Year 9 Conjecturing and generalising

How much can you read into a T-shirt?

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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

What do you notice about the sum of two identical triangular numbers?

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

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?

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.

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

How much of the square is coloured blue? How will the pattern continue?

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

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

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

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...

Is there an efficient way to work out how many factors a large number has?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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?

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?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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

Can you minimise the amount of wood needed to build the roof of my garden shed?

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

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?

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 find an efficent way to mix paints in any ratio?