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KS3 Mathematics Pack A: Level 4 Number and Algebra
Pembrokeshire e-Portal Licence exp 31Aug10
7 6 5 4 3 2
Seven hundred thousands
Five thousands Three tens
Two unitsSix ten thousands
Four hundreds
Place value
Exercises
1 What is the next whole number after one hundred thousand? Write your answer infigures. _____________________________________________________________________
2 What is the last whole number before twenty-five thousand? Write your answer infigures. _____________________________________________________________________
3 Write a quarter of a million in figures. __________________________________________
4 Write the following numbers in words:
a 72 368 ______________________________________________________________
b 4726 ______________________________________________________________
c 203 652 ______________________________________________________________
d 752 473 ______________________________________________________________
e 829 878 ______________________________________________________________
5 In the following lists of numbers put a circle around the smallest number andunderline the largest:
a 732 1011 899 6732 3005 8049
b 12 736 2385 1729 5621 10 999 2003
c 689 372 4593 78 736 4999 18 213 582 731
d 1001 2022 80 030 4000 3040 50 201
e 2386 4752 3913 6862 1479 5368
6 Place the following numbers in ascending order, ie smallest first:
KS3 Mathematics Pack A: Level 4 Number and Algebra
Pembrokeshire e-Portal Licence exp 31Aug10
Solving problems without a calculator
If the examination has this means you must not use a calculator.
If the examination question states ‘show your working’, you must show your working.If you do not you will lose marks.
Answering problems
Read the question carefully. Try to decide if it is an add, take away, multiply or dividequestion.
If the numbers are large and you do not know if you should add, take away, multiply ordivide try putting easier numbers in the question to help you decide.
Questions
1 Work out the following:
a 3 6 b 92 ÷ 4x 8___
c 8 2 7 d 4 7 2+ 1 8 9 - 1 3 9_______ _______
2 48 sweets were divided equally between 8 girls.How many sweets did each girl receive? _________
KS3 Mathematics Pack A: Level 4 Number and Algebra
Pembrokeshire e-Portal Licence exp 31Aug10
C = / x
7 8 9 +
4 5 6 -
1 2 3
.0 =
The boat problem
Once there was a man whohad to take a fox, a chickenand a sack of grain across ariver. He had a boat, but hecould only fit himself andone other object in theboat.
He must never leave the foxand the chicken togetherfor, unless he is with them,the fox will eat the chicken.He must never leave thechicken and the sack ofgrain together for, unless heis with them, the chickenwill eat the grain.
Fill in the pictures to show how the man takes everything across the river. Use a pencil,then you can rub out if you make a mistake.
KS3 Mathematics Pack A: Level 4 Number and Algebra
Pembrokeshire e-Portal Licence exp 31Aug10
The soldiers problem
Two soldiers needed to cross a river. The river was too dangerous to swim and therewas no bridge. Nearby, two small girls were rowing a small boat. The soldiers asked ifthey could borrow the boat. The girls agreed, but explained that the boat was so smallthat it could only carry one adult or two children.
Explain how the two soldiers and two girls reached the other side of the river. Use apencil on the diagrams, then if you make a mistake you can rub it out.
Now investigate what happens if there are 3 soldiers, 4 soldiers, 5 soldiers, etc.
What do you notice about the number of moves? How do they increase?
KS3 Mathematics Pack A: Level 4 Using and Applying Mathematics
Pembrokeshire e-Portal Licence exp 31Aug10
FinishSoldierSoldier
GirlGirl
StartSoldierSoldier
GirlGirl
Two girls One soldierOne girlor or
Formulae expressed in words
This is a formula
Telephone bill = rental charge + cost of telephone calls
The telephone bill is calculated by adding the rental charge and the cost of thetelephone calls.
This is an instruction
Choose a number, double it, then add 3 to your answer.
If you choose the number 8:
Start number, double it, add 38 16 19
Questions
1 Use the telephone bill formula.
a What is the bill if the rental charge is £12 and the cost of the calls is £41?____________
b What is the cost of the telephone calls if the rental charge is £12 and thetelephone bill is £76? ____________
2 Use the number instructions with the following start numbers:
a 7 ______ b 12 ______ c 0 ______
d Find the start number if the result is 37. _________
Answers1 a Telephone bill = £53
b Cost of telephone calls = £64
2 a 17b 27c 3
d To find the start number, the formula must be reversed:Instead of adding 3, we take away 3.Instead of doubling, we halve the number.37 - 3 = 34half of 34 = 1717 is the start number
KS3 Mathematics Pack A: Level 4 Shape, Space and Measures
FLAP
FLAP
FLAP
FLAP
FLAP
Cut along the solid lines.
Fold along the dotted lines.
Stick together with glue.
Pembrokeshire e-Portal Licence exp 31Aug10
Magic squares
This is a 3 x 3 magic square. All of the rows, all ofthe columns and both of the diagonals add up tothe same number – 15.
Cut out the numbers 1 to 16 at the bottom of thesheet and place them on the 4 x 4 square. Everyrow, every column and each of the diagonals mustadd up to the same number.
When you have solved this problem, try again witha 5 x 5 square using the numbers 1 to 25.
When attempting the last two questions on this page it may help to trace the shape ontracing paper and then turn the tracing paper to find where the new shape is formed.
