Eyes down for a full house!

Bingo is one of those simple ideas that works so well for certain topics so I thought I’d collate some resources.  I recently went to a parents social at my son’s school where we spent 2 hours playing “Rock ‘n’ Roll bingo” (whilst eating Fish and Chips and drinking beer). OK, so maybe Maths bingo isn’t quite as much fun as trying to spot 80s song titles, but it did inspire me to have a go as it is something I haven’t done much of lately.

It’s a format that works well for topics that students are familiar with but which need more practice.  They need to be able to get 90% plus of the questions correct first time and in about the same amount of time across the room.  Use it as a revision aid but not the first time you introduce a new topic.  It’s likely to get loud, so save it for the end of lessons, maybe those Friday afternoon lessons…

Here are some tips for how to run sessions:

1. Bingo cards.  Some resources come with bingo cards to print out.  This is good for longer games – say 20-25 minutes, maybe as an end-of-term “treat”. However, some resources are designed to do as “quick bingo” by putting up, say 16 answers on the board and then getting students to make their own cards by choosing a random 9.  Make sure they write these in pen and that everyone has all 9 clearly written down before starting. No cheating!
2. Keeping track and checking. Some of these resources have answers provided, but I think it is better if you do the questions as you go along, just write them down on a scrap of paper as you go and use this to check once a claimant has called out. Do make sure you check answers carefully.  It doesn’t matter if it takes a minute or two, it adds to the suspense!  As soon as kids get an inkling that you are not checking carefully they WILL cheat!
3. Prizes.  I have a natural aversion to extrinsic motivation, but hey, a prize just makes it more fun, no matter how cheap or naff! If you are using a bigger bingo card with, say 20 answers then you can also offer line prizes, i.e. a prize to whoever gets the first line, maybe a sticker.
4. Ham it up! OK, this is very much down to your personal style and relationship with the class but have some fun with it! Live your dream of being a gameshow host. Pretend like these prizes are the most exciting thing anyone has ever won!

 

Here are some Bingo resources which cover a decent range of topics.  There are various Powerpoint resources on TES too, but I like these sites because they are simple and don’t require log-ins.

1. Interactive Maths

There are lots of topics on this site and various options for displaying random-generated questions.  Many of the topics include bingo options, here is an example:

Once you are in, there are further options to cover exactly what type of questions you want to display, and whether you want a 4×4 or 3×3 bingo grid. You then display all the answers for your students to randomly pick 9 or 16 from.  I really like the way it gives you the option to keep track of the answers as you go which makes checking at the end a whole lot easier!

2. Maths Starters

There are lots of topics on this site, handily listed in menus. Students make their own cards by choosing 9 out of 16.

3. WMNet

There are lots of basic number topics in this collection with an emphasis on place value. Students choose 5 out of 12.

 

4. Mathsbox

There are some provided for free on mathsbox.org.uk which are designed to have the bingo cards printed out. I’ve used the Simplifying Surds ones which worked very well. Each topic contains 30 questions, 16 per card so take about 15 minutes. Presumably if your school pays the £60 annual subscription you get a lot more topics.

 

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Going off piste with the difference of two squares

Sometimes it’s worth taking a risk and changing course of a lesson halfway through. And sometimes it pays off.

Today’s lesson was supposed to be about algebraic proof and we started with these nice questions from Don Steward. I thought they looked like good practice for multiplying out double brackets at the same time as introducing algebraic proof.

By the way question 3 is particularly tricky.

Following on from the previous lesson, lots of them started by trying values for n.  Great to then have the discussion on what makes a proof vs. an example.

We got into a good discussion on Question 5 and I wanted to know if they were familiar with the difference of two squares.  This is where the lesson changed course completely.  None of them could tell me what it was called but I got the sense that they had seen it before. So next, I wrote these questions on the board:

Factorise:

1. n² – 9
2. 4n² – 25
3. 81 – n²
4. 100 – 81

They raced through these because they had all spotted the short cut.  So next, I put this up, again from Don Steward:

Which followed on nicely from the final of the 4 questions I had put on the board.  Many of them initially struggled to see the link immediately or see the pattern in the numbers.  But with a bit of time and just the right amount of help (i.e. not much actual help, just encouragement!) they started to find others.  I heard them forming statements like: “I need to number that multiply to give 2016, then I need another two numbers that add to give one of those number and subtract to give the other.”

About 5 minutes before it was time to pack away there was a great buzz in the room as 3 students found some other numbers and then the race was on. Lots of solutions started coming, but nobody got all 12 (including me!).

I went away and built a spreadsheet to investigate further, but I still didn’t find all 12.  Can you help???

Do you understand reciprocals?

These questions test a lot of things so use them carefully.

Firstly there is what do we understand about reciprocals, namely:

These are tricky concepts to grasp. This is the order in which I teach them, but I don’t think the “flow” through these 4 concepts is particularly obvious and students need to be carefully led with lots of examples using Mini Whiteboards.

Other understanding required includes:

• Finding equivalent fractions
• Finding common denominators and using them to find the right equivalent fractions
• Adding fractions
• Converting between Mixed Number and Top-Heavy fractions
• Negative fractions

And the last question took me a good 3-4 minutes to convince myself I had the right answer.  Which always makes me stop to think – am I being fair to my students here?

 

Pythagoras and Trigonometry Revision

I used these cards for revision of Pythag and Trig recently.

They are really nice and there are lots of them so you can decide how far you want to go. I just have the file and I’m not sure who created them, so if you know, let me know so I can credit them / link directly.

