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.

5 Maths Gems #81

Happy New Year! Welcome to my 81^st gems post. This is where I portion roughly of the latest news, ideas in addition to resources for maths teachers.

1. Number Properties
In Gems 79 I shared this lovely puzzle from Chris Smith (@aap03102):

Since in addition to then I've seen 2 peachy resources based on a similar idea. The commencement is the interactive 'Consecutive Number Types' puzzles from Jonathan Hall (@StudyMaths):

And the minute is this complimentary worksheet 'Consecutive Chains' from MathsPad.

I recall these would locomote actually good at Key Stage 2, iii or 4 for exploring issue properties.

2. Online Textbooks 
After I blogged almost a 1950s textbook final month, I gathered together a grouping of volunteers to type upwards former algebra exercises into Word in addition to locomote out the answers. Thank y'all thus much to everyone who has contributed. The projection is ongoing in addition to I volition spider web log almost it soon. In the meantime, y'all tin come across our progress here. Also, give cheers y'all to @EmporiumMaths for sharing roughly 1950s algebra questions from past times London O flat papers here.

Huge cheers to @NetNym for sharing a beautiful Victorian maths textbook 'Elementary Algebra for Schools' that has been fully digitised. This actually is lovely in addition to good worth looking through (I'm a chip addicted to it!). The zoom business office plant good thus the exercises tin hold upwards used inwards degree if desired - answers are included, in addition to the whole mass tin hold upwards downloaded every bit a PDF.

I recall that nosotros bring a lot to larn from the explanations in addition to examples inwards this textbook. I've started writing a post almost this which I promise to break adjacent week.

Meanwhile, a instructor inwards Commonwealth of Australia (@adaprojectnet) has created a website adaproject.net which is an opened upwards online textbook for all to use, roofing topics from Key Stage 1 to 5. It's worth having a await at this projection which is growing all the time. 

3. Primary Resources

It's peachy to come across John Corbett (@Corbettmaths) publishing lots of novel primary 5-a-day content amongst his real pop GCSE 5-a-day collection. Each twenty-four hr catamenia at that spot are v KS2 SATs trend questions at 4 dissimilar hard levels.

Also for primaries, Dr Frost (@DrFrostMaths) has right away added Primary Maths Challenge questions to his website with the aid of @Mathematical_A. You tin browse past times theme or past times paper.

Primary Maths Challenge questions

4. Influenza A virus subtype H5N1 Level Resources
StudyWell (@_StudyWell) has published a twosome of practice papers for the novel Influenza A virus subtype H5N1 flat - these are complimentary for a express time.

Tom Bennison (New GCSE: Ratio

Jo's Blog Posts inwards 2017

New this Christmas

Algebraic Fluency - 50s Style

Mock Season

You tin read the latest eNews from the Mathematical Association here.

I'm excited that I've right away booked a identify at post almost it. The cost goes upwards afterwards 31st Jan thus mass quickly!

I besides promise to come across lots of y'all at #mathsconf14 inwards Kettering on Sabbatum tenth March, in addition to for drinks the black before. I had a wonderful fourth dimension at all the maths events I attended inwards 2017 - if you've non been to a maths conference before, why non bring a become inwards 2018? All events are listed here.

I'll acquire out y'all with this lovely graph, shared by @simongerman600, showing what people actually hateful when they purpose vague terminology describing the likelihood of an event. There are other cool graphs here. I recall this 1 would brand an fantabulous give-and-take indicate when teaching probability.

Have a fantastic term maths teachers! And all the best for 2018.

Equations Exercises

I was looking at roughly of the one-time maths textbooks at my schoolhouse in addition to noticed than fifty-fifty equally latterly equally the 1980s, textbook exercises contained a lot to a greater extent than do questions than modern textbooks. Below is an instance comparison the same theme inward a 1980s textbook ('Negative Numbers in addition to Graphs' past times Heylings) in addition to a electrical flow GCSE textbook ('Edexcel GCSE Maths Higher' published past times Oxford University Press). The exercises encompass the same science only the root exercise is double the length of the second. I approximate modern textbooks convey to tally an entire GCSE course of didactics into a unmarried book, restricting the sum of do questions they tin include.

From 'Negative Numbers in addition to Graphs', root published 1984

From 'Edexcel GCSE Maths Higher', root published 2015

Last calendar month I wrote a post service virtually a 1950s algebra textbook called 'A Classbook of Algebra'. The questions inward this textbook are by in addition to large to a greater extent than challenging than questions inward most modern textbooks. In response to this post service a issue of rattling generous volunteers stepped forrad offering to type upward roughly of the exercises in addition to thence that teachers tin purpose them inward lessons. I am rattling grateful for the fourth dimension in addition to test that has gone into this. In this post service I convey provided links to all the exercises typed upward in addition to thence far which relate to the science of solving equations. I convey an additional xviii exercises on other topics which I volition collate over the side past times side few weeks.

These exercises are all rather long in addition to the thought is non necessarily to purpose them inward their entirety. Because they convey all been typed upward inward in Word, teachers volition easily endure able to edit the exercises or cutting in addition to glue item questions to purpose equally examples inward class.

