What is the units digit in this sum of powers of 9?
Resources to accompany Charlie's workshops and presentation.
Let N be the smallest positive integer whose digits add up to 2015. What is the sum of the digits of N+1?
Amy misread a question and got an incorrect answer. What should the answer have be?
Explore a task from our Wild site on each day in the run up to Christmas
A collection of short Stage 3 and 4 problems on Reasoning, Justifying, Convincing and Proof.
We have been exploring what mastering mathematics in the context of problem solving means to us at NRICH.
Resources to accompany NRICH team presentations at UKMT 2015 Teacher Meetings.
NQT Inspiration Day: Nurturing Creative Problem Solvers - Summer 2015 event in Cambridge
A collection of short Stage 3 and 4 problems on Thinking Strategically.
A collection of short problems on transformations.
A collection of short Stage 3 and 4 problems on Working Systematically.
Test yourself with these short challenges
A collection of short Stage 3 and 4 problems on Visualising.
Resources to accompany Charlie's workshop at the Prince's Teaching Institute's Residential Summer School in Cambridge.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Resources to accompany Tabitha's and Charlie's workshops at the Prince's Teaching Institute's New Teacher Days.
A collection of short Stage 3 and 4 problems on Representing.
Resources to accompany Fran's and Charlie's workshops at the ATM & MA Easter Conferences.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
A collection of short problems on area and volume.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Resources to accompany Charlie's 2015 presentation at PLT Day in Devonport High School for Boys.
Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
Explore the effect of reflecting in two parallel mirror lines.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
A collection of short problems on creating algebraic expressions.
Explore the effect of combining enlargements.
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
How many ways can you find to put in operation signs (+ - x ÷) to make 100?
What are the possible areas of triangles drawn in a square?
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?
Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
Explore the effect of reflecting in two intersecting mirror lines.
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Can you deduce the perimeters of the shapes from the information given?
If you move the tiles around, can you make squares with different coloured edges?
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
A collection of short problems on 3D shapes.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
There are lots of ideas to explore in these sequences of ordered fractions.