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U n t er r i ch t spl a n
Lo ng Divis io n wit h R e maind e rs
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 4 .4 a, 4 .4 c
Virginia - Mathematics Standards of Learning (2016): 4 .2.c , 4 .4 .a,
4 .4 .c , 4 .4 .d
Fairfax County Public Schools Program of Studies: 4 .4 .a.1, 4 .4 .a.2,
4 .4 .c .1, 4 .4 .c .2
Online-Ressourcen: Go t t o S pl i t
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
8
12
15
8
4
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 writing numbers in non-standard ways
P r ac t i c e identifying multiples of a number
L e ar n to divide 3- and 4-digit numbers by 1-digit numbers
De v e l o p an understanding of the long division algorithm
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Ope ni ng | 8 min
S ay: Let’s practice our division facts.
Verbally quiz the students on their division facts with two-digit
dividends and one-digit divisors. Try to ask each student at least
one question. Emphasize that they need to memorize their facts.
S ay: Let’s suppose we wanted to divide 37 by 5. Thirty-seven is not
a mul t i pl e of 5. What happens when we divide?
When we divide, we are left with a r e mai nde r . Seven fives make
35. So 37 divided by 5 is 7 remainder 2, since 37 is 2 larger than
35.
S ay: This is the same thing that happens with long division. If the
dividend is not a multiple of the divisor, we will be left with a
remainder.
T e ac he r pr e se nt s M at h game : Go t t o S pl i t - Di v i de 3 Di gi t N umbe r s w i t h R e mai nde r | 12 min
Present Matific ’s episode Go t t o S pl i t - Di v i de 3 - Di gi t
N umbe r s w i t h R e mai nde r to the class, using the projector.
The goal of the episode is to explore and practice the long division algorithm
in situations where there will be a remainder.
E x a m p le :
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S ay: Please read the instructions.
The instructions say, “Fill in the boxes to make the quantities
equal.”
S ay: Notice the scale in the background. The number on the left
needs to balance with the number on the right. Let’s compare the
two numbers. What is the same and what is different?
The number in the hundreds place is the same on the right and the
left. The number in the tens place is different. And there is no
number in the ones place on the right.
A sk: How do the numbers in the tens place differ?
The number in the tens place on the right is one bigger than the
number in the tens place on the left.
A sk: What number belongs in the ones place on the right so that
the scales balance?
Enter the number that the students suggest by clicking on the
Then click
.
.
If the answer is correct, the episode will proceed to the next problem.
If the answer is incorrect, the ones place will turn brown and the instructions
will wiggle.
The second problem is the same type as the first. Again, prompt the
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students to figure out what number to enter in the missing place.
The third problem will present a division problem.
A sk: What is the di v i so r ?
Students can respond based on the episode.
S ay: Let’s look at each digit of the di v i de nd . Is each digit a
mul t i pl e of the divisor? If not, we can move numbers from the
hundreds place to the tens place and from the tens place to the
ones place. What do we need to move so that the number in the
hundreds place and the tens place are multiples of our divisor?
Move numbers as the students suggest by clicking on
.
A sk: What happens to the tens place when we move 1 hundred to
the right? What happens to the ones place when we move 1 ten to
the right? Why is this happening?
When we move 1 hundred to the right, the tens place increases by
10. When we move 1 ten to the right, the ones place increases by
10. This happens because 10 ones make 10, and 10 tens make 100.
In order to keep the value of the number, 1 hundred becomes 10
tens, and 1 ten becomes 10 ones.
S ay: Now that the hundreds place and tens place are multiples of
the divisor, we can divide.
A sk the students for each digit of the q uo t i e nt . The ones place
may not be a multiple of the divisor, so prompt students to
determine the remainder.
Click on each to enter the students’ answers. Enter the answer by
clicking on each .
If the answer is correct, the episode will proceed to the next problem.
If the answer is incorrect, the incorrect digit in the work will turn brown and
the problem will wiggle.
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The episode will present a total of six problems. The first two are
balancing scales and the last four are long division problems.
S t ude nt s pr ac t i c e M at h game : Go t t o S pl i t - Di v i de 3 Di gi t N umbe r s w i t h R e mai nde r | 15 min
Have the students play G o t t o S p lit - Div id e 3 - Dig it N u m b e r s w it h
R e m a in d e r and G o t t o S p lit - Div id e 4 - Dig it N u m b e r s w it h
R e m a in d e r on their personal devices. Circulate, answering questions as
necessary
C l ass di sc ussi o n | 8 min
Display the following problem:
S ay: In the episode, we would move the 2 in the hundreds place to
the tens place to get 26. Why can we do this?
The 2 represents 200. So we need 20 tens to make 200. So the 20
tens plus the 6 that are already there make 26 tens.
Display the following:
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S ay: But 26 is not a multiple of 6. So we need to make some more
changes. What do we do next?
We need to move 2 tens to the ones place. Then we will have 24
tens and 22 ones.
Display the following:
S ay: Now we can divide 6 into the tens place. What do we get?
We get 4 tens.
A sk: What happens when we divide 6 into 22, in the ones place?
We get 3 remainder 4.
A sk: So what is the final answer to 262 divided by 6?
The answer is 43 remainder 4.
A sk: How could we check our work?
We could multiply 43 by 6 and add 4 to make sure we got 262.
Display the following work:
S ay: We do indeed get 262 as our answer. So our work is correct.
State a division problem of a two-digit number divided by a onedigit number where there is a remainder as part of the answer.
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A possible response: Forty-five divided by 6 has a remainder. The
answer is 7 remainder 3.
A sk: What is a real world problem that we might solve using this
division?
A possible response: You have 45 candies. You want to divide the
candies up fairly among yourself and your 5 friends. How much
candy does each person receive?
A s k: What is the meaning of a remainder? What does the remainder
mean in this problem?
Forty-five is not divisible by 6. Here, each person can get 7
candies, but there are 3 candies left over that have not been
distributed. The remainder here is the part that is left over.
Distributing it (without cutting it up) would not be fair. Some
friends would get 7 candies and some would get 8.
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C l o si ng | 4 min
Display the following problem:
Distribute a small piece of paper. Ask students to solve the division
problem on the paper. They should rewrite the number as many
times as necessary as they move numbers from the hundreds place
to the tens place, and from the tens place to the ones place.
When the students are done, collect papers, to review later.
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