List

Year 9 Conjecturing and Generalising

Parallel lines
problem
Favourite

Parallel lines

Age
11 to 14
Challenge level
filled star empty star empty star
How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
Reflecting Lines
problem
Favourite

Reflecting Lines

Age
11 to 14
Challenge level
filled star empty star empty star
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.
Translating Lines
problem
Favourite

Translating Lines

Age
11 to 14
Challenge level
filled star empty star empty star
Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
Cyclic Quadrilaterals
problem
Favourite

Cyclic Quadrilaterals

Age
11 to 16
Challenge level
filled star empty star empty star

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

Diminishing Returns
problem
Favourite

Diminishing Returns

Age
11 to 14
Challenge level
filled star empty star empty star
How much of the square is coloured blue? How will the pattern continue?
Growing Surprises
problem
Favourite

Growing Surprises

Age
11 to 14
Challenge level
filled star empty star empty star
Can you find the connections between linear and quadratic patterns?
Days and Dates
problem
Favourite

Days and Dates

Age
11 to 14
Challenge level
filled star empty star empty star
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Largest product
problem
Favourite

Largest product

Age
11 to 14
Challenge level
filled star empty star empty star
Which set of numbers that add to 100 have the largest product?
Picturing Triangular Numbers
problem
Favourite

Picturing Triangular Numbers

Age
11 to 14
Challenge level
filled star empty star empty star
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Tilted Squares
problem
Favourite

Tilted Squares

Age
11 to 14
Challenge level
filled star empty star empty star

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

Tower of Hanoi
problem
Favourite

Tower of Hanoi

Age
11 to 14
Challenge level
filled star filled star empty star
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Opposite vertices
problem
Favourite

Opposite vertices

Age
11 to 14
Challenge level
filled star filled star empty star

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

What numbers can we make now?
problem
Favourite

What numbers can we make now?

Age
11 to 14
Challenge level
filled star filled star empty star

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

Wipeout
problem
Favourite

Wipeout

Age
11 to 16
Challenge level
filled star filled star empty star
Can you do a little mathematical detective work to figure out which number has been wiped out?
Terminating or not
problem
Favourite

Terminating or not

Age
11 to 14
Challenge level
filled star filled star empty star
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
Counting Factors
problem
Favourite

Counting Factors

Age
11 to 14
Challenge level
filled star filled star empty star
Is there an efficient way to work out how many factors a large number has?
Legs Eleven
problem
Favourite

Legs Eleven

Age
11 to 14
Challenge level
filled star filled star empty star
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?
1 Step 2 Step
problem
Favourite

1 Step 2 Step

Age
11 to 14
Challenge level
filled star filled star empty star
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?
How Many Miles To Go?
problem
Favourite

How Many Miles To Go?

Age
11 to 14
Challenge level
filled star filled star filled star
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?
Generating Triples
problem
Favourite

Generating Triples

Age
14 to 16
Challenge level
filled star empty star empty star
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?
Mixing More Paints
problem
Favourite

Mixing More Paints

Age
14 to 16
Challenge level
filled star filled star filled star
Can you find an efficent way to mix paints in any ratio?