Year 9 Exploring and noticing

How much can you read into a T-shirt?

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

Engage in a little mathematical detective work to see if you can spot the fakes.

Can you find the connections between linear and quadratic patterns?

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

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

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

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

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?

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

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.

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

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?

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

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.

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

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

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

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

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

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

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

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

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

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?

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?

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

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

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

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

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?

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.

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?

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

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?