Being resourceful - Secondary students

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Can you find the values at the vertices when you know the values on the edges?

Observe symmetries and engage the power of substitution to solve complicated equations.

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Use the differences to find the solution to this Sudoku.

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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?

There are nasty versions of this dice game but we'll start with the nice ones...

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

One day, five small animals in my garden had a sports day. Who do you think won each race?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Can you select the missing digit(s) to find the largest multiple?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

If you move the tiles around, can you make squares with different coloured edges?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Dotty Six is a simple dice game that you can adapt in many ways.

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

What can you see? What do you notice? What questions can you ask?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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?

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?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

How many different symmetrical shapes can you make by shading triangles or squares?

Can you find the hidden factors which multiply together to produce each quadratic expression?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Can you do a little mathematical detective work to figure out which number has been wiped out?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Can you find a way to identify times tables after they have been shifted up or down?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

How much can you read into a T-shirt?