This sort of activity works really well with a class that will have productive and supportive conversations about the maths and enjoy challenging each other.  It gets them out of their seats and they start to get a sense of which questions are straightforward and which will present more of a challenge. I’m on the look out for similar things for other topics.

I’ll be setting this for homework as it has explanations as well as examples all in one place:

 

Hippocrates First Theorem

Another one from the fabulous Don Steward:

You could of course just go straight for the algebraic proof but it does require a level of confidence with surds.  So you might want to scaffold this task. Maybe start by putting some numbers in for the radius of the smaller semi-circle, maybe 2.  You could then do it again with 4 and ask students if they are convinced by that.  (Here are some examples to warn against the dangers of extrapolating what appears to be a pattern).  If you do take the numbers approach it’s good calculator practice.  Can you type the whole expression for the area of the curved shape into the calculator to get an exact answer?

And here is a little GeoGebra drawing to go with it.

 

A simple circle problem

My high attaining Year 9 class didn’t quite get this on their own yesterday but they enjoyed the challenge and were able to follow the explanation.

The crux of the problem is getting a right angle triangle with sides 1, (1+x) and (2-x).  It is the (2-x) side which is hardest to spot.  There were groans when I finally showed them.

Then it requires some algebra – namely expanding (1+x)² and (2-x)² which Year 9 hadn’t had much practice in, so it was good to show them why (1+x)²≠1²+x²

I gave them the problem printed out, here they are 2 to a page.

Here is link to the Geogebra file that I created this on.

I had a few Twitter responses to this including @ProfSmudge who kindly set us an extension question:

It’s an example of an Apollonian gasket, apparently (thanks to @mathforge for pointing that out!).  That gets properly hard, involving Cosine Rule.  Certainly not something I’d give to my students, but I’ve got a few teachers working on it!

 

Writing Ratios as 1:n

This sheet practices getting ratios into 1:n for the Unitary Method but also interleaves sequences.  It’s low threshold, high ceiling in that students can just manipulate ratios (simplify in the first set) but you can ask some fairly challenging questions including:

What would Q 50) be?

What would Q n) be?

Write a rule explaining the sequence

What would happen if you kept this sequence going?

Here is a simple pdf document (with them printed 2 to a page):

Here is the original spreadsheet where you can hide / reveal the answers or tinker with the questions. Pretty tricky to work out the generalised 1:x form for some of these!

Great problem solving tasks from FMSP

My Year 10 class did these 3 this week:

They have their GCSE RS and Science exams next week, so I needed to find something a bit “fun” but still wanted it to be “mathsy”.  They are a strong group with enough keen beans amongst them for me to feel confident that something like this would work.  I was impressed with their teamwork and tenacity.  At first it seems hard because you are faced with a blank sheet (their words). It took the quickest group 20 mins, 1 out of the five didn’t finish after 30 minutes.

Something I always bear in mind when doing any sort of team activity (see my earlier blog post) is that everyone should have a clear role to play and something to contribute. In this task everyone has their own set of clues, that they are not allowed to show to the others. I encouraged them to make sure they were the experts in their own clues so that when proposals were made they could say if this proposal broke any of their rules.

There is no need to cut up these sheets into “cards” as the resource suggests.  Quicker and better if you just cut them into strips:

That way you can give a strip to each student. They are less likely to drop a card on the floor which kind of ruins it! If you cut some horizontally and some vertically as shown you can cater for groups of 4 or 5 students.

We finished with 10 minutes to spare and had a pretty good discussion about the task.  Questions I asked them:

How did they start the task? (Talking or just reading)

Did it help to group the clues in any way?

Were they tempted to share the clues? (I told them I’d give them 30s time penalty if they were caught sharing.) Or were they happy having their own? (most were)

How did you work well as a team? What did you think went well?

Was it hard? What made it hard?

 

Introduction to Factorising Quadratics

Useful as a starter / drills for a lesson teaching how to factorise quadratics.  Should provide some number confidence before then tackling actual quadratics, although beware it doesn’t just become another method to learn without the understanding.

A simple template for capturing Lesson Observations

When observing lessons, whether as part of a Lesson Study, collaborative planning, a learning walk or something more formal, it is, of course, essential to take notes on what you are seeing in the classroom. Scribbling notes in a notebook is simple, but if you need to “type it up” to formalise it, or even just to share it with other colleagues, that becomes another task on the to-do list and yet another burden on your time.  Better to take a laptop into the lesson with you so you at least have the undistllled notes in a digital format.

Here is a really simple Google Sheets template that adds a timestamp as you type the comments. I’m no expert in writing scripts but this guy is, so thanks Azad!

It works like this:

1. When you are ready to start select the Draft tab at the bottom.
2. During the lesson, write in the Comments column. Each time you press enter it automatically fills in the Time column.
3.  When you have finished, copy the cells you need from the Draft sheet to the Final sheet and fill in whatever other detail you need at the top.

I find that I tend to write a lot when doing lesson observations even though some of it isn’t relevant or worth sharing with the teacher.  I can easily delete that extraneous waffle by deleting rows from the Final sheet.

I have kept the template really simple, because I don’t like templates much.  However, it would be easy enough to adapt this to two columns, e.g. www, ebi if you wish.  Also, you can play around with the Final sheet to make it look like your school’s lesson observation template with all the extra fields you need in the space at the top.

Hope this works for you, please get in touch with any comments or to let me know how you are using it.