Algebraic Fluency - 50S Style

Whilst visiting the Mathematical Association inwards Leicester on Saturday, I picked upwardly a duet of onetime maths textbooks from the 1950s. 'A Classbook of Algebra' is my favourite.

In it I establish about wonderful exercises for developing algebraic fluency, including this fix of questions on 'Miscellaneous Factors':

The pedagogy 'factorise where possible' adds a delightful extra marking of intrigue in addition to challenge to this exercise. I dear these questions...

Factorise c - 3 + 2x(3 - c)

Factorise c² - (c - d)²

Factorise ef - 1 + e - f

Factorise -14yz + y² + 49z²

Factorise 81 - 9a  + 0.25a²

When I larn a run a jeopardy I'll type them all up. It does brand you lot wonder why the vast bulk of textbooks in addition to worksheets on factorising these days merely pick out questions similar this:

Factorise x² +7x

Factorise x² + 5x + 6

Factorise x² - 9

in addition to possibly this sort of affair for stretch:

Factorise 3x² + 10x + 8

Factorise 2x² - 18

Is that actually the best nosotros tin do? We could at to the lowest degree modify the gild of the terms! No wonder in addition to hence many of our students lack algebraic fluency when they larn to Influenza A virus subtype H5N1 level.

If you're thinking that this factorising usage from the 1950s is a flake tricky, you lot volition live on relieved to take away heed that inwards the same mass at that spot are a position out of exercises breaking downwardly the factorising skills into stages, leading upwardly to the 'Miscellaneous Factors' activity which brings it all together. For instance at that spot is a whole department on 'Factors past times Grouping' which explains how to factorise expressions similar ax + 2x + 3a + 6. I'm non certain this science is widely taught these days.

I pick out enough of students who would dear to larn stuck into these questions. Back inwards 2015 I wrote the shipping service 'Stretching Practice' which is nigh where to detect expert practise resources for high attainers. There's a decent alternative of resources available, but zip quite at the same marking equally the exercises from 1950s textbooks. I intend that the closest online resources for developing algebraic fluency are about of Don Steward's tasks, similar this first-class difference of 2 squares exercise:

I want I could present you lot every usage from 'A Classbook of Algebra'. There are in addition to hence many smashing questions. I'll exactly percentage a few to a greater extent than examples...

Under the championship 'Easy Brackets' nosotros detect questions that many teachers would right away role equally extension function inwards a lesson on expanding unmarried brackets:

And nether 'Miscellaneous Easy Brackets' the questions await real dissimilar to what nosotros right away regard to live on 'easy':

 

When nosotros learn 'collecting similar terms' I dubiety many of us role exercises similar this 1 on 'Addition in addition to Subtraction of Polynomials':

Check out the final question: 'To the excess of six - x + x² over 5 + x² - 3x add x² -3x + 4'!

Do you lot desire to banking enterprise gibe that your students really know how to expand brackets in addition to solve equations? Try about of these:

Here nosotros pick out double brackets too:

I wrote nigh multiplying negatives inwards this post, but the resources I featured didn't include algebra similar this usage does:

Finally (though I could become on all day!), here's something for your indices lesson:

If alone I had fourth dimension to type all these up!

I promise you lot enjoyed looking at exercises from the 1950s equally much equally I did.

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