Working systematically - Lower Secondary

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

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

Can all unit fractions be written as the sum of two unit fractions?

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

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

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

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?

There are lots of different methods to find out what the shapes are worth - how many can you find?

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.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Can you find the squares hidden on these coordinate grids?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

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

A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?

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?

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

Can you find triangles on a 9-point circle? Can you work out their angles?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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 parallelogram.

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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 rhombus.

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

How many questions do you need to identify my quadrilateral?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

What's the largest volume of box you can make from a square of paper?

We started drawing some quadrilaterals - can you complete them?

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

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Five equations and five unknowns. Is there an easy way to find the unknown values?

Use the differences to find the solution to this Sudoku.

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?