Mental multiplication strategies – multiply by 10s, 100s and 1 000s
When we multiply by 10 we move the number one place value to the left.
When we multiply by 100 we move the number two place values to the left.
When we multiply by 1 000 we move the number three place values to the left.
Look at how this works with the number 45:
Ten Thousands Thousands Hundreds Tens Units
4 5
4 5 0 × 10
4 5 0 0 × 100
4 5 0 0 0 × 1 000
1 Multiply the following numbers by 10, 100 and 1 000:
a T Th Th H T U b T Th Th H T U
1 7 4 3
× 10 × 10
× 100 × 100
× 1 000 × 1 000
c T Th Th H T U d T Th Th H T U
8 5 9 9
× 10 × 10
× 100 × 100
× 1 000 × 1 000
2 Try these:
a 14 × 10 = b 14 × 100 = c 14 × 1 000 =
d 92 × 10 = e 92 × 1 000 = f 92 × 100 =
g 11 × 1 000 = h 11 × 100 = i 11 × 10 =
3 You’ll need a partner and a calculator for this activity. Take turns giving each other problems such as
�Show me 100 × 678�. The person whose turn it is to solve the problem, writes down their prediction
and you both check it on the calculator. 10 points for each correct answer, and the first person to
50 points wins.
Multiplication and Division
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SERIES TOPIC
Mental multiplication strategies – multiply by 10s, 100s and 1 000s
It is also handy to know how to multiply multiples of 10 such as 20 or 200 in our heads.
4 × 2 helps us work out 4 × 20: 4 × 2 = 8 4 × 20 = 80
We can express this as 4 × 2 × 10 = 80 How would you work out 4 × 200?
4 Use patterns to help you solve these:
a 5 × 2 _____________ 5 × 20 _____________ 5 × 200 ___________
b 2 × 9 _____________ 2 × 90 _____________ 2 × 900 ___________
c 6 × $4 _____________ 6 × $40 _____________ 6 × $400 ___________
d 8 × 3 _____________ 8 × 30 _____________ 8 × 300 ___________
e 3 × $7 _____________ 3 × $70 _____________ 3 × $700 ___________
f 2 × 8 _____________ 20 × 8 _____________ 200 × 8 ___________
g 3 × 9 _____________ 30 × 9 _____________ 300 × 9 ___________
5 Answer these problems: If you’re struggling with
a Jock runs 50 km per week. How far does he run over 10 weeks? your tables, get onto Live
Mathletics and practise!
b Huy earns $20 pocket money per week. If he saves half of this, how much
will he have saved at the end of 8 weeks?
c The sum of two numbers is 28. When you multiply them together, the
answer is 160. What are the numbers?
6 Finish these counting patterns:
a 10 20 30
__________ __________ ___________ 60
__________
b 20 40 __________ 80
__________ ___________ __________
c 30 60 __________ __________ 150
___________ __________
d 40 80 __________ __________ 200
___________ 240
__________
e 50 100 150
__________ __________ ___________ __________
f 100 200 __________ 400
__________ ___________ __________
g 200 400 __________ __________ ___________ 1 200
__________
4 F 1 Multiplication and Division
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Mental multiplication strategies – factors and multiples
Factors are the numbers we multiply together to get to another number:
factor × factor = whole number
How many factors does the number 12 have? 4 × 3 = 12, 6 × 2 = 12, 1 × 12 = 12
4, 3, 6, 2, 1 and 12 are all factors of 12.
1 List the factors of these numbers:
a 18 b 25
c 14 d 9
e 16 f 15
g 30 h 42
2 Fill the gaps in these sentences. The first one has been done for you.
1 or _____
a _____ 16 or _____
2 or _____
8 or _____
4 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.
3 Use a calculator to help you find as many factors of 384 as you can:
A factor divides into
a number evenly
with no remainder.
Multiplication and Division
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SERIES TOPIC
Mental multiplication strategies – factors and multiples
Multiples are the answers we get when we multiply 2 factors.
Think about the 3 times tables where 3 is always a factor.
What are the multiples of 3?
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 and 36 … 3 × factor = multiple
4 Fill in the gaps on these multiple boards:
a 4 b 5 c 9 d 7
8 10
16
35
63
Numbers can be either factors or multiples depending on where they sit in the number sentence.
