DivisionGrade 5

OutcomeApply 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 halvingto 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 = 246 x 4 = 2424 ÷ 6 = 424 ÷ 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.

PracticeState 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

QuotientDivisor )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 OneWhen you divide by one the quotient is

the same as the dividend.

For example:12 ÷ 1 = 12

Dividing by TwoWhen dividing by 2, you can half the dividend.

For example:24 ÷ 2 = 12Half of 24 is 12.

Dividing by FourWhen dividing by 4, you can half the dividend twice.

For example:24 ÷ 4 = 624 ÷ 2 = 12 ÷ 2 = 6Half of 24 is 12, half of 12 is 6

Dividing by FiveWhen dividing by five you can count up to the dividend by 5s.

For example:35 ÷ 5 = 75, 10, 15, 20, 25, 30, 35 is 7 groups of 5.

Dividing by EightWhen dividing by 8, you can half the dividend three times.

For example:32 ÷ 8 = 432 ÷ 2 = 16 ÷ 2 = 8 ÷ 2 = 4Half of 32 is 16, half of 16 is 8, half of 8 is

4.

Dividing by SixWhen dividing by 6, you can half the dividend and then divide by 3.

For example:42 ÷ 6 = 742 ÷ 2 = 21 ÷ 3 = 7Half 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 = 601500 ÷ 5 = 300240 ÷ 80 = 33200 ÷ 40 = 802800 ÷ 700 = 4

PracticeUse basic facts to calculate each of the following: 2400 ÷ 8 = ___ 560 ÷ 7 = ___ 4800 ÷ 6 = ___

Student booklet

Estimation

Front End EstimationLook 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 is100. 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 NumbersLook 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

OverestimatingSometimes 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 needed23 ÷ 5 = 4 R3It doesn’t make sense to leave three people behind, so 6 cars are needed.

PracticeThere 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.

RemaindersSometimes 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