List

SEAMC published shorts

Place value, integers, ordering and rounding - Short Problems
problem

Draining a pool

Age
11 to 14
Challenge level
filled star empty star empty star

The water is being drained from a pool. After how long will the depth of the pool be 144 cm?

Adding and multiplying
problem

Adding and multiplying

Age
11 to 14
Challenge level
filled star empty star empty star
Amy misread a question and got an incorrect answer. What should the answer have be?
Bouncing ball
problem

Bouncing ball

Age
11 to 14
Challenge level
filled star empty star empty star
A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.
Split clock face
problem

Split clock face

Age
11 to 14
Challenge level
filled star empty star empty star
Use 2 straight lines to split the clock face into 3 parts so that the sums of the numbers in each of the parts are equal.
Handling Data - Short Problems
problem

Strange dice

Age
11 to 14
Challenge level
filled star empty star empty star

If two of these unusually numbered dice are thrown, how many different sums are possible?

Giant Rubik's Cube
problem

Giant Rubik's cube

Age
11 to 14
Challenge level
filled star empty star empty star

How many cubes would be visible in a 12 by 12 by 12 Rubik's cube?

Handling Data - Short Problems
problem

Range of averages

Age
11 to 14
Challenge level
filled star empty star empty star

Find these 4 numbers, given their mode, median and range.

Brothers and sisters
problem

Brothers and sisters

Age
11 to 14
Challenge level
filled star empty star empty star
Can you work out how many brothers and sisters are in the family?
Missing Digits
problem

Missing digits

Age
11 to 14
Challenge level
filled star empty star empty star
Can you find the missing digits in this calculation?
speed over a bridge
problem

Speed over a bridge

Age
11 to 14
Challenge level
filled star empty star empty star
How fast is the train travelling as it goes over the bridge?
Place value, integers, ordering and rounding - Short Problems
problem

Rough rectangle

Age
11 to 14
Challenge level
filled star empty star empty star

What is the smallest possible area that this rectangle could have?

Hot Dogs
problem

Hot dogs

Age
11 to 14
Challenge level
filled star empty star empty star
How many hot dogs did this hot dog lover eat on the first day of her binge?
Geometry and Measure - Short Problems
problem

Rotation identification

Age
11 to 14
Challenge level
filled star empty star empty star

Which of these can be obtained by rotating this shape?

Overlapping beer mats
problem

Overlapping beer mats

Age
11 to 14
Challenge level
filled star empty star empty star
Can you find the area of the overlap when these two beer mats are placed on top of each other?
Identical digit multiplication
problem

Identical digit multiplication

Age
11 to 14
Challenge level
filled star empty star empty star
77 is multiplied by another two-digit number with identical digits. What is the product?
Divisible digits
problem

Divisible digits

Age
11 to 14
Challenge level
filled star empty star empty star
Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?
Geometry and Measure - Short Problems
problem

Multiplication cube

Age
11 to 14
Challenge level
filled star empty star empty star

The net shown is folded up to form a cube. What is the largest possible vertex product?

2014 even numbers
problem

2014 even numbers

Age
11 to 14
Challenge level
filled star empty star empty star
What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?
Geometry and Measure - Short Problems
problem

Nested squares

Age
11 to 14
Challenge level
filled star empty star empty star

What proportion of the diagram is shaded?

Building Up
problem

Sum and differences

Age
11 to 14
Challenge level
filled star empty star empty star

Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?

Cuboid faces
problem

Cuboid faces

Age
11 to 14
Challenge level
filled star empty star empty star
Can you find the volume of a cuboid, given the areas of its faces?
Choose the mean
problem

Choose the mean

Age
11 to 14
Challenge level
filled star empty star empty star
Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.
Reverse ages
problem

Reverse ages

Age
11 to 14
Challenge level
filled star empty star empty star
When is the next time that Brian's age will be the reverse of his father's age?
Handling Data - Short Problems
problem

Clubs

Age
11 to 14
Challenge level
filled star filled star empty star

How many students are in the maths club and the science club?