5 Choose 2 numbers between 2 and 5 and put them in the first frame as factors. Your answer is the
multiple. Now take that multiple and make it a factor in another number sentence. Write in the other
factor and solve the problem. Then make the answer a factor again. Can you fill the grid? Use a calculator
for the larger problems. The first one has been done for you.
a 3 × 4 = 12 12 × 2 = 24 24 × 2 = 48
b × = × = × =
c × = × = × =
d × = × = × =
10 F 1 Multiplication and Division
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Volume and capacity – millilitres and litres
6 Answer these problems to do with mixing drinks:
a Tyler has poured cordial syrup into this jug. b This jug contains some lemonade. Lucy pours
How much water will he add to make 1 L of in another 80 mL of lemonade. Draw a line to
cordial drink? show the new amount of liquid in the jug.
500
400
300
200
100
7 Look at the pictures, then answer the questions below:
50 mL 600 mL 300 mL 1L 5 mL 200 mL
True or False True or False
a
The mug holds the same b The tea cup needs to be
amount of liquid as six full filled 3 times to equal a full
medicine cups. water bottle.
c The medicine cup holds d More than 2 L of liquid is
10 times more liquid than needed to fill the water
the teaspoon. bottle three times.
e The water bottle holds half as f The mug holds half as
much as the juice bottle. much as the water bottle.
g The juice bottle holds the h The tea cup holds one
same amount of liquid as four tenth the amount the juice
tea cups. bottle holds.
2 F 1 Volume, Capacity and Mass
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Volume and capacity – cubic centimetres and cubic metres
Volume is the amount of space occupied by an object or substance.
Commonly used volume measurements are the cubic centimetre and the cubic metre.
ne cubic centimetre is 1 cm long,
O ne cubic metre is 1 m long,
O
1 cm wide and 1 cm high. The 1 m wide and 1 m high. The
symbol we use for cubic cm is cm3. symbol we use is m3.
1 cm × 1 cm × 1 cm = 1 cm3 1 m × 1 m × 1 m = 1 m3
1 For this activity you will need 48 centicubes or centimetre blocks. Work with a friend and record your
answers in the table as you go:
a Use all 48 cubes to make a block 4 cubes wide and 4 cubes high. Before you begin, predict how long you
think it will be. How long is it? Record your answer in the table below.
b Now use all 48 cubes to make a block 12 cubes long. Before you begin, predict how wide and high it will
be. How wide and high is it?
_____________________________________________________________________________________
c Can you make a block that is still 12 cubes long, but is a different height and width?
_____________________________________________________________________________________
d Take turns choosing a length between 1 and 48. The other person tries to make a cube with that length.
If it can be done, add it to the table. If not, list it to the right of the table. Why do you think these lengths
won’t work?
_____________________________________________________________________________________
e Can you see a pattern in your results?
_____________________________________________________________________________________
f Now for each row, put a multiplication symbol between the width and height and then the height and
length. Put an equals sign between the length and number of cubes. Do the number sentences work?
If so, you have worked out the formula for volume: length × width × height = volume
_____________________________________________________________________________________
Width Height Length Number of Cubes
Lengths that won't work:
48
____________________
48
____________________
48
____________________
48
____________________
48
48 ____________________
Volume, Capacity and Mass
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SERIES TOPIC
Measuring mud investigate
Getting
ready 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.
What
to do 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?
What to Find a rock that has the same volume as the lost water. How will
do next
you do this? How will you know that it has the same volume?
Volume, Capacity and Mass
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SERIES TOPIC
Registered School: Wyrallah Road Public School (EAST LISMORE NSW)
APSMO OLYMPIAD
2019 : DIVISION J
WEDNESDAY 31 JULY 2019 3
Total Time Allowed: 30 Minutes
3A. Suggested Time: 3 minutes Write your
A prime number has exactly two different factors. answers in the
For example, 11 is prime because it has two factors: boxes on the
1 and 11. back.
A spinner has eight equal sections as shown in the
diagram.
←
Keep your
The sections labelled with a prime number are painted red. answers
What fraction of the spinner is painted red? hidden by
folding
backwards on
3B. Suggested Time: 5 minutes this line.
Phil 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 minutes
A 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 C A T S
a different digit and the same letter always + D O G S
represents the same digit. P A L S
What is the greatest value that PALS could equal?
Copyright © 2019 Australasian Problem Solving Mathematical Olympiads (APSMO) Inc. and Mathematical Olympiads for Elementary and Middle Schools. All rights reserved.
Registered School: Wyrallah Road Public School (EAST LISMORE NSW)
APSMO OLYMPIAD
2019 : DIVISION J
WEDNESDAY 31 JULY 2019 3
3A.
Student Name:
Fold here. Keep your answers hidden.
3B.
3C.
3D.
3E.
Copyright © 2019 Australasian Problem Solving Mathematical Olympiads (APSMO) Inc. and Mathematical Olympiads for Elementary and Middle Schools. All rights reserved.
