Digitising Old Textbook Exercises

I have a pretty extension collection of old maths books. They’re very cheap to pick up in second hand bookstores, and the only thing stopping me from buying them all the time is the lack of space in my house!

I was browsing through ‘A New Course in Algebra’ this morning. It’s from 1959, so not particularly old compared to some other textbooks in my collection. It’s full of long algebra exercises with tonnes of challenge. I’m not suggesting we use these exercises in their entirety (I may be old fashioned, but even I draw the line at giving my students fifty sets of double brackets to expand!). But they do provide some nice ideas, particularly for extension questions.

I've blogged about the treasures I've found in old textbooks many times before (for example in my post about Elementary Algebra for Schools), and once I even had a team of teachers type up some of the exercises. I also have page on my blog where teachers can access online versions of old textbooks, going back to the 1500s. 

Today I thought I’d try something different. I took some pictures of exercises and tried converting them to PDFs using mathpix.com.

I didn't really know what to expect, but the quality of the output blew my mind! 

I randomly took some photos of pages from the textbook on my phone. I uploaded them to Mathpix and it instantly converted them to very high quality electronic versions. I'm shocked that it was able to read the pictures so well! Below are my initial attempts (note that I was randomly taking photos of various pages in the book, hence these aren't full exercises).

Here's the first photo I took:

And here's what Mathpix gave me. It is spot on.

I tried something which I thought might be harder to read (the indices in the textbook are a bit blurry):

But it had no trouble with this at all (this is an extract from this exercise - I have rearranged it in Word. I love these questions...)

I wondered if it could cope with surds and the answer is yes. 

This exercise on expanding double brackets came out clearly too. 

Compare this exercise with equivalent exercises in modern textbooks. So much thought has gone into it. I suspect that many modern day Key Stage 3 'top set' classes just practise the basics of expanding double brackets and then move on, instead of being given the opportunity to really strengthen their algebraic fluency by attempting questions like these.

And one final example - solving quadratic equations. 

Again, Mathpix converted it perfectly. Again, there are some great questions in this exercise.

Just as I got very excited about all this, I realised that Mathspix limits me to only ten free snips, and I used them all very quickly...

But it's so interesting to see that there's huge potential here to make very useable versions of some these old exercises. And yes - the answers are at the back of the book! So they could be converted too.

5 Maths Gems #174

Welcome to my 174^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Menu Maths

I saw a tweet about #menumath last week. These lovely tasks have been around for years but I realised that I've never featured them in a gems post.

This idea from @NatBanting is designed to generate 'low floor, high ceiling' challenges. Visit natbanting.com/menu-math to see the collection of tasks from various authors. In these tasks, students are given a 'menu' (a collection of constraints) and they have to create an object (e.g. an equation, a number or a shape) that satisfies these constraints. 

Teachers can make this task accessible by asking students to design objects that satisfy only one or two constraints, but can easily add challenge by asking students to satisfy more constraints. Students can also be asked to analyse which constraints pair well together and which cannot pair together.

Here are a couple of examples:

 

2. Rehearsal Strips

Thanks to @mrmorleymaths for sharing a new collection of tasks inspired by Dr Austin's practice strips. These Rehearsal Strips are designed to encourage rehearsal of taught content, but also allow students the opportunity to reason and explain, and test their understanding of the topic by applying it to another area of maths.

3. Eedi

@mrbartonmaths has launched a brand new collection of resources for every topic in maths. This free collection includes diagnostic questions, videos, fluency practice, intelligent practice and problem-solving questions. To access these materials, login at eedi.com (DQ logins will work here) and visit the Curriculum Mapping page.  Click 'View the collection', find a topic you are teaching soon and click on the Eedi link. 

Diagnostic Questions have always been brilliant for identifying and understanding misconceptions, so it's fantastic to see them supplemented with all these extra teaching resources.

4. A Level Knowledge Organisers

Thanks to @mrsd_maths for sharing an excellent collection of A level knowledge organisers. They can be downloaded from TES. I think these will be really helpful for revision. 

5. Fraction Bar

MathsPad has shared a free Interactive Fraction Bar Tool for finding fractions of an amount. The tool enables you to switch fraction families with the same amount, so for example, if you have already found a third of the amount, you can demonstrate how to use this to find a sixth. You can also start with different fractions, use different units (money and metric units) and extend the bar to show fractions greater than one whole.

Marvellous Maths 3
Tickets are selling fast for Marvellous Maths 3 - a full day of top quality maths CPD, presented by Craig Barton and myself. We are going on tour with this course: on 18th October we'll be at my lovely school in Sutton, South London. Then on 19th October we'll be at Worcester Racecourse, and on 20th October we'll be in Craig's hometown of Bolton at the Science and Technology Centre. It will be wonderful to be in a room full of maths teachers three days in a row! Book now at mathscpd.weebly.com.

AQA Webinar

I'm looking forward to taking part in AQA's free webinar at 4pm on 21st September. I'll be speaking about Level 2 Further Maths and Andrew Taylor will be speaking about the Summer '23 exam series.  There will be a live Q&A. You can sign up here. 

