Year 9 Exploring and noticing

problem

Favourite

Xavi's T-shirt

Age

7 to 16

Challenge level

How much can you read into a T-shirt?

problem

Favourite

Growing surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?

game

Favourite

Diamond collector

Age

11 to 16

Challenge level

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

problem

Favourite

Days and dates

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...

problem

Favourite

What's it worth?

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?

problem

Favourite

Largest product

Age

11 to 14

Challenge level

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

problem

Favourite

Cinema problem

Age

11 to 14

Challenge level

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

problem

Favourite

Special numbers

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?

problem

Favourite

Tilted squares

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?

problem

Favourite

How far does it move?

Age

11 to 14

Challenge level

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.

problem

Favourite

Parallel lines

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?

problem

Favourite

In the bag

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?

problem

Favourite

Elevenses

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?

problem

Favourite

Reflecting lines

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.

problem

Favourite

Translating lines

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.

problem

Favourite

Cyclic quadrilaterals

Age

11 to 16

Challenge level

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

problem

Favourite

What's the weather like?

Age

11 to 14

Challenge level

With access to weather station data, what interesting questions can you investigate?

problem

Favourite

Wipeout

Age

11 to 16

Challenge level

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

problem

Favourite

Star polygons

Age

11 to 14

Challenge level

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

problem

Favourite

Triangle in a trapezium

Age

11 to 16

Challenge level

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

problem

Favourite

Terminating or not

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?

problem

Favourite

Marbles in a box

Age

11 to 16

Challenge level

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

problem

Favourite

Think of two numbers

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?

problem

Favourite

Sending a parcel

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?

problem

Favourite

Square coordinates

Age

11 to 14

Challenge level

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

problem

Favourite

Subtended angles

Age

11 to 14

Challenge level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

problem

Favourite

Mixing paints

Age

11 to 14

Challenge level

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

problem

Favourite

Speeding up, slowing down

Age

11 to 14

Challenge level

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

problem

Favourite

Twisting and turning

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.

problem

Favourite

How many miles to go?

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?

problem

Favourite

Up and across

Age

11 to 14

Challenge level

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.

problem

Favourite

Generating triples

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?