Place value, integers, ordering and rounding - Short Problems
problem

The elephant diet

Age
11 to 14
Challenge level
filled star filled star empty star

Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day

Building Up
problem

Linear area

Age
11 to 14
Challenge level
filled star filled star empty star

Find the area of the triangle enclosed by these lines.

Lattice points on a line
problem

Lattice points on a line

Age
11 to 14
Challenge level
filled star filled star empty star

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

Handling Data - Short Problems
problem

French test

Age
11 to 14
Challenge level
filled star filled star empty star

What was the average score in this French test?

Building Up
problem

Tiled floor

Age
11 to 14
Challenge level
filled star filled star empty star

This tiled floor has 109 purple tiles. How many tiles are there altogether?

Scalene area
problem

Scalene area

Age
11 to 14
Challenge level
filled star filled star empty star
Can you find the area of this scalene triangle?
Geometry and Measure - Short Problems
problem

Diagonal side

Age
11 to 14
Challenge level
filled star filled star empty star

Can you work out the area of a square drawn on a diagonal?

Place value, integers, ordering and rounding - Short Problems
problem

Smallest fraction

Age
11 to 14
Challenge level
filled star filled star empty star

Which of these is the smallest?

Handling Data - Short Problems
problem

Average temperature

Age
11 to 14
Challenge level
filled star filled star empty star

The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?

Graph Area
problem

Graph area

Age
11 to 14
Challenge level
filled star filled star empty star
Can you find the area between this graph and the x-axis, between x=3 and x=7?
Place value, integers, ordering and rounding - Short Problems
problem

Between a sixth and a twelfth

Age
11 to 14
Challenge level
filled star filled star empty star

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

Place value, integers, ordering and rounding - Short Problems
problem

Charlie's money

Age
11 to 14
Challenge level
filled star filled star empty star

How much money did Charlie have to begin with?

Geometry and Measure - Short Problems
problem

Packing small boxes

Age
11 to 14
Challenge level
filled star filled star empty star

How many small boxes will fit inside the big box?

Palindromic milometer
problem

Palindromic milometer

Age
11 to 14
Challenge level
filled star filled star empty star
At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?
Handling Data - Short Problems
problem

Shifting average

Age
11 to 14
Challenge level
filled star filled star empty star

What happens to the average if you subtract 8 from all of the numbers?

Geometry and Measure - Short Problems
problem

Tile border

Age
11 to 14
Challenge level
filled star filled star empty star

What is the largest possible number of yellow tiles in this pattern?

Dividing a square
problem

Dividing a square

Age
11 to 14
Challenge level
filled star filled star empty star
A square is divided into three shapes which all have equal areas. Can you find the length of this side?
Building Up
problem

Square grid

Age
11 to 14
Challenge level
filled star filled star empty star

Can you work out what fraction of this grid is shaded?

Tilted tank
problem

Tilted tank

Age
11 to 14
Challenge level
filled star filled star empty star
Can you find the height of the water in this tilted tank when it is flat?
Handling Data - Short Problems
problem

The average age

Age
11 to 14
Challenge level
filled star filled star empty star

Given this information about averages, find the ages of these teachers.

Multiplication Mistake
problem

Multiplication mistake

Age
11 to 14
Challenge level
filled star filled star empty star
Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?
Missing 9s
problem

Missing 9s

Age
11 to 14
Challenge level
filled star filled star empty star
Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?
Red card blue card
problem

Red card blue card

Age
11 to 14
Challenge level
filled star filled star empty star
Can you arrange the red and blue cards so that the rules are all followed?
Place value, integers, ordering and rounding - Short Problems
problem

Roses and carnations

Age
11 to 14
Challenge level
filled star filled star empty star

How many different bunches of flowers can this class buy for their teacher?

