To be updated Saturday 18th June 2022 following my session at UCL Institute of Education.

Explaining to my Advanced level students recently that they need to know material like the laws of logs backwards and forwards because they don’t always immediately recognise the right hand side of a rule they know when seen in isolation, it struck me how often I talk about going backwards!

So, this week some ideas and resources for thinking backwards! (The presentation has been added to the series of Presentations pages in case I, or anyone else wishes to easily find it again!)

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8 comments on “Good Mathematicians Can Go Backwards”

I really enjoyed reading your post on how important it is to be able to think backwards in math. I loved Slide #5 of your presentation “If I know this, I also know this . . . ” and the slide on Building an Equation. I look forward to checking some of the resources that you included.
I feel like my sixth grade students coming up from elementary school have a pretty good understanding of inverse operations with addition/subtraction and multiplication/division. I think it is so important to build on that foundation with new concepts like squares/square roots, cubes/cube roots, distributive property/factoring, conversions between fraction/percent and decimal/percent. I like to play a game called Name that Operation with my students where they find all the ways to go from 2 to 8 and then all the ways to go backwards from 8 to 2. This game has been a nice way to introduce the units on square roots and factoring algebraic expressions as simply the reverse of squaring and distributive property.

When my son was in year 1 he didn’t learn addition and subtraction in the traditional way, he learnt to balance an equation, so the direction he was working in just depended on where the empty number box was. I thought this was great as so many year 7s arrive we the idea that the sum is on the left of the equals and the answer is on the right.

Great presentation, Colleen. Learning everything from right to left as well as left to right makes sense. I wonder how early this could start? Doing equations only from left to right goes on for years in elementary school. Do you think that, right from the beginning of learning, that this could be started? This approach seems to recognize that math is about relationships, rather than just calculations.

I wonder if we should do more of this earlier Paula – I found myself thinking as I prepared this – why do we currently have the gap that we do between teaching simple multiplication of brackets and factorising. Perhaps we should do it all together!

Pingback:434 Going Backwards Is Important! | Find the FactorsI really enjoyed reading your post on how important it is to be able to think backwards in math. I loved Slide #5 of your presentation “If I know this, I also know this . . . ” and the slide on Building an Equation. I look forward to checking some of the resources that you included.

I feel like my sixth grade students coming up from elementary school have a pretty good understanding of inverse operations with addition/subtraction and multiplication/division. I think it is so important to build on that foundation with new concepts like squares/square roots, cubes/cube roots, distributive property/factoring, conversions between fraction/percent and decimal/percent. I like to play a game called Name that Operation with my students where they find all the ways to go from 2 to 8 and then all the ways to go backwards from 8 to 2. This game has been a nice way to introduce the units on square roots and factoring algebraic expressions as simply the reverse of squaring and distributive property.

Sara thank you so much for your comment – I like the sound of your game “Name that Operation”!

Our latest problem is “backwards”:

http://fivetriangles.blogspot.com/2015/03/227-black-and-white-card-game.html

When my son was in year 1 he didn’t learn addition and subtraction in the traditional way, he learnt to balance an equation, so the direction he was working in just depended on where the empty number box was. I thought this was great as so many year 7s arrive we the idea that the sum is on the left of the equals and the answer is on the right.

That sounds like great teaching Nikki. Don’t we want to see more of this kind of thinking with young children?

Great presentation, Colleen. Learning everything from right to left as well as left to right makes sense. I wonder how early this could start? Doing equations only from left to right goes on for years in elementary school. Do you think that, right from the beginning of learning, that this could be started? This approach seems to recognize that math is about relationships, rather than just calculations.

I wonder if we should do more of this earlier Paula – I found myself thinking as I prepared this – why do we currently have the gap that we do between teaching simple multiplication of brackets and factorising. Perhaps we should do it all together!