trickier. Let’s consider what
happens when we multiply 261 by 3.
Display the following:
3 x 261 = 3 x (200 + 60 + 1)
A sk: What should we do next?
We should multiply 3 by each of the adde nds inside the
parentheses.
Display the following:
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A sk: Why is this more complicated than when we multiplied 4 by
102?
When we multiplied 4 by 102, we could multiply each digit in 102
by 4 and get a one-digit answer. When we multiply each digit in
261 by 3, we don’t always get a one-digit answer. When we
multiply the 6 in the tens place by 3, we get 18. The 8 remains in
the tens place, but the 1 is in the hundreds place, and gets added
to the 6 in the hundreds place that we get when multiplying 3 by 2.
Display the following:
S ay: Sometimes we see multiplication written as in the display.
Where does the small 1 above the 2 come from?
That 1 is from the 18 we obtain when we multiply the 6 by the 3. It
gets carried into the hundreds place, just as it did when we wrote
it out using the Distributive Property.
C l o si ng | 3 min
Hand out a small piece of paper. Ask students to write a
multiplication problem of a three-digit number by a one-digit
number that has an answer between 300 and 400. They should write
the problem and the product.
Collect the papers to review later.
A possible response: 103 x 3 = 309
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