Building Up
problem

Adding in pairs

Age
11 to 14
Challenge level
filled star filled star empty star

These are the results when 3 numbers were added in pairs. What were the numbers?

Leap Monday
problem

Leap monday

Age
11 to 14
Challenge level
filled star filled star filled star

Can you find the next time that the 29th of February will fall on a Monday?

Clock angle
problem

Clock angle

Age
11 to 14
Challenge level
filled star filled star filled star
What is the angle between the the hands of a clock at 8:24?
Handling Data - Short Problems
problem

Number of arms

Age
11 to 14
Challenge level
filled star filled star filled star

What is the probability that the next person you meet has an above average number of arms?

Geometry and Measure - Short Problems
problem

Add all the angles

Age
11 to 14
Challenge level
filled star filled star filled star

Find the sum of all of the angles denoted by letters in this diagram

last digit
problem

Last digit

Age
11 to 14
Challenge level
filled star filled star filled star

What is the last digit in this calculation involving powers?

Place value, integers, ordering and rounding - Short Problems
problem

Washing elephants

Age
11 to 14
Challenge level
filled star filled star filled star

How long will it take Mary and Nigel to wash an elephant if they work together?

tricky fractions
problem

Tricky fractions

Age
11 to 14
Challenge level
filled star filled star filled star
Use this series of fractions to find the value of x.
Place value, integers, ordering and rounding - Short Problems
problem

Divisible by 55

Age
11 to 14
Challenge level
filled star filled star filled star

Choose the digits $a$ and $b$ so that this number is divisible by 55.

Handling Data - Short Problems
problem

Rain

Age
11 to 14
Challenge level
filled star filled star filled star

How many dry days did Aisha have on her holiday?

Committees
problem

Committees

Age
11 to 14
Challenge level
filled star filled star filled star
Every member of the club is a member of two committees. How many members are there in the club?
Sum of 1s
problem

Sum of 1s

Age
11 to 14
Challenge level
filled star filled star filled star
Can you find the last 5 digits of this sum?
Place value, integers, ordering and rounding - Short Problems
problem

How shady?

Age
11 to 14
Challenge level
filled star filled star filled star

What fraction of this triangle is shaded?

Black and gold storeys
problem

Black and gold storeys

Age
11 to 14
Challenge level
filled star filled star filled star
25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...
Table Total
problem

Table total

Age
14 to 16
Challenge level
filled star empty star empty star
Can you find the sum of all of the numbers in the table?
Swapping Sweets
problem

Swapping sweets

Age
14 to 16
Challenge level
filled star empty star empty star
If two girls each take a sweet from each other's bags, what is the probability that they end up with what they started with?
Place value, integers, ordering and rounding - Short Problems
problem

The power of the sum

Age
14 to 16
Challenge level
filled star empty star empty star

What is this sum, expressed as a power of 2?

Place value, integers, ordering and rounding - Short Problems
problem

Power up to 1000

Age
14 to 16
Challenge level
filled star empty star empty star

Find $x+y$, where $2^x\times5^y=1000$

Geometry and Measure - Short Problems
problem

Stacked cubes

Age
14 to 16
Challenge level
filled star empty star empty star

What is the total surface area of this shape?

Geometry and Measure - Short Problems
problem

Cat on a wall

Age
14 to 16
Challenge level
filled star empty star empty star

How high is the wall that this cat is lying on?

Building Up
problem

Length, width and area

Age
14 to 16
Challenge level
filled star empty star empty star

The area of a rectangle is 225 square units. Find its width.

Geometry and Measure - Short Problems
problem

Ratio of areas

Age
14 to 16
Challenge level
filled star empty star empty star

What is the ratio of the area of the hexagon to the area of the triangle?

