Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three
square grid, so that there is only one of each colour in every row
and every column
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Jack has nine tiles. He put them together to make a square so that
two tiles of the same colour were not beside each other. Can you
find another way to do it?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
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?
If you put three beads onto a tens/ones abacus you could make the
numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Investigate the different shaped bracelets you could make from 18
different spherical beads. How do they compare if you use 24 beads?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Arrange any number of counters from these 18 on the grid to make a
rectangle. What numbers of counters make rectangles? How many
different rectangles can you make with each number of counters?
Use the ratio of cashew nuts to peanuts to find out how many
peanuts Rachel has. What would the ratio be if Rachel and Marianne
mixed their bags?
Can you deduce the pattern that has been used to lay out these
A fun game for two. You'll need some counters.
The game uses a 3x3 square board. 2 players take turns to play,
either placing a red on an empty square, or changing a red to
orange, or orange to green. The player who forms 3 of 1 colour in a
line. . . .
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.