Year 9 Conjecturing and generalising

problem

Xavi's T-shirt

Age

7 to 16

Challenge level

How much can you read into a T-shirt?

problem

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

Blue and white

Age

11 to 14

Challenge level

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

problem

Largest product

Age

11 to 14

Challenge level

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

problem

Picturing triangular numbers

Age

11 to 14

Challenge level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

problem

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

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

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

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

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

Diminishing returns

Age

11 to 14

Challenge level

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

problem

Growing surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?

problem

Counting factors

Age

11 to 14

Challenge level

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

problem

Legs eleven

Age

11 to 14

Challenge level

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?

problem

1 step 2 step

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?

problem

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

Tower of Hanoi

Age

11 to 14

Challenge level

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

problem

Opposite vertices

Age

11 to 14

Challenge level

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

problem

What numbers can we make now?

Age

11 to 14

Challenge level

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

problem

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

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

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

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?

problem

Mixing more paints

Age

14 to 16

Challenge level

Can you find an efficent way to mix paints in any ratio?

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For younger learners

Year 9 Conjecturing and generalising

Xavi's T-shirt

Days and dates

Blue and white

Largest product

Picturing triangular numbers

Tilted squares

Parallel lines

Reflecting lines

Translating lines

Cyclic quadrilaterals

Diminishing returns

Growing surprises

Counting factors

Legs eleven

1 step 2 step

Subtended angles

Tower of Hanoi

Opposite vertices

What numbers can we make now?

Wipeout

Terminating or not

How many miles to go?

Generating triples

Mixing more paints