This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
These practical challenges are all about making a 'tray' and covering it with paper.
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
How many triangles can you make on the 3 by 3 pegboard?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
Can you draw a square in which the perimeter is numerically equal
to the area?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Investigate the different ways you could split up these rooms so
that you have double the number.
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Ben has five coins in his pocket. How much money might he have?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?