Transcript KS2 Maths Challenge Sample

PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Pinocchio's nose is 5cm long.
Each time he tells a lie his nose doubles.
How long is his nose after telling 9 lies?
2560 cm or 25.6 metres
Start
5cm
Lie 1
10cm
Lie 2
20cm
Lie 3
40cm
Lie 4
80cm
Lie 5
160cm
Lie 6
320cm
Lie 7
640cm
Lie 8
1280cm
Lie 9
2560cm
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
9
How many triangles can you find in the drawing?
9
6
7
8
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A
B
C
D
E
Steve is snookered on all the reds by the yellow.
He plays the cue ball (white) along the line
shown.
The ball rebounds at right angles at all times.
C
Which red is he most likely to hit?
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
1st
2nd
3rd
Sam continues this pattern of discs.
How many discs will there be in the 4th pattern?
32
4th
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
10
(1,5)
(-3,4)
(2,1)
-5
0
5
The triangle is translated to a new position.
One line of the new position has been drawn for you.
What are the new co-ordinates of the triangle after
translation?
(1,5)
(2,1)
(-3,4)
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The two red triangles are both the same size and are equilateral
The three blue squares are the same size
The total area of the three squares is 75cm2
What is the total perimeter of both the triangles when
added together?
60cm
The area of one square is 75cm2 ÷ 3 = 25cm2
The length of one side of a square is 5cm
The length of one side of a triangle is 5cm x 2 = 10cm
The perimeter of a triangle is 10cm x 3 = 30cm
The perimeter of two triangles is 30cm x 2 = 60cm
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Joe adds 0.25 to the red decimals and subtracts 0.3 from the blue
decimals in this list. He then writes his new decimals in order
starting with the largest.
0.5
0.45 0.35 0.55
0.7
0.05
1.2
0.2
0.15
0.4
0.3
0.9
0.6
0.8
Write the new order in the boxes below
0.9
0.8
0.6
0.4
0.3
0.2
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0.15
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The chart shows the results of Premier League Football matches
and the attendance figures
Arsenal 3
53 000
Wigan 1
52 655
Everton 2 Man. City 0
40 000
39 677
Spurs 0 Aston Villa 0
27 000
27 402
Ben rounds each attendance to the nearest thousand and uses this
information to then find the average attendance.
What is the average attendance for the three games?
40 000
53 000 + 40 000 + 27 000 = 120 000
120 000 ÷ 3 = 40 000
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Lucy has a six-sided spinner.
2
3
5
6
3
A.
1
Which of her statements below are
true or false?
I have a 50% chance of spinning a 3.
F
I have a 33% chance of spinning a 3.
B.
I have a 1 in 3 chance of spinning an even number.
T
I have a 2 in 6 chance or a 1 in 3 chance of spinning
an even number.
C.
If I spin the spinner twice and add the outcomes together
the total will always be three or more.
F
I could spin a 1 twice, making a total of 2
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
On a digital clock the numbers are made up of a series of small bars.
E.g.
Basic design
The number 6
Jack converts the time 3:38 p.m. and records it on to a 24-hour
digital clock.
How many small bars will he fill in altogether to show the
digital time?
3:38 is 15:38 on a 24 hour clock
19
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
In a standard set of 28 dominoes the largest number of spots on any domino
is 12 ( the double six)
Jade sorts out all the dominoes that have a
four on them.
She adds together all the spots on all of these
dominoes.
What is the total number of spots she
counts?
4
9
4
5
6
7
8
9
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10
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Put the numbers 1
2
3 4 and 5 in the drawing below so that
each line totals 9
There are several different orientations of the answer.
The key number is 3 in the middle.
1
4
2
3
2
1
5
2
3
4
2
3
5
5
3
5
4
1
5
4
1
5
3
2
1
4
3
4
2
Etc.
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1
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
If you look directly down on this shape which of the
plan views below will you see?
A
B
C
D
A
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E
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
11 33 22 44
Each number in the boxes that make the pyramid is the sum of
the two numbers immediately above
What number goes in the grey box?
