good mathematicians can go backwards!
TRANSCRIPT
![Page 1: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/1.jpg)
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
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
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
![Page 2: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/2.jpg)
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
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
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
![Page 3: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/3.jpg)
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
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
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
![Page 4: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/4.jpg)
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
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
![Page 5: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/5.jpg)
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
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
![Page 6: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/6.jpg)
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
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
![Page 7: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/7.jpg)
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
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
![Page 8: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/8.jpg)
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
![Page 9: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/9.jpg)
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
![Page 10: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/10.jpg)
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
![Page 11: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/11.jpg)
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
![Page 12: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/12.jpg)
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
![Page 13: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/13.jpg)
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
![Page 14: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/14.jpg)
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
![Page 15: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/15.jpg)
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
![Page 16: Good mathematicians Can Go Backwards!](https://reader031.vdocument.in/reader031/viewer/2022032113/55a5c8271a28abeb308b45ad/html5/thumbnails/16.jpg)
Mathematics for Students Mathematics Learning and Technology