Speaking of Further Maths, @westiesworkshop has gone through the whole of AQA's L2 Further Maths course and grouped questions by topic. The whole PowerPoint is available on TES and it's also broken down a bit more on his website.stions/aqa-level-2-further-maths/

Calculators

There's a lot of negativity about Casio's new calculator model, but we do need to learn how to use it now that the old model has been discontinued. Thank you to my colleague Morgan for providing me with an excellent poster for my classroom wall.

Check out Casio's upcoming calculator webinars, and recent blog posts on calculators from @cclay8.

Update

Here are some things you might have missed:

• @MissNorledge has created a searchable database of all Edexcel GCSE maths past paper questions (June 2017+). It's very quick and easy access to GCSE questions by topic, including mark schemes. Just type in a topic name and it takes you straight to the relevant page!
• Festival of the Spoken Nerd are performing An Evening of Unnecessary Detail in London in October and November, with the events being live streamed for those unable to attend in person. I've seen a couple of Festival of the Spoken Nerd performances in the past and hugely recommend them to maths teachers! 
• Chris Smith's excellent weekly maths newsletter is back - if you want to subscribe, email Chris at aap03102@gmail.com.
• In time for the new school year, the creators of my favourite game Nerdle (which I have played for 545 days in a row!) have launched 'Super Nerdle'. This allows teachers to customise Nerdle games for their students.
• The annual Big MathsJam takes place on 11 - 12 November. It’s a weekend of recreational mathematics, with cool people and interesting maths! 
• I thought some teachers might like to see my updated posters which I made on Canva. I blogged about these initiatives last year. The main difference this year is that we've changed the name 'Maths Clinic' to 'Maths Extra' in response to an idea from a local Head of Maths who suggested that students might not respond well to the term clinic. 

Finally, thank you to James Greenland for sending me a lovely book of Additional Mathematics O Level Papers from 1968 - 1971. I've shared an example below. I like it that students had some choice over which questions they answered. Here I've just shared the pure sections: there were mechanics and statistics sections in the exam too.

Gem Awards 2022

Last week it was resourceaholic.com's eighth birthday! It's become a tradition for me to mark the anniversary of my blog by publishing an annual 'Gem Awards' post. Here I look back at all the ideas I've shared in my gems posts over the last year and choose some of my favourites.

1. Mathematics Award
The beautiful website Mathigon won Best Website in my first ever Gems Awards back in in 2015. This time I'm giving it an award in my Mathematics Category, which has previously been won by Nicholas Rougeux for his stunning interactive recreation of Byrne's 1847 edition of Euclid's Elements. 

The website Mathigon has gone from strength to strength. It features an incredible online textbook, a brilliant interactive tool PolyPad, and a collection of lesson plans and activities that are well worth exploring. 

The two features that make it worthy of my Mathematics Award are its Timeline of Mathematics and its Almanac of Interesting Numbers. There's even a timeline scavenger hunt - a really well-designed activity where students can explore the history of maths. This kind of thing is perfect for extra-curricular maths clubs. It's also great for teachers looking to expand their subject knowledge.

Highly commended in this category are:

The History of Mathematics Project from Momath and Wolfram, which is like an online maths museum. I featured this in Gems 151.

And the mathematician profile cards and accompanying activity from Amplify that I featured in Gems 155.

2. Most Useful Resource Award

Never has a resource saved me so much time as @gcse_math's collated GCSE questions. I featured this resource in Gems 155. The key difference between this and similar resources is that it includes questions from three awarding bodies, meaning there's an abundance of exam questions for each topic. They're really well organised, meaning it takes seconds to find what I'm looking for. I'm finding this resource incredibly helpful when planning my GCSE lessons, and when making end of unit tests. I'll also make use of it when planning CPD sessions. Thank you to @gcse_math for taking the time to make this resource and for so generously sharing it. I should also thank the awarding bodies for writing the questions - there are often brilliant questions in GCSE exams!

Highly commended in this category are the NCETM Checkpoints, and the DfE's Key Stage 3 Maths Guidance. Both resources are very high quality, which is not surprising when you look at the team of experts behind them. The Key Stage 3 Guidance provides valuable CPD for Key Stage 3 maths teachers, with plenty of prompts for department discussion. 

Checkpoints are diagnostic activities designed for Year 7 children. Do check them out if you haven't already. 

3. Hidden Gem Award

Richard Tock has shared some fantastic resources this year through his blog and TES account. I love the clutter-free style of his resources and the carefully thought-out examples and tasks. I'm giving him the 'Hidden Gem' award because I think his lovely resources are relatively unknown and more teachers should check them out.

In Estimating the mean from a grouped frequency table, his lesson starts with some work on finding midpoints. 

and leads onto to a well scaffolded task on finding the mean.

Half or two? was designed as a starter task in response to a misconception Richard identified in his class. 

In Venn Diagrams and Simultaneous Equations, Richard shares a nice idea for a task that students might do by trial and error, before learning a method to work out the coordinates.