11 33 22 44
44 55 66
99 121
220
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
To buy one pencil costs 30p
Jack buys a total of 26 pencils.
How much change does he receive from £10?
£3.40
Packs of four pencils £1 per pack
Jack can buy 6 packs (24) of pencils for £6
He then buys 2 separate pencils for a cost of 60p
£6 + 60p = £6.60
£10 - £6.60 = £3.40
Use the information on the page to the best advantage
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
50c
m
The radius of each circle is 25mm.
Each vertex of the hexagon lies at the centre of a circle.
What is the perimeter of the hexagon in centimetres?
50mm
50mm
50mm
50mm
50mm
50mm
50mm
50mm
50mm
50mm
10 x 50 mm = 500 mm = 50cm
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Amy works out the two number problems below.
She then subtracts one answer from the other.
( 5 x 14 ) - ( 13 + 27 )
=
100 - ( 3 x 6) + ( 8 x 4 ) =
What are her two possible answers?
84 and - 84
( 5 x 14 ) - ( 13 + 27 )
=
70 - 40 = 30
100 - ( 3 x 6) + ( 8 x 4 ) =
100 - 18 + 32 = 114
114 - 30
30
- 114
= 84
= - 84
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A school netball ball match is played in two halves and lasts a total
of 20 minutes.
Westside School score a goal on average every 2½ minutes
throughout the match.
Eastside school score a goal on average every 2 minutes in the
first half and a goal every ten minutes in the second half.
How many goals are scored altogether?
15 goals
Westside school score 8 goals
Eastside school score 5 goals in the first half and 2
goals in the second half; a total of 7 goals
8 + 7 = 15
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
To find the volume of a cube the length of the cube is multiplied by
its width and height.
height
width
Tom arranges four cubes the same size
as shown. The total volume of the
shape is 108cm3
length
What is the length of each edge of the cubes?
3cm
One cube has a volume of 108cm3 ÷ 4 = 27cm3
Length x width x height = 27cm3 so each edge is 3cm
3cm x 3cm x 3cm = 27cm3
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
17
14
A
25
16
30
20
22
18
The average of the four corner numbers in the number square is 21
What number is missing from square A?
29
If the average is 21 then the total must be 21 x 4 = 84
The total for the three known squares is
17 + 20 + 18 = 55
Square A is 84 - 55 = 29
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The drawing is reflected in the dotted mirror line.
Write the letter of the shape that shows this reflection
A
C
B
D
E
E
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F
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Ben puts the numbers on the left into a function machine.
His outcomes are on the right.
What process did the function machine perform to change the
numbers?
5
8
17
?
11
29
41
Multiply by 4 and subtract 3
5 x 4 = 20
20 - 3 = 17
8 x 4 = 32
32 - 3 = 29
11 x 4 = 44
44 - 3 = 41
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
All the hexagons are regular.
The perimeter of the white hexagon is 90cm
What is the outer perimeter of
A the striped shape
B the checked shape?
Each side of the white hexagon is 90cm ÷ 6 = 15cm
The striped shape has 18 sides
15cm x 18 = 270cm
The checked shape has 30 sides
15cm x 30 = 450cm
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Lucy finds 1/3 of a number, Jack finds ¼ of Lucy’s number, Tom
finds 1/12 of Lucy’s number and Amy finds 1/8 of Jack’s number.
Lucy’s answer is 32.
What numbers do Jack, Tom and Amy have?
Lucy’s number is 32 x 3 = 96
Jack’s number is 96 ÷ 4 = 24
Tom’s number is 96 ÷ 12 = 8
Amy’s number is 24 ÷ 8 = 3
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PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Five children each have five hats. Each hat has five badges. Each
badge has 5 stars. Each star has five points.
How many points are there altogether?
3125
children
5
badges
x
5
hats
x
5
points
x
5
x
stars
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5
PRINTABLE VERSION OF EACH SLIDE
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Pinocchio's nose is 5cm long.
Each time he tells a lie his nose doubles.
How long is his nose after telling 9 lies?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
How many triangles can you find in the drawing?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A
B
C
D
E
Steve is snookered on all the reds by the yellow.
