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U n t er r i ch t spl a n
Divis io n – One Unkno wn F ac t o r
Altersgruppe: 3 r d Gr ade , 4 t h Gr ade , 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .6, 4 .4 a,
4 .4 b, 4 .4 c
Virginia - Mathematics Standards of Learning (2016): 3 .1.a, 3 .4 .a,
3 .4 .b, 3 .4 .d, 4 .4 .d
Fairfax County Public Schools Program of Studies: 3 .6.a.1, 3 .6.a.2,
3 .6.a.3 , 4 .4 .a.1, 4 .4 .b.2, 4 .4 .c .1
Online-Ressourcen: Di v i si o n o f f t he Gr i d
T eacher
present s
Mat h game
St udent s
pract ice
Mat h game
10
8
min
min
Opening
Class
discussion
Mat h
Worksheet
Pract ice
12
3
12
min
min
min
M at h Obj e c t i v e s
E x pe r i e nc e a graphic display of multiplication
P r ac t i c e multiplication and division up to 100
L e ar n several methods of multiplication and division
De v e l o p understanding of the connection between division
and multiplication
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Ope ni ng | 10 min
Draw 12 squares on the board:
A sk : How many squares are there in total?
There are 12 squares.
A sk : Can anyone think of a different way to draw this which would
make it easier and faster to count the squares?
The answers may vary. Point out 2 options:
S ay : The arrangement on the left represents the equation
6+6=6×2=12. The arrangement on the right represents the equation:
4+4+4=4×3=12.
Make sure that the students understand the connection between repeated
addition and multiplication.
Next, set up a similar scenario, with a small tweak: Consider an arrangement
of 21 squares with 3 rows. How many columns will this arrangement have?
This problem is similar to the earlier one. The sum of three unknown but
equal rows can be thought of as: 3 × (number of columns) = 21
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Thus, finding the unknown number of columns requires division:
21 squares ÷ 3 rows = 7 columns
Your students may have already arrived at this answer, but it is important to
investigate their reasoning.
"Guess and check" or "counting the squares" are likely methods for your
students to try here, but of course these are methods that require very little
analytical thinking. While encouraging all possible solution strategies, point
out that not all problems can be solved by counting or guessing, so knowing
other methods is crucial.
T e ac he r pr e se nt s M at h game : Di v i si o n o f f t he Gr i d - One
Unkno w n F ac t o r | 8 min
Using Preset mode, present Matific ’s episode Div is io n o f f t h e G r id On e Un k n o w n F a c t o r to the class, using the projector.
This episode practices finding an unknown factor when the other factor and
the product are given. Construct a rectangle of given area and given length of
one of its edges.
E x a m p le :
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S ay: Please read the instructions at the bottom of the screen.
A sk : If we need to create a rectangle with a total area of 24 square
units, what are our options?
While several students may have correct answers, be sure to
inquire about the process they used to arrive at those answers.
Show the students (on the grid in the episode) that a rectangle with a total
area of 24 square units can be one anyone of the following:
1. 1 unit edge x 24 unit edge.
2. 2 unit edge x 12 unit edge.
3. 3 unit edge x 8 unit edge.
4. 4 unit edge x 6 unit edge.
S ay : In addition, the episode tells us that the rectangle must also
have one side that is 4 units long. In that case we have to choose
option number 4.
Make a rectangle with sides 4 and 6 units long (mention both options,
horizontal and vertical).
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E x a m p le :
A sk : Who has another way of solving the problem?
The problem can be thought of as: 4 × (second side length) = 24.
Thus, finding the unknown side requires division: 24 square units
÷ 4 units = 6 units.
A sk : Who has another way of solving the problem?
Another way to solve the problem is by adding 4-unit rows (or
columns) one next to the other until we have a rectangle with a
total area of 24 square units, and then count the number of
columns (or rows) we created.
S ay : In order to solve this kind of problems there are two
preferable methods: We can turn the problem into a division
equation, find the quotient and create a rectangle with the given
edge and the edge we found. Alternatively, we can create the
rectangle with the given edge and stop enlarging the rectangle when
reaching the required size.
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S t ude nt s pr ac t i c e M at h game : Di v i si o n o f f t he Gr i d - One
Unkno w n F ac t o r | 12 min
Have students play Div is io n o f f t h e G r id - On e Un k n o w n F a c t o r on
their personal devices.
Advanced students can move on to play Div is io n o f f t h e G r id - Div id e
up t o 5 00
Circulate among the students, answering questions as necessary.
C l ass di sc ussi o n | 3 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.
M at h W o r kshe e t P r ac t i c e : P r o pe r t i e s o f Di v i si o n M ul t i pl i c at i o n w i t h Unkno w ns | 12 min
Have the students work on the following worksheets:
1. Pr o p e r t ie s o f Div is io n - M u lt ip lic a t io n w it h Un k n o w n s .
2. Div id in g w it h Un k n o w n s - Un k n o w n Div id e n d u p t o 1 0 0 .
3. Div id in g w it h Un k n o w n s - Un k n o w n Div is o r u p t o 1 0 0 .
Circulate among the students answering questions as necessary.
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