SERIES TOPIC

9F 1Multiplication and DivisionCopyright © 3P Learning

Factors are the numbers we multiply together to get to another number:

How many factors does the number 12 have? 4 × 3 = 12, 6 × 2 = 12, 1 × 12 = 124, 3, 6, 2, 1 and 12 are all factors of 12.

Mental multiplication strategies – factors and multiples

List the factors of these numbers:1

Fill the gaps in these sentences. The first one has been done for you.

a _____ or _____ or _____ or _____ or _____ people can share 16 lollies evenly.

b _____ or _____ or _____ or _____ or _____ or _____ people can share 20 slices of pie evenly.

c _____ or _____ or _____ or _____ or _____ or _____ or _____ or _____ people can share 24 cherries.

d _____ or _____ or _____ or _____ or _____ or _____ or _____ or _____ people can share 30 pencils.

e _____ or _____ people can share 5 balls evenly.

2

Use a calculator to help you find as many factors of 384 as you can:3

factor factor whole number× =

1 2 4816

a

c

e

g

b

d

f

h

18

14

16

30

25

9

15

42

A factor divides into a number evenly with no remainder.

SERIES TOPIC

3G 1Copyright © 3P Learning

Multiplication and Division

Practise your doubles and halves. You get double points for correct double answers and half points for correct half answers. What is your score?

Mental multiplication strategies – doubling and halving

We can use the double and halve strategy to get to an easy multiplication fact.

15 × 18 Double 15 and halve 18 30 × 9 This is an easier fact to work with. = 270

Solve these using the double and halve strategy:

Look at the options below:a Circle the ones you could use the double and halve strategy with.

Doubles score

Halves score

Total score

a 6 × 14 = × =

c 25 × 16 = × =

b 4 × 16 = × =

d 25 × 12 = × =

6

4

5

Double

32 84

48 96

55 19

Halve

68 48

150 50

144 122

e Reuben buys 16 boxes of golf balls. Each box costs $25.00. How much does he spend?

16 × = × =

f Anna has arranged her magazines onto 5 shelves. Each shelf holds 22 magazines. How many magazines does she have?

5 × = × =

odd number × even number

15 × 8

even number × even number

30 × 18

odd number × odd number

13 × 13

b Use the examples to help explain your choice:

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SERIES TOPIC

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Multiplication and Division

Multiply the numbers below as shown:

Choose a method to solve these problems:

a It is said the average adult laughs around 20 times per day. How many laughs a day would 9 adults have?

__________ × __________ × __________ =

b Children are said to laugh 400 times a day. How many laughs per day would the 9 adults have had when they were young?

__________ × __________ × __________ =

c Small hummingbirds can beat their wings 60 times per second. How many times do they beat their wings in a minute? (Hint: how many seconds in a minute?)

__________ × __________ × __________ =

d Great white sharks have around 3 000 teeth. How many teeth would 20 sharks have?

__________ × __________ × __________ =

e The mandrill is the largest monkey in the world with male mandrills weighing up to 51 kg. What would be the weight of 300 large male mandrills?

__________ × __________ × __________ = kg

Multiplying a whole number by 10 makes a number larger by one place value: 10 × 4 = 40

Multiplying by 100 makes it larger by two place values: 100 × 4 = 400

Multiplying by 1 000 makes it larger by three place values: 1 000 × 4 = 4 000

We multiply by a multiple of 10 such as 20 or 40 in two parts. Look at 40 × 7: (4 × 7) × 10 = 280 OR (10 × 7) × 4 = 280 Either method will work.

We can do the same with hundreds or thousands: 400 × 7 = 4 × 7 × 100 = 2 800

Mental multiplication strategies – multiplying by multiples of ten

1

a 10 × 42 =

d 100 × 42 =

g 1 000 × 42 =

b 10 × $98 =

e 100 × $98 =

h 1 000 × $98 =

c 10 × 5.5 =

f 100 × 5.5 =

i 1 000 × 5.5 =

2

SERIES TOPIC

9GCopyright © 3P Learning

Multiplication and Division 2

Find the answer to these:

a What are the common factors of 24 and 60?

b What is the highest common factor of 75 and 125?

c What is the highest common factor of 36 and 63?

Practise finding factors by completing these factor trees:

Complete these factor activities:

a List all the factors of the following numbers. The first one has been b Generate 2 sets of factors done for you. for each number. The first one has been done for you.

Factors are numbers you multiply together to get to another number:

Knowing the factors of numbers is helpful when solving multiplication and division problems.

Factor trees help us work out the prime factors of numbers. Prime factors are the factors that can be divided no further, except by themselves and one.

Mental division strategies – using factors

64 8 × 8 32 × 2

42

24

90

120

132

240

36 1, 36, 2, 18, 3, 12, 4, 9, 6

45

72

144

100

48

64

1

2

3

factor factor whole number× =

a

____ × ____ × ____ = 50

b

____ × ____ × ____ = 18

c

___ × ___ × ___ × ___ = 16

5

50

2

18

4

16

SERIES TOPIC

1G 1Copyright © 3P Learning

Volume, Capacity and Mass

Capacity refers to the amount a container can hold and is usually associated with liquid.Common capacity measurements are millilitres and litres. 1000 millilitres = 1 litre 1000 mL = 1 L

Volume and capacity – millilitres and litres

1 When we convert:

a millilitres to litres, we by 1000

b litres to millilitres, we by

Convert these amounts to litres:

a 3 452 mL = b 7 895 mL =

c 10 000 mL = d 12 674 mL =

e 56 780 mL = f 235 mL =

2

3

Solve these word problems. They all involve conversion.

a Omar was filling up a 3 L container with cordial. He only had a small 300 mL jug. How many times did he have to fill the jug to totally fill the container?

