List

Year 9 Conjecturing and Generalising

Days and Dates
problem
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Days and Dates

Age
11 to 14
Challenge level
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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
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Largest product

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

Age
11 to 14
Challenge level
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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
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Tilted Squares

Age
11 to 14
Challenge level
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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Parallel lines
problem
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Parallel lines

Age
11 to 14
Challenge level
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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
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Reflecting Lines

Age
11 to 14
Challenge level
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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
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Translating Lines

Age
11 to 14
Challenge level
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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
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Cyclic Quadrilaterals

Age
11 to 16
Challenge level
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Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Diminishing Returns
problem
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Diminishing Returns

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

Age
11 to 14
Challenge level
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Can you find the connections between linear and quadratic patterns?
Counting Factors
problem
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Counting Factors

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

Age
11 to 14
Challenge level
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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
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1 Step 2 Step

Age
11 to 14
Challenge level
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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?
Tower of Hanoi
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Tower of Hanoi

Age
11 to 14
Challenge level
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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
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Opposite vertices

Age
11 to 14
Challenge level
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Can you recreate squares and rhombuses if you are only given a side or a diagonal?

What numbers can we make now?
problem
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What numbers can we make now?

Age
11 to 14
Challenge level
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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Wipeout
problem
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Wipeout

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

Age
11 to 14
Challenge level
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Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
How Many Miles To Go?
problem
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How Many Miles To Go?

Age
11 to 14
Challenge level
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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
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Generating Triples

Age
14 to 16
Challenge level
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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
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Mixing More Paints

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