Division
Grade 5
Outcome
Apply mental math strategies and number
Properties by:
 skip counting from a known fact
 using doubling or halving
 using patterns in 9s facts
 using repeated doubling or halving
to determine answers for basic multiplication
facts to 81 and related division facts.
Fact Families
 Multiplication
and Division are related.
 There are two multiplication and two
division equations.
For example:
4 x 6 = 24
6 x 4 = 24
24 ÷ 6 = 4
24 ÷ 4 = 6
Arrays/Rectangles
 Using
colored tiles, create as many
rectangles as possible that have 12
square units. Write the multiplication facts
for each square. Next split each
rectangle into each equal groups of
colored tiles to match your division facts.
Practice
State all multiplication and related division
facts for each:
 48
 36
 18
 56
Activity
 Student
text: page 300, # 3, 4
 Student booklet
Math Strategies
The Division Equation
Quotient
Divisor )Dividend
OR
Dividend ÷ Divisor = Quotient
Division by Zero


You cannot divide 0.
This is a Principle of Division.
For example,
20 ÷ 5 = 4 because 20 – 5 – 5 – 5 – 5 = 0.
However 5 ÷ 0 is undefined because no
matter how many times 0 is subtracted from
5, you will never reach 0,
5 – 0 – 0 – 0 – … = 5, not 0.
Dividing by One
When you divide by one the quotient is the
same as the dividend.
For example:
12 ÷ 1 = 12
Dividing by Two
When dividing by 2, you can half the
dividend.
For example:
24 ÷ 2 = 12
Half of 24 is 12.
Dividing by Four
When dividing by 4, you can half the
dividend twice.
For example:
24 ÷ 4 = 6
24 ÷ 2 = 12 ÷ 2 = 6
Half of 24 is 12, half of 12 is 6
Dividing by Five
When dividing by five you can count up to
the dividend by 5s.
For example:
35 ÷ 5 = 7
5, 10, 15, 20, 25, 30, 35 is 7 groups of 5.
Dividing by Eight
When dividing by 8, you can half the
dividend three times.
For example:
32 ÷ 8 = 4
32 ÷ 2 = 16 ÷ 2 = 8 ÷ 2 = 4
Half of 32 is 16, half of 16 is 8, half of 8 is 4.
Dividing by Six
When dividing by 6, you can half the
dividend and then divide by 3.
For example:
42 ÷ 6 = 7
42 ÷ 2 = 21 ÷ 3 = 7
Half of 42 is 21, 21 divided by 3 is 7.
Activity
 Student
text: page 303, # 2, 4
 Student booklet
Dividing by Multiples of 10 and
100
 You
can use the basic division facts to
calculate larger division problems.
120 ÷ 2 = 60
1500 ÷ 5 = 300
240 ÷ 80 = 3
3200 ÷ 40 = 80
2800 ÷ 700 = 4
Practice
Use basic facts to calculate each of the
following:
 2400 ÷ 8 = ___
 560 ÷ 7 = ___
 4800 ÷ 6 = ___
 Student
booklet
Estimation
Front End Estimation
Look at the first numbers only.
829 ÷ 42 =
800 ÷ 40 = 20
Compensation
Look at the front-end, then compensate for the
other numbers.
589 ÷ 5 using front-end would be 500 ÷ 5 which is
100. An adjustment should be made for the
remaining 89 ÷ 5 which is close to 100 ÷ 5 = 20 for a
final estimate of 120.


Round one number up and the other down
329 ÷ 9 =
300 ÷ 10 = 30
Compatible Numbers
Look for numbers that are easy to compute
mentally. Round numbers so that familiar
facts can be used.
643 ÷ 8 =
640 ÷ 8 = 80
Other Strategies
 Round
one or both numbers to the
nearest 10, 100, or 1000.
 Round both numbers up or down.
372 ÷ 9 =
400 ÷ 10 = 40
Overestimating
Sometimes when estimating it is important
to overestimate.
For example, there are 23 people travelling
to a sports event, 5 people can travel in
each car. How many cars are needed
23 ÷ 5 = 4 R3
It doesn’t make sense to leave three
people behind, so 6 cars are needed.
Practice
There are 336 students traveling to a hockey
tournament on buses. There are 6 busses.
How many students will be on each bus?
Did you overestimate or underestimate?
Student Booklet
Outcome
 Demonstrate,
with and without concrete
materials, an understanding of division (3
digit by 1-digit) and interpret remainders
to solve problems.
Base Ten Division
 Use
base ten blocks to model 253 shared
equally among 7 groups.
 Represent your answer using diagrams
and a number sentence.
Base Ten Division
 Use
base ten materials to solve 320 ÷ 8.
How could you then use the answer to
solve 3200 ÷ 8?
Student Booklet
Remainders
 Anna
solved the following problem: There
were 367 fans going to a hockey game.
Each SUV can carry 7 fans. How many
SUV are needed?
 Her answer was 367 ÷ 7 = 52 R3.
 What does the remainder 3 represent?
 Anna’s final answer was 53. Explain.
Remainders
Sometimes
 a. ignore the remainder
 b. round up the quotient
 c. express as a fraction.
Problems (What do you do
with the remainders?)



(i) William has 185 hockey cards that he wants
to share equally among his three friends. How
many cards will each person receive?
(ii) Mrs. Peabody has 9 bars of Swiss chocolate
to share equally among her 4 nephews. How
much chocolate will each nephew receive?
(iii) Ian can transport 3 people in his canoe.
How many trips would take him to transport 35
people across a river?
Long Division
Student Booklet