Questions
1 ABCD is a rectangle. Complete the diagram.
2 EFGH is a square. Complete the diagram.
3 The shape JKLM is turned and moved. J'K' are shown. Complete the diagram andmark the points L'M'.
4 The shape PQRS is turned and moved. P'Q' are shown. Complete the diagram andmark the points R'S'.
KS3 Mathematics Pack A: Level 4 Shape, Space and Measures
Pembrokeshire e-Portal Licence exp 31Aug10
A
B
C
E
X
W
L
M
J
R'
P'
Q'
Y
D
B'
A'
I
H
R
U
PQ
S
T
Congruent shapes
If two shapes are identical then they are congruent.Look at these two rectangles:
The rectangles have the same length and breadth.Therefore the shapes are congruent.
Shapes are congruent if one shape can be cut out and fitted exactly onto the othershape. An easy way to check is to use tracing paper. Trace the first shape, and see if itwill fit exactly onto the other shape. You can turn the shape or flip the shape.
These triangles are congruent.If you flip the left triangle it will fit onto the other triangle exactly.
Question
Here are four shapes. Which two are congruent? _______________
AnswerA and D are congruent. (If you trace shape A you will find that it fits onto shape D exactly.)
KS3 Mathematics Pack A: Level 4 Shape, Space and Measures
Pembrokeshire e-Portal Licence exp 31Aug10
A
B
L
O
M
P Q
K
G
F
H
N
R
J
I
C
E
D
Rotational symmetry
A shape has rotational symmetry if it fits exactly onto its original outline more than oncein a complete turn. The number of times that it fits is called the order of rotationalsymmetry. If a shape only fits onto itself once we say that it has no rotational symmetry,or that it has order 1.
X marks the centre of rotation.
To find the centre of rotation: If a shape has an even number of sides, join oppositecorners. If a shape has an odd number of sides, join each corner to the centre of theopposite side.
Question
What is the order of rotational symmetry of this regular octagon? ____________
Mark the centre of rotational symmetry.
AnswerMake a tracing of the octagon. Turn the tracing through one complete turn ie 360°. It fits the original octagon exactly 8 times. Therefore the order of rotational symmetry is 8.
KS3 Mathematics Pack A: Level 4 Shape, Space and Measures
Pembrokeshire e-Portal Licence exp 31Aug10
Shape Name a Square b Rectangle c Equilateral Triangle d Regular Pentagon e Regular Hexagon
a
b
c
d
e
Order of rotational symmetry
4
2
3
5
6
Rotational symmetry
Exercises
Look at these shapes. If a shape does not have rotational symmetry, write ‘none’. Ifit does have rotational symmetry, write the order and mark the centre of rotationwith an X.
KS3 Mathematics Pack A: Level 4 Shape, Space and Measures
Pembrokeshire e-Portal Licence exp 31Aug10
A B
C
D
E
F G H I
J
K
L
M N
A _____
B _____
C _____
D _____
E _____
F _____
G _____
H _____
I _____
J _____
K _____
L _____
M _____
N _____
Reflection
The image you see in a mirror is a reflection. The image is exactly the same but it hasbeen flipped over.
Note: The object and the image are equal distances from the mirror line.
How to use tracing paper to reflect an object
Question
Draw the reflection of the triangle.
Answer
If you do not have a mirror, check your answer using the display on your calculator. Tilt the calculatortoward the object and place on the mirror line (the same way you would use a mirror). Look into the answerdisplay to see where the image should be. Remove the calculator and check your drawn image is in thesame place.
KS3 Mathematics Pack A: Level 4 Shape, Space and Measures
Pembrokeshire e-Portal Licence exp 31Aug10
Measurement
Length
We use millimetres, centimetres, metres and kilometres.
This is a millimetre (1 mm):
This is a centimetre (1 cm):
A metre (1 m) is about one large pace.
A kilometre (1 km) is about one thousand large paces.
It takes about ten minutes to walk one kilometre.
Mass
A paper-clip has a mass of about one gram (1 g).
A bag of sugar has a mass of about one kilogram (1 kg).
A small car has a mass of about one tonne (1 t).
Capacity
A small spoon for medicine has a capacity of 5 millilitres (5 ml).
A teaspoon holds about one centilitre (1 cl).
An orange juice container holds about 1 litre (1 l).
Questions
1 What units would you use to measure the length of this piece of paper? Choosefrom millimetres, centimetres, metres, kilometres. ________________________
2 What is the missing number in the following sentence?
A bag of crisps has a mass of ______ grams.Choose from 5, 25, 500, 1000.
Answers1 Centimetres would be the most appropriate units. Millimetres would be acceptable.
1 A six-sided die is thrown. Decide, for each of the following events, if the event hasan even chance of happening, a less than even chance or a more than even chance.
even less more
a The die landing on a 6
b The die landing on an even number
c The die landing on a 1, 2, 3, 4, or 5
d The die landing on a 5
e The die landing on a 3 or less
f The die landing on a 3 or more
g The die landing on less than 5
h The die landing on more than 3
i The die landing on 5 or 6
j The die landing on 1, 2, or 3
2 State whether the chance of each of the following events happening is certain,likely, even, unlikely or impossible.
a Your television breaking down tonight ____________________
b Your pen running out of ink during this lesson ____________________
c An alien walking into your maths lesson today ____________________
d A coin landing on heads ____________________
e Your teacher falling over ____________________
f Your watch stopping today ____________________
g The school bell ringing at the end of the day ____________________
h A die landing on a 6 or less ____________________
3 In a game, a die is thrown. If a 6 is thrown, Lucy wins. If any other number is thrown,Matt wins. Does Lucy have a fair chance of winning? Explain your answer.