Have a look through Richard's blog for lots more great ideas for lessons and tasks.

Highly commended in this category is Segar Rogers (@SegarRogers), a maths teacher and talented task designer who shares his tasks on startingpointsmaths.com. Examples of his recent work include this task on the mean which utilises Pointon and Sangwin’s Taxonomy. 

It's also worth checking out his recent work on speed, orders of operations, fractions of fractions, cuboid volumes and vectors.

4. Best Blog Award

This year's Best Blog Award goes to Dan Draper (@MrDraperMaths) for his excellent blog 'Opinions Nobody Asked For'. Dan regularly posts witty and insightful pieces about his experiences in the classroom. He thinks deeply about topics and freely shares the excellent resources he has developed.

Here are a few examples of tasks - first, an exercise from his excellent post about the order of operations:

And from the post x=a, y=b: When?, a task where pupils practise filtering information on a diagram.

And finally, from his post Interleaving Circle Theorems 1, an example of a circle theorems question that brings together loads of previously taught content including trigonometry and area.

Highly commended in this category is Paul Rowlandson's (@Mr_Rowlandson) blog 'Pondering Planning in Mathematics' which won my 'Best New Blog' award in the 2019 Gem Awards. I always enjoy reading Paul's ideas - his blog posts have a lot of influence on what I do in my classroom. His recent post 'Using Numbers to Highlight Connections' got me thinking about connections between topics that I'd not really considered before. 

5. Teacher Website Award
The award for Best Teacher Website goes to Amanda Austin (@draustinmaths) for her brilliant website draustinmaths.com. When Amanda makes a resource for her own students, she publishes it on her website so we can all benefit from it for free. This is a really kind thing to do, and is much appreciated by teachers like me who make a lot of use of her resources. I particularly like all her 'Fill in the blanks activities' which feature both scaffolding and challenge.

A number of other websites deserve a special mention in this category, including:

• mathswhiteboard.com from @PiXLMattTheApp. This rapidly developing website features loads of useful functions like worksheet generators and QLA tools.
• @nathanday314 has two excellent websites: mrdaymaths.com which features tasks and teaching resources, plus the recently launched website interwovenmaths.com.

Running (and regularly adding to) a high-quality website whilst teaching full time is no mean feat.

6. Best Game Award

I absolutely love Nerdle. This quick daily maths puzzle has become part of my morning routine. The format isn't really new (I used to play the mastermind board game in the 80s which based on a similar logic) but the online games of this ilk that sprung up at the start of 2022 have become hugely popular and there are now loads to choose from: Wordle, Nerdle, Heardle, Movidle etc. 

This award goes to Numble, an app made by Olivia Gibson and shared by her teacher @mathsDJ. This game is impressive for a number of reasons, including:

• it's easy to play
• it helps students learn divisibility rules
• it's fun
• it was created by a sixth form student.

Highly commended in this category is MathsPad for their Times Table Sequences Game which is a really fun way to practise both times tables and sequences, and is great for both primary and secondary children. I enjoy playing this with my Year 5 daughter.

Also Highly Commended in this category is the excellent No More Primes from Nathan Day. 

7. Best CPD Award
The Best CPD Award goes to the book If I Could Tell You One Thing which was published by The MA and edited by Ed Southall. What I love about this book is that is features a wide range of advice from experienced maths teachers and experts on lots of different topics. There's something for everyone here, and because it's a collection of short chapters, it's easy for a busy maths teacher to dip into it.

Highly Commended in this category is the new podcast from Craig Barton 'Tips for Teachers'. This fantastic new initiative brings us snippets of sensible advice from expert teachers, available in either podcast or video format. 

Can I give myself a special mention for a gem award? Maybe that's not cool, but I was really pleased with how many teachers made use of my CPD video "Key Stage 2 Maths Curriculum Summary for Secondary Teachers". 

I should also say that all the CPD providers I mentioned in last year's Gem Awards are still awesome.

8. Best Resources Award
James and Nicola from MathsPad are the winners of the Best Resources Award this year for their fantastic collection of resources, particularly their new range of curriculum booklets. Their booklets are available for Year 7, 8 and 9 (so far) and are packed full of brilliant tasks for each topic, featuring lots of depth and challenge. Here are some examples of their activities:

What a fantastic collection of resources.

*****

Well done to all the winners of the Gem Awards 2022! And thank you to all the maths teachers who share their ideas and resources. There are many people who I've not mentioned here who have helped to fill my gems posts over the last year. We are lucky to have such a strong and supportive community.

If you're new to my blog and you enjoyed this post then visit my Gems Archive you'll find an index of 157 gems posts - they are all full of great ideas and resources. For the 'best of the gems', you might also want to check out the Gem Awards 2021, Gem Awards 2019, Gem Awards 2018, Gem Awards 2017, Gem Awards 2016 and Gem Awards 2015 to see who has won awards previously. 

Happy 8th birthday resourceaholic.com. Thank you to my readers for all your support!