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Resources tagged with Manipulating algebraic expressions/formulae similar to Breaking the Equation ' Empirical Argument = Proof ':

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Broad Topics > Algebra > Manipulating algebraic expressions/formulae

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Sums of Pairs

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

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Algebra Match

Stage: 3 and 4 Challenge Level: Challenge Level:1

A task which depends on members of the group noticing the needs of others and responding.

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Magic Sums and Products

Stage: 3 and 4

How to build your own magic squares.

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Algebra from Geometry

Stage: 3 and 4 Challenge Level: Challenge Level:1

Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.

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Multiplication Square

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

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Perimeter Expressions

Stage: 3 Challenge Level: Challenge Level:1

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

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Your Number Was...

Stage: 3 Challenge Level: Challenge Level:1

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

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Crossed Ends

Stage: 3 Challenge Level: Challenge Level:1

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

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Partitioning Revisited

Stage: 3 Challenge Level: Challenge Level:1

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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Adding in Rows

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

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Cubes Within Cubes Revisited

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

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Matchless

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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Temperature

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?