List

Creating and manipulating linear and quadratic expressions - Stage 3

Special Numbers
problem

Special numbers

Age
11 to 14
Challenge level
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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?

Number Pyramids
problem

Number pyramids

Age
11 to 14
Challenge level
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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

More Number Pyramids
problem

More number pyramids

Age
11 to 14
Challenge level
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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Your number is...
problem

Your number is...

Age
7 to 14
Challenge level
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Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
Harmonic Triangle
problem

Harmonic triangle

Age
14 to 16
Challenge level
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Can you see how to build a harmonic triangle? Can you work out the next two rows?
Crossed Ends
problem

Crossed ends

Age
11 to 14
Challenge level
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Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Always a multiple?
problem

Always a multiple?

Age
11 to 14
Challenge level
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Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Perimeter Expressions
problem

Perimeter expressions

Age
11 to 14
Challenge level
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Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
Beach Huts
problem

Beach huts

Age
11 to 14
Challenge level
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Can you figure out how sequences of beach huts are generated?
Reversals
problem

Reversals

Age
11 to 14
Challenge level
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Where should you start, if you want to finish back where you started?
Fibonacci Surprises
problem

Fibonacci surprises

Age
11 to 14
Challenge level
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Play around with the Fibonacci sequence and discover some surprising results!

Puzzling Place Value
problem

Puzzling place value

Age
14 to 16
Challenge level
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Can you explain what is going on in these puzzling number tricks?