You have a set of the digits from 0 – 9. Can you arrange
these in the 5 boxes to make two-digit numbers as close to the
targets as possible?
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?
Use these four dominoes to make a square that has the same number
of dots on each side.
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.
You have two sets of the digits 0 – 9. Can you arrange these
in the five boxes to make four-digit numbers as close to the target
numbers as possible?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
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.
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Charlie has moved between countries and the average income of both
has increased. How can this be so?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Can you rearrange the cards to make a series of correct
How many different cubes can be painted with three blue faces and
three red faces? A boy (using blue) and a girl (using red) paint
the faces of a cube in turn so that the six faces are painted. . . .
Investigate how you can work out what day of the week your birthday
will be on next year, and the year after...
A walk is made up of diagonal steps from left to right, starting at
the origin and ending on the x-axis. How many paths are there for 4
steps, for 6 steps, for 8 steps?
It is impossible to trisect an angle using only ruler and compasses
but it can be done using a carpenter's square.
Relate these algebraic expressions to geometrical diagrams.
This is a beautiful result involving a parabola and parallels.
Can you invert the logic to prove these statements?
Can you work through these direct proofs, using our interactive
The solutions we received for this short challenge were very well
explained and you found several different ways of approaching it.
Rowena's approach to this problem was particularly methodical - she
made sure she found all the possible solutions.
We received good solutions to this problem, many offering insights
into the properties of the numbers that were paired off.
Daniel used connections between each of the ideas to help him solve
the problem. He explained his thinking very well.
An article that reminds us about the value and importance of communication in the mathematics classroom.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Kirsti Ashworth, an NRICH Teacher Fellow, talks about her
experiences of using rich tasks.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.