In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
This challenge extends the Plants investigation so now four or more children are involved.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
How many triangles can you make on the 3 by 3 pegboard?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
What happens when you try and fit the triomino pieces into these
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?