He plays the cue ball (white) along the line
shown.
The ball rebounds at right angles at all times.
Which red is he most likely to hit?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
1st
2nd
3rd
Sam continues this pattern of discs.
How many discs will there be in the 4th pattern?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
10
-5
0
5
The triangle is translated to a new position.
One line of the new position has been drawn for you.
What are the new co-ordinates of the shape after
translation?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The two grey triangles are both the same size and are equilateral
The three squares are the same size
The total area of the three squares is 75cm2
What is the total perimeter of both the triangles when
added together?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Joe adds 0.25 to the red decimals and subtracts 0.3 from the blue
decimals in this list. He then writes his new decimals in order
starting with the largest.
0.5
0.45 0.35 0.55
0.7
0.05
1.2
Write the new order in the boxes below
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The chart shows the results of Premier League Football matches
and the attendance figures
Arsenal 3
Wigan 1
52 655
Everton 2 Man. City 0
39 677
Spurs 0 Aston Villa 0
27 402
Ben rounds each attendance to the nearest thousand and uses this
information to then find the average attendance.
What is the average attendance for the three games?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Lucy has a six-sided spinner.
2
3
5
6
3
1
Which of her statements below are
true or false?
A.
I have a 50% chance of spinning a 3.
B.
I have a 1 in 3 chance of spinning an even number.
C.
If I spin the spinner twice and add the outcomes together
the total will always be three or more.
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
On a digital clock the numbers are made up of a series of small bars.
E.g.
Basic design
The number 6
Jack converts the time 3:38 p.m. and records it on to a 24-hour
digital clock.
How many small bars will he fill in altogether to show the
digital time?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
In a standard set of 28 dominoes the largest number of spots on any domino
is 12 ( the double six)
Jade sorts out all the dominoes that have a
four on them.
She adds up the spots on all of these
dominoes.
What is the total number of spots she
counts?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Put the numbers 1
2
3 4 and 5 in the drawing below so that
each line totals 9
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
If you look directly down on this shape which of the plan
views below will you see?
A
B
C
D
E
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
11 33 22 44
Each number in the boxes that make the pyramid is the sum of
the two numbers immediately above
What number goes in the grey box?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
To buy one pencil costs 30p
Jack buys 26 pencils.
How much change does he receive from £10?
Packs of four pencils £1 per pack
Use the information on the page to the best advantage
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The radius of each circle is 25mm.
Each vertex of the hexagon lies at the centre of a circle.
What is the perimeter of the hexagon in centimetres?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Amy works out the two number problems below.
She then subtracts one answer from the other.
( 5 x 14 ) - ( 13 + 27 )
=
100 - ( 3 x 6) + ( 8 x 4 ) =
What are her two possible answers?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A school netball ball match is played in two halves and lasts a total
of 20 minutes.
Westside School score a goal on average every 2½ minutes
throughout the match.
Eastside school score a goal on average every 2 minutes in the
first half and a goal every ten minutes in the second half.
How many goals are scored altogether?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
To find the volume of a cube the length of the cube is multiplied by
its width and height.
height
width
Tom arranges four cubes the same size
as shown. The total volume of the
shape is 108cm3
length
What is the length of each edge of the cubes?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
17
14
A
25
16
30
20
22
18
The average of the four corner numbers in the number square is 21
What number is missing from square A?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The drawing is reflected in the dotted mirror line.
Write the letter of the shape that shows this reflection
A
C
B
D
E
F
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Ben puts the numbers on the left into a function machine.
His outcomes are on the right.
What process did the function machine perform to change the
numbers?
5
8
11
17
?
29
41
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
All the hexagons are regular.
The perimeter of the white hexagon is 90cm
What is the outer perimeter of
A the striped shape
B the checked shape?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Lucy finds 1/3 of a number, Jack finds ¼ of Lucy’s number, Tom
finds 1/12 of Lucy’s number and Amy finds 1/8 of Jack’s number.
Lucy’s answer is 32.
What numbers do Jack, Tom and Amy have?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Five children each have five hats. Each hat has five badges. Each
badge has 5 stars. Each star has five points.
How many points are there altogether?