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b I poured 375 mL out of a 2 L milk container. How much was left? I then poured out another 375 mL. How much is left now?

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c How many 315 mL glasses can be filled from a 1.7 L jug? How much is left over?

____________________________________________________________________________________

d Paula is making a punch for her party. She uses 1.5 L of orange juice, 750 mL pineapple juice, 1.25 L of lemonade and 1.25 L of ginger ale. How much punch does she have altogether? How many 250 mL cups will she be able to fill?

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4

Convert these amounts to millilitres:

a 2.568 L = b 3.999 L =

c 10.566 L = d 1.78 L =

e 7.305 L = f 0.35 L =

SERIES TOPIC

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Volume, Capacity and Mass

Volume and capacity – millilitres and litres

5

6

7

8

How much liquid is in each jug? Answer in both litres and millilitres. The first one has been done for you.

Fill the jugs below to the amount shown:

Below is a recipe for the delicious summer drink, Lava Flow. The capacity measurements are expressed in cups or teaspoons. Express them in millilitres:

Lava FlowIngredients (for one drink)

• 12 cup of pineapple juice _______ mL

• 12 cup of cream _______ mL

• 12 a banana

• 3 teaspoons of coconut cream _______ mL

• 4 strawberries

• 1 cup ice _______ mL

If you were going to make this drink for your entire class, what amounts of each ingredient would you need to purchase? Use a calculator if you wish. What is the most effective unit in which to express the amounts?

a ________ L

________ mL

b ________ L

________ mL

c ________ L

________ mL

d ________ L

_________ mL

e ________ L

________ mL

a 600 mL b 0.4 L c 1800 mL d 1.6 L e 500 mL

1 L

1 L 1 L2 L

1 L

2 L

1 L

1 L

1 L 1 L1 L 1 L

These capacity measurements are useful to know: 1 teaspoon = 5 mL 1 cup = 250 mL

0.5

500

MethodBlend all ingredients (except strawberries) until smooth. Put the strawberries in the bottom of a tall glass and add the blended mixture. Decorate with a drizzle of strawberry topping.

1 L

SERIES TOPIC

7G 1Copyright © 3P Learning

Volume, Capacity and Mass

Measuring mud investigate

In this activity you are going to use what you know about the relationship between mass and volume to calculate the volume of the water in mud. You will need a cup, some newspaper and a scale.

Work with a partner. This experiment may take a day or so to complete and is probably best done outside.

Collect a cupful of mud or damp soil. Make sure the mud is not too sloppy. Find its mass by weighing it. How will you do this? Perhaps you could weigh the empty cup and then subtract the weight of the cup.

Now spread out your mud onto sheets of newspaper and leave it to dry in the sun. It may help to place weights on the paper or tape it down. You may also need to label your experiment so it doesn’t get accidentally cleaned up!

Once your mud has dried, carefully collect it and measure its mass. Remember to use the same cup. Why do you need to do this?

What was the volume of water in the mud?

How do you know?

Find a rock that has the same volume as the lost water. How will you do this? How will you know that it has the same volume?

What to do

What to do next

Getting ready

Registered School: Wyrallah Road Public School (EAST LISMORE NSW)

Copyright © 2019 Australasian Problem Solving Mathematical Olympiads (APSMO) Inc. and Mathematical Olympiads for Elementary and Middle Schools. All rights reserved.

OLYMPIAD

3APSMO2019 : DIVISION J

WEDNESDAY 31 JULY 2019

3A. Suggested Time: 3 minutesA prime number has exactly two different factors.

For example, 11 is prime because it has two factors: 1 and 11. A spinner has eight equal sections as shown in the diagram.The sections labelled with a prime number are painted red.

What fraction of the spinner is painted red?

3B. Suggested Time: 5 minutesPhil went to the mall with some money to spend.He spent one-half of his money on a pair of pants.He spent two-thirds of his remaining money on a shirt.He spent his last $8 on ice cream and snacks.

How much money did Phil have at the start of the day?

3C. Suggested Time: 5 minutesA given cube has a volume of 125 cm3.A rectangular prism is constructed such that, when compared to the original cube, the height is doubled, the width is reduced by 3 cm, and the depth is increased by 1 cm.

Determine the number of cubic centimetres in the volume of the newly constructed prism.

3D. Suggested Time: 6 minutes If 3 identical robots can make 5 widgets in 2 hours, how many widgets can 15 identical robots make in 8 hours?

3E. Suggested Time: 7 minutes

In the following cryptarithm, each letter represents a different digit and the same letter always represents the same digit.

What is the greatest value that PALS could equal?

Total Time Allowed: 30 Minutes

Write your answers in the boxes on the back.

Keep your answers hidden by folding backwards on this line.

←

C A T S+ D O G S

P A L S

Registered School: Wyrallah Road Public School (EAST LISMORE NSW)

Copyright © 2019 Australasian Problem Solving Mathematical Olympiads (APSMO) Inc. and Mathematical Olympiads for Elementary and Middle Schools. All rights reserved.

OLYMPIAD

3APSMO2019 : DIVISION J

WEDNESDAY 31 JULY 2019

3A.

3B.

3C.

3D.

3E.

Student Name:

Fold here. Keep your answers hidden.