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 = ÷ 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 = ÷ 5 = ÷ 80 = ÷ 40 = ÷ 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  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