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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Exploring and Noticing Structure

### Consecutive Numbers

### Calendar Capers

### Have You Got It?

### Summing Consecutive Numbers

### What's Possible?

### Marbles in a Box

### Attractive Tablecloths

### 1 Step 2 Step

### Pick's Theorem

### Pair Products

### Number Pyramids

### Tilted Squares

### Painted Cube

### Arithmagons

### Route to Infinity

### Impossible Triangles?

### Interactive Spinners

### Keep it Simple

### Cyclic Quadrilaterals

### How Much Can We Spend?

### Shifting Times Tables

### Charlie's Delightful Machine

### What Numbers Can We Make?

### Vector Journeys

### Steel Cables

### Magic Letters

### Seven Squares

### Exploring and Noticing Structure - Short Problems

## Related Collections

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Age 7 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

Choose any three by three square of dates on a calendar page...

Age 11 to 14

Challenge Level

Can you explain the strategy for winning this game with any target?

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?

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?

Age 11 to 16

Challenge Level

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

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?

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?

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.

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?

Age 11 to 14

Challenge Level

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

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?

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?

Age 11 to 16

Challenge Level

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

Age 11 to 14

Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

Age 16 to 18

Challenge Level

Which of these triangular jigsaws are impossible to finish?

Age 11 to 14

Challenge Level

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Age 11 to 14

Challenge Level

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

Age 11 to 16

Challenge Level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Age 11 to 14

Challenge Level

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?

Age 11 to 14

Challenge Level

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

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?

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?

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?

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?

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?

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?

Age 11 to 16

A collection of short Stage 3 and 4 problems on Exploring and Noticing Structure.