Multiplication and Division Lesson 1: Multiplication models, properties and basic facts

Practice questions

1. Explain these words mean:

• multiplier: the number of repeated sets in a multiplication problem.
• multiplicand: The amount in each set in a multiplication problem
• factor: either of the numbers (number or sets or amount in each set) multiplied together in a multiplication problem
• product: the result (total) of multiplying numbers.

2. Explain how a child might solve 15 ÷ 3 by direct modeling in a partitive way

• take out 15 counters
• do something to show where the 3 groups will be
• give counters one at a time (or two at a time) to each group until the counters are gone, and the groups all have the same amount
• count the amount in 1 group.

(other variations are possible)

3. Explain how a child might solve 15 ÷ 3 by direct modeling in a measurement way.

• take out 15 counters
• make a set of 3 from the 15 counters, and then continue making sets of 3 until all of the counters are used
• count how many sets of 3 you have made.

(other variations are possible)

4. Explain how a child might solve 3x5 by direct modeling.

• Make 3 groups of 5 counters (the group may be represented by a counter)
• Count the total (of the counters in the 3 groups of 5)

5. Draw a bar diagram that shows a partitive representation of 15 ÷ 3

At least one "?" should be labelled (black), the others are optional (gray).

6. Draw a bar diagram that shows a measurement representation of 15 ÷ 3

At least one of the 3's should be written in, and the "?" and "..." should be shown (black), the other 3 is optional (gray)

7. Draw a bar diagram for 3x5

At least one of the 5's should be written in, as should the "?" (black), the other 5's are optional (gray)

8. Write a partitive division word problem. [many, many correct answers are possible]

9. Write a measurement division word problem. [many, many correct answers are possible]

10. Tell whether each of these word problems is a multiplication problem, a partitive division problem or a measurement division problem. If you can't figure one out, it sometimes helps to start direct modeling it with cubes or writing it in a bar diagram or as a repeated addition problem.

a. Sally has 4 times as many pencils as Jan. Jan has 5 pencils. How many pencils does Sally have?

i. Multiplication (multiplicative comparison)

ii.

iii. 4 × 5 = ?

b. A pack of Pokemon cards costs $4. If I have $12, how many packs of Pokemon cards can I buy?

i. Measurement division

ii.

iii. 12 ÷ 4 = ? or ? × 4 = 12

c. I have 3 times as many pencils as pens. I have 15 pencils. How many pens do I have?

i. Partition division (multiplicative comparison)

ii.

iii. 15 ÷ 3 = ? or 3 × ? = 15

d. An eraser costs $0.12. How much do 4 erasers cost?

i. Multiplication

ii.

iii. 4 × $.12 = ?

e. Ellen has 4 green erasers and 12 pink erasers. How many times as many pink erasers as green erasers does she have?

i.Measurement division (multiplicative comparison)

ii.

iii. 12 ÷ 4 = ? or ? × 4 = 12

f. Ms Anderson has 5 pencil boxes. Each box has 6 pencils. How many pencils does she have?

i. Multiplication

ii.

iii. 5 × 6 = ?

g. Four children share 12 apple slices evenly. How many apple slices does each child get?

i. Partition division

ii.

iii. 12 ÷ 4 = ? or 4 × ? = 12

h. Mark can read 4 pages of his book in 1 minute. How many pages can he read in 5 minutes?

i.Multiplication (rate)

ii.

iii. 5 × 4 = 12

i. I have 10 ounces of cinnamon. If I put 2 ounces of cinnamon in each jar, how many jars can I fill?

i. Measurement division

ii.

iii. 10 ÷ 2 = ? or ? × 2 = 10

j. Kyle can make 15 paper airplanes in 5 minutes. How many paper airplanes can he make in 1 minute?

i. Partition division (rate)

ii.

iii. 15 ÷ 5 = ? or 5 × ? = 15

k. If it costs $12 for 4 boxes of colored pencils, how much does one box of colored pencils cost?

i. Partition division

ii.

iii. 12 ÷ 4 = ? or 4 × ? = 12

l. I can walk 3 miles in 1 hour. How long will it take me to walk 9 miles?

i. Measurement division (rate)

ii.

iii. 9 ÷ 3 = ? or ? × 3 = 9