Tilted Squares
Age 11 to 14
Challenge Level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Interactive Spinners
Age 11 to 14
Challenge Level
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
What Numbers Can We Make?
Age 11 to 14
Challenge Level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Calendar Capers
Age 11 to 14
Challenge Level
Choose any three by three square of dates on a calendar page...
Shape Products
Age 11 to 14
Challenge Level
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Keep it Simple
Age 11 to 14
Challenge Level
Can all unit fractions be written as the sum of two unit fractions?
Have You Got It?
Age 11 to 14
Challenge Level
Can you explain the strategy for winning this game with any target?
Summing Consecutive Numbers
Age 11 to 14
Challenge Level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Magic Letters
Age 11 to 14
Challenge Level
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Number Pyramids
Age 11 to 14
Challenge Level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Shifting Times Tables
Age 11 to 14
Challenge Level
Can you find a way to identify times tables after they have been shifted up or down?
1 Step 2 Step
Age 11 to 14
Challenge Level
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Route to Infinity
Age 11 to 14
Challenge Level
Can you describe this route to infinity? Where will the arrows take you next?
Seven Squares
Age 11 to 14
Challenge Level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Exploring and Noticing Structure - Short Problems
Age 11 to 16
A collection of short Stage 3 and 4 problems on Exploring and Noticing Structure.
Charlie's Delightful Machine
Age 11 to 16
Challenge Level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Arithmagons
Age 11 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges?
Cyclic Quadrilaterals
Age 11 to 16
Challenge Level
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Steel Cables
Age 14 to 16
Challenge Level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Pair Products
Age 14 to 16
Challenge Level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Attractive Tablecloths
Age 14 to 16
Challenge Level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Painted Cube
Age 14 to 16
Challenge Level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Pick's Theorem
Age 14 to 16
Challenge Level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
What's Possible?
Age 14 to 16
Challenge Level
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Vector Journeys
Age 14 to 18
Challenge Level
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Simply Graphs
Age 16 to 18
Challenge Level
Look for the common features in these graphs. Which graphs belong together?
Impossible Triangles?
Age 16 to 18
Challenge Level
Which of these triangular jigsaws are impossible to finish?
Polite Numbers
Age 16 to 18
Challenge Level
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
Fix Me or Crush Me
Age 16 to 18
Challenge Level
Can you make matrices which will fix one lucky vector and crush another to zero?
NRICH is part of the family of activities in the Millennium Mathematics Project.