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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Year 9 Exploring and Noticing

### Reflecting Lines

### Largest Product

### Translating Lines

### Parallel Lines

### Cinema Problem

### Days and Dates

### Special Numbers

### Growing Surprises

### In the Bag

### Tilted Squares

### Elevenses

### Think of Two Numbers

### Mixing Paints

### Twisting and Turning

### Terminating or Not

### Sending a Parcel

### How Many Miles to Go?

### Cyclic Quadrilaterals

### Diamond Collector

### What's it Worth?

### Marbles in a Box

### Generating Triples

### Tree Tops

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Age 11 to 14

Challenge Level

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Age 11 to 14

Challenge Level

Which set of numbers that add to 100 have the largest product?

Age 11 to 14

Challenge Level

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

Age 11 to 14

Challenge Level

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

Age 11 to 14

Challenge Level

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.

Age 11 to 14

Challenge Level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Age 11 to 14

Challenge Level

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?

Age 11 to 14

Challenge Level

Can you find the connections between linear and quadratic patterns?

Age 11 to 14

Challenge Level

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

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 11 to 14

Challenge Level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Age 11 to 14

Challenge Level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Age 11 to 14

Challenge Level

Can you work out how to produce different shades of pink paint?

Age 11 to 14

Challenge Level

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

Age 11 to 14

Challenge Level

Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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 16

Challenge Level

Collect as many diamonds as you can by drawing three straight lines.

Age 11 to 16

Challenge Level

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

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

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Age 14 to 16

Challenge Level

Can you make sense of information about trees in order to maximise the profits of a forestry company?