Good Mathematicians Can Go Backwards

Colleen Young

Going Backwards

There is so much opportunity for thinking backwards when we teach ndash a great learning opportunity and also a problem solving strategy

Going Backwards

The following slides include ideas and resources for thinking backwards

Many of the slides have hyperlinks for further information and resources

Tables

Learn them backwards too

Try Transumrsquos Fast Factors

Going Backwards

There is so much opportunity for thinking backwards when we teach ndash a great learning opportunity and also a problem solving strategy

Going Backwards

The following slides include ideas and resources for thinking backwards

Many of the slides have hyperlinks for further information and resources

Tables

Learn them backwards too

Try Transumrsquos Fast Factors

Going Backwards

The following slides include ideas and resources for thinking backwards

Many of the slides have hyperlinks for further information and resources

Tables

Learn them backwards too

Try Transumrsquos Fast Factors

Tables

Learn them backwards too

Try Transumrsquos Fast Factors

Number Operations

Manipulate numerical expressions

Percentages

The price of a dress is increased by 10 the original price is pound40 what is the new price

Solve then pose the same question backwards

After an increase of 10 a dress costs pound44 what was the original price

Factorising

If you can multiply out brackets you can factorise

4(x+y) = 4x+4y 6aminus6b = 6(a-b)

(x+4)(x+2) = x2+6x+8x2-5x+6 = (x-2)(x-3)

Standards Unit ndash Build an Equation

pdf file

Factorising

If you can multiply out brackets you can factorise

4(x+y) = 4x+4y 6aminus6b = 6(a-b)

(x+4)(x+2) = x2+6x+8x2-5x+6 = (x-2)(x-3)

Standards Unit ndash Build an Equation

pdf file

Standards Unit ndash Build an Equation

pdf file

From Nrich

Working backwards at KS2 the ideas here could also be used at KS3See this Nrich article from Liz Woodhamon Developing Problem-solving skills which includes the link above

Arithmagons

Perfect for any topic for thinking backwards

See the ideas and resources here ndasheverything from simple arithmetic to Calculus

Arithmagons from Flash Maths

Problems

See for example the AQA problems included here

This type of backwards problem really helps students think deeply

Herersquos the diagram

For a variation on herersquos the answer whatrsquos the question

Try herersquos the diagram whatrsquos the question

Or try Algebra Snippets

Puzzles

bull Sudoku see these Nrich resources

bull Ken Ken

bull Find the Factors

Laws of logs

Learn everything from right to left as well as left to right

Learn it both ways

Learn everything from right to left as well as left to right

If you know your laws of indices you should recognise that x10 = x1 times x9

For every derivative you know you also know an integral

and so onand onand on

Mathematics for Students Mathematics Learning and Technology

Learn it both ways

Learn everything from right to left as well as left to right

If you know your laws of indices you should recognise that x10 = x1 times x9

For every derivative you know you also know an integral

and so onand onand on

Mathematics for Students Mathematics Learning and Technology

Mathematics for Students Mathematics Learning and Technology