Place value, integers, ordering and rounding - Short Problems
problem

Root 2017

Age
14 to 16
Challenge level
filled star empty star empty star

Between which two whole numbers is $\sqrt{2017}$ $?$

Bobbly perimeter
problem

Bobbly perimeter

Age
14 to 16
Challenge level
filled star empty star empty star
Find the perimeter of this shape made of semicircles
Mean balance
problem

Mean balance

Age
14 to 16
Challenge level
filled star empty star empty star
Given information about the mean, can you work out the missing numbers?
Flipping coins
problem

Flipping coins

Age
14 to 16
Challenge level
filled star empty star empty star
A coin is flipped 4 times. What is the probability of getting heads at least 3 times?
Geometry and Measure - Short Problems
problem

Which face?

Age
14 to 16
Challenge level
filled star empty star empty star

Which faces are opposite each other when this net is folded into a cube?

Place value, integers, ordering and rounding - Short Problems
problem

Pineapple juice

Age
14 to 16
Challenge level
filled star filled star empty star

What percentage of this orange drink is juice?

Geometry and Measure - Short Problems
problem

Photocopied map

Age
14 to 16
Challenge level
filled star filled star empty star

What will the scale on this map be after it has been photocopied?

Place value, integers, ordering and rounding - Short Problems
problem

How many squares?

Age
14 to 16
Challenge level
filled star filled star empty star

How many 4-digit numbers are perfect squares?

Semicircle distance
problem

Semicircle distance

Age
14 to 16
Challenge level
filled star filled star empty star
Can you find the shortest distance between the semicircles given the area between them?
Geometry and Measure - Short Problems
problem

Arc radius

Age
14 to 16
Challenge level
filled star filled star empty star

Two arcs are drawn in a right-angled triangle as shown. What is the length $r$?

Geometry and Measure - Short Problems
problem

Rotation and area

Age
14 to 16
Challenge level
filled star filled star empty star

Point A is rotated to point B. Can you find the area of the triangle that these points make with the origin?

Place value, integers, ordering and rounding - Short Problems
problem

Root estimation

Age
14 to 16
Challenge level
filled star filled star empty star

Which of these is the best approximation for this square root?

Geometry and Measure - Short Problems
problem

Climbing ropes

Age
14 to 16
Challenge level
filled star filled star empty star

Given how much this 50 m rope weighs, can you find how much a 100 m rope weighs, if the thickness is different?

Building Up
problem

Thousands of x

Age
14 to 16
Challenge level
filled star filled star empty star

Can you solve this scary-looking equation?

Place value, integers, ordering and rounding - Short Problems
problem

Big product

Age
14 to 16
Challenge level
filled star filled star empty star

How many digits are there in this product?

Cones and spheres
problem

Cones and spheres

Age
14 to 16
Challenge level
filled star filled star empty star
A solid metal cone is melted down and turned into spheres. How many spheres can be made?
Building Up
problem

Difference sequence

Age
14 to 16
Challenge level
filled star filled star empty star

When will 2000 appear in this sequence?

Growing Triangle
problem

Growing triangle

Age
14 to 16
Challenge level
filled star filled star empty star
If the base and height of a triangle are increased by different percentages, what happens to its area?
3-4-5 circle
problem

3-4-5 circle

Age
14 to 16
Challenge level
filled star filled star empty star
Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?
Place value, integers, ordering and rounding - Short Problems
problem

Roots near 9

Age
14 to 16
Challenge level
filled star filled star empty star

For how many integers n is the difference between √n and 9 less than 1?

Place value, integers, ordering and rounding - Short Problems
problem

Dolly dolphin

Age
14 to 16
Challenge level
filled star filled star empty star

Can you find Dolly Dolphin's average speed as she swims with and against the current?

Slide height
problem

Slide height

Age
14 to 16
Challenge level
filled star filled star empty star
How high is the top of the slide?
Geometry and Measure - Short Problems
problem

Square and triangle

Age
14 to 16
Challenge level
filled star filled star empty star

Can you find the area of the yellow square?

Building Up
problem

Order the products

Age
14 to 16
Challenge level
filled star filled star empty star

Can you put these products in order of size?