Most exercises include answers. I volition edit this post service if anything is updated. For each exercise listed below I convey included a minor extract in addition to thence you lot tin preview the type of questions covered.

1. Very Easy Equations (four exercises) - alongside thank you lot to Caroline Beale (@cbealemaths)

2. Easy Equations I - alongside thank you lot to Claire Willis (@MissWillisMaths)

3. Easy Equations II - alongside thank you lot to Caroline Beale (@cbealemaths)

4. Equations Involving Fractions - alongside thank you lot to Michael Allan (@mrallanmaths)

5. Equations Involving Brackets - alongside thank you lot to Jane Appleton (@JaneAppleton24)

6. Equations alongside Brackets in addition to Harder Equations alongside Brackets - alongside thank you lot to Justin Thompson 

7. Equations Involving Directed Numbers - alongside thank you lot to Caroline Beale (@cbealemaths)

8. Easy Literal Equations - alongside thank you lot to Sandra Douglas (@mathsbox1)

9. Miscellaneous Simultaneous Equations - alongside thank you lot to Fee Wilson (@fionajw)

10. Miscellaneous Equations - alongside thank you lot to Dan Rodriguez-Clark (@InteractMaths). 

I promise this is useful. Thank you lot in 1 trial again to everyone who has worked on this. And of course of didactics total credit to Sidney Trustram, the master writer of these exercises which, lxx years on, are all the same making us think. Look out for my side past times side posts inward which I'll percentage exercises on simplifying algebra, expanding, factorising, writing algebraically in addition to working alongside directed numbers.

Algebra Exercises

A few weeks agone I published a postal service called 'Equations Exercises' inwards which I shared about exercises that induce got been typed upward from a 1950s algebra textbook. In my persuasion these are good written exercises amongst a proficient degree of stretch in addition to challenge. The thought is non necessarily to purpose these exercises inwards their entirety. They are provided inwards Word format then it's slowly to re-create in addition to glue extracts in addition to examples to purpose inwards class.

In today's postal service I've provided links to about other develop of exercises from the same textbook. They cover simplifying algebra, including index laws in addition to algebraic fractions. There's likewise an practise on exchange in addition to i on writing algebraically. For each practise listed below I induce got included an extract then yous tin preview the type of questions covered.

1. Notation, Addition in addition to Subtraction I in addition to II - amongst thank yous to Katie Pollard (@takepi21)

2. Notation, Multiplication in addition to Indices I - amongst thank yous to Phil Bruce (@pbrucemaths)

3. Notation, Multiplication in addition to Indices II - amongst thank yous to Daniel Udall (@DJUdall)

4. Simple Powers - amongst thank yous to Larissa Alsford (@lolsford)

5. Notation - Division - amongst thank yous to Caroline Beale (@cbealemaths)

6. Simple Multiplication of Fractions - amongst thank yous to Alice Dwyer (@littlemissdwyer)

7. Simplification of Fractions yesteryear Factors II - amongst thank yous to Sandra Douglas (@mathsbox1)

8. Easy Fractions, Substitution - amongst thank yous to Steve Bishop (@stevebishop100)

9.  Translation I in addition to II - amongst thank yous to Ben Gordon (@mathsmrgordon)

I'll disclose i to a greater extent than develop of exercises side yesteryear side calendar week - about on directed numbers, in addition to about on factorising in addition to expanding.

Huge thank yous i time to a greater extent than to the teachers who typed these exercises up. I actually appreciate the fourth dimension in addition to try that has gone into this. Excellent teamwork!

Old Textbook Exercises

This is the final inwards my serial of 3 posts sharing the last of a squad of teachers who bring been busy typing upward exercises from a 1950s algebra textbook.

In today's post service I've provided links for ii topics:

A. Directed Numbers 

B. Factorising together with Expanding. 

For each practice I've included an extract together with therefore you lot tin preview the type of questions covered. The thought is non necessarily to purpose these exercises inwards their entirety. They are provided inwards Word format together with therefore it's slow to re-create together with glue extracts together with examples to purpose inwards class.

1. Use of Directed Numbers - alongside thank you lot to Dee Vijayan (@DeeVijayan)

2. The Products of Directed Numbers - with thank you lot to Alice Dwyer (@littlemissdwyer)

3. Quotients of Directed Numbers - alongside thank you lot to Dee Vijayan (@DeeVijayan)

4. Easy Brackets I - alongside thank you lot to Michael Devine (@FitzchivalryF)

5. Miscellaneous Easy Brackets - alongside thank you lot to Dan Rodriguez-Clark (@InteractMaths)

6. Factors yesteryear Grouping - alongside thank you lot to Paul Rodrigo (@PaulRodrigo2718)

7. Miscellaneous Factors - alongside thank you lot to Dan Rodriguez-Clark (@InteractMaths)

I volition add together these exercises to my resources libraries. Huge thank you lot to the teachers who typed these up, I actually appreciate it.

Here are my ii previous posts from this series:

• Equations Exercises
• Algebra Exercises

I promise these are helpful.