Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
Choose a symbol to put into the number sentence.
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you use the information to find out which cards I have used?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you substitute numbers for the letters in these sums?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find the sum of all three-digit numbers each of whose digits is
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you hang weights in the right place to make the equaliser
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Find all the numbers that can be made by adding the dots on two dice.
If you have only four weights, where could you place them in order
to balance this equaliser?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?