17 January 2018

Equations Exercises

I was looking at some of the old maths textbooks at my school and noticed than even as recently as the 1980s, textbook exercises contained a lot more practice questions than modern textbooks. Below is an example comparing the same topic in a 1980s textbook ('Negative Numbers and Graphs' by Heylings) and a current GCSE textbook ('Edexcel GCSE Maths Higher' published by Oxford University Press). The exercises cover the same skill but the first exercise is double the length of the second. I guess modern textbooks have to fit an entire GCSE course into a single book, restricting the amount of practice questions they can include.
From 'Negative Numbers and Graphs', first published 1984

From 'Edexcel GCSE Maths Higher', first published 2015

Last month I wrote a post about a 1950s algebra textbook called 'A Classbook of Algebra'. The questions in this textbook are generally more challenging than questions in most modern textbooks. In response to this post a number of very generous volunteers stepped forward offering to type up some of the exercises so that teachers can use them in lessons. I am very grateful for the time and effort that has gone into this. In this post I have provided links to all the exercises typed up so far which relate to the skill of solving equations. I have an additional eighteen exercises on other topics which I will collate over the next few weeks.

These exercises are all rather long and the idea is not necessarily to use them in their entirety. Because they have all been typed up in in Word, teachers will easily be able to edit the exercises or cut and paste particular questions to use as examples in class.

Most exercises include answers. I will edit this post if anything is updated. For each exercise listed below I have included a small extract so you can preview the type of questions covered.

1. Very Easy Equations (four exercises) - with thanks to Caroline Beale (@cbealemaths)

2. Easy Equations I - with thanks to Claire Willis (@MissWillisMaths)

3. Easy Equations II - with thanks to Caroline Beale (@cbealemaths)

4. Equations Involving Fractions - with thanks to Michael Allan (@mrallanmaths)

5. Equations Involving Brackets - with thanks to Jane Appleton (@JaneAppleton24)

6. Equations with Brackets and Harder Equations with Brackets - with thanks to Justin Thompson 
7. Equations Involving Directed Numbers - with thanks to Caroline Beale (@cbealemaths)

8. Easy Literal Equations - with thanks to Sandra Douglas (@mathsbox1)

9. Miscellaneous Simultaneous Equations - with thanks to Fee Wilson (@fionajw)
10. Miscellaneous Equations - with thanks to Dan Rodriguez-Clark (@InteractMaths). 

I hope this is useful. Thank you again to everyone who has worked on this. And of course full credit to Sidney Trustram, the original author of these exercises which, 70 years on, are still making us think. Look out for my next posts in which I'll share exercises on simplifying algebra, expanding, factorising, writing algebraically and working with directed numbers.

1 comment:

  1. Solving equations with the unknown on one side can rapidly become very difficult. I used to have great success helping students to use the cover-up method, expecially using the old WisWeb Java Applets. Big thanks to Colleen Young for pointing out that HTML versions of the Applets can now be found at the Freudenthal Institute Digital Mathematics Environment: https://app.dwo.nl/en/student/ and logging in as a guest. The cover-up applets can then be found by following Secondary Education/Algebra/Exercises-Equations/The Cover Up Method. I used to find that students worked out how to solve very difficult linear equations using this method - they used to surprise themselves!