Category Archives: Number

317. Pyramid Power

Just a quick post today – it’s such a busy time of year.

I’ve recently used Nrich resources on sequences with Year 7. These two activities encouraged good discussion and practical thinking.

Function machines

Pyramid Numbers

We used multilink to build pyramids which allowed students to develop their ideas. There were four different pyramids commonly built. The discussions the students had showed a real insight into their thinking.

After the lesson this photo of a golf ball stack appeared on my Twitter feed. This provided me with a starter for the following lesson – how many balls in the stack?

314. Maths is a foreign language 

If I had £1 for every time I heard ‘I don’t get it!’, I could probably buy a new (modestly sized) car. That phrase is banned in my classroom. What does ‘get’ mean? What is ‘it’? Did you actually read the question?

And there we have it: reading the question.

Today’s little life skill strategy can work for all levels of literacy – because you don’t need any! I’ve taught a lot of students who just shut down when they see wordy questions and don’t look at the big picture – literally. There can be a really obvious diagram and they will skip the question. They just don’t try!

Now as you may be aware, I’m based in Wales in the UK. For those outside the UK, Wales is a principality within Great Britain. Although everyone speaks english, the traditional mother tongue is welsh – it’s particularly spoken in the North/West of the country. If you attend a welsh language school, you can do all your exams in welsh. A GCSE is called a TGAU.

But why am I telling you this?

Well, this means that the WJEC/CBAC exam board publishes their exam papers in welsh and english. Identical papers, different languages. I teach over the border in England, where only one or two students per year can speak welsh. This is where it gets interesting …

I went through a welsh language ‘Mathemateg’ paper and picked out the questions which involved diagrams – I also picked out the matching English questions so I was clear on the questions (not a native welsh speaker, just a learner). I gave my GCSE class the Welsh questions and told them to figure out what was going on. After the initial disbelief they had a really good go at the questions. Their comments included:

‘Well, it’s obvious it’s a tally chart’ 


‘Just fill in the table with the numbers from the pattern’


‘That’s got to be a special type of triangle’ (answer isn’t correct, but idea was)


‘Just use angles in a triangle to work it out’


I was impressed – they were constructively arguing about questions and covering diagrams in good maths. When we went over the questions they were telling me how easy it was, yet the week before they’d skipped questions like the angle problem in an assessment! I explained why I’d done it and told them they didn’t need to keep the worksheets as I’d made my point. I was stunned by the number of students who wanted to take them home to show their parents – they were proud of their problem solving – 16 year olds wanting to show off their Maths skills!

This idea can be used with any bilingual exam board or any language that you speak that the students don’t. It’s a good tool for getting over ‘question blindness ‘ and literacy confidence issues too.

These are the exam papers I used:

WJEC GCSE Maths 

CBAC TGAU Mathemateg

If you look at the web addresses there is one digit difference to differentiate between the languages, meaning if you go on the WJEC english language website you can find the welsh equivalent by swapping a 0 for a 5 in the second to last digit.

311. Sales starter

Here is a neat little starter photograph (click on the image to enlarge) – get the mini whiteboards at the ready!

Sale price starter

Possible questions

  • How much money could be saved with the different reductions?
  • What are the percentage discounts?
  • What is the price as a percentage of the original?
  • What is the exchange rate between pounds and euros (using the original prices)?
  • What would the sale prices be in Euros?

If you can’t read the data clearly, the prices are: £45, £30, £22.50, £13.50, 70 euros

305. Get Carter

Seriously, you need to Get Carter ….

Get Carter 1971 Poster

Or rather head over to the amazing website by Mr Darren Carter: MrCarterMaths.com

I don’t know where to start – in a few clicks you have access to tiered questions on a multitude of topics with answers. Answer in an exercise book or on a mini whiteboard – it’s genius! Another click and the questions change.

If that wasn’t enough, you can print out individual worksheets at each level – differentiation without a headache.

I chose to print out the three tiers and award them points. Bronze = 1 point, Silver = 2 points, Gold = 3 points. I put together a cover sheet with instructions and the students instantly had control of their homework. All I asked for was 20 points of answers. The ones who need the practise can do lots of low scoring questions, the ones who need a challenge can do fewer questions at a harder level. My task is available to download below (full credit to Mr Carter given) – It prints nicely as an A5 booklet.

Tiered Proportion Homework Booklet

Once you’ve visited the site, follow him on Twitter @MrCarterMaths

301. How much is my sandwich?

A visual discussion starter for you:

image

These three pots of sandwich filling cost £1 each. The flavours are egg mayo, chicken & bacon and cheese & onion.
How much would the 182g chicken filling cost if it weighed the same as the others?
The large pots contain 5 servings and the small pot contains 3 servings – are they the same size serving?

If you zoom in on the picture you could generate your own questions based on the nutritional information eg calories per serving.

You could extend this to the snacks in students’ bags. Are they as healthy as they think?

300. Name that Number

Simple little starter for you today. Minimum preparation, personalised challenge.

Equipment

  • Paper or whiteboards

Instructions

  • Hand out mini whiteboards or use paper.
  • Write the alphabet on the board.
  • Assign each letter a value. You can go for the standard 1 to 26 or choose a mixture of big/small numbers – maybe a negative number or two.
  • Get each student to write down their name and associated numbers.
  • Write a target number eg 100 on your board.
  • Each student must use the numbers of their name to make the target. If they can’t, they must get as close as they can.
  • If they make that target either find another way or change the target number.
  • Alternatively once they’ve finished they could use their classmate’s name – did they use the same method?

Variations

  • You can make this as easy or difficult as you want by changing the target or the alphabet numbers.
  • Throw in some fractions or decimals – go all the way and thrown in algebraic indices or standard form. You are the best person to judge your students’ level of challenge..
  • You could allow surnames, you could insist all numbers are used.
  • Put three alphabet variations on the board for mixed ability teaching.
  • If you are teaching a class not in the English language (eg Welsh, Greek, Russian), where the alphabet is different, this still works just assign each letter/character a number in the same way.
  • The possibilities are huge – have fun!

Note: this isn’t numerology, it’s proper Maths!

299. Is it good value for money?

Those ‘value for money’ or ‘best buy’ questions always put some students into a muddle. The usual response is ‘The bigger pack is always better value for money, so why have I got to do working out?’

Really? Is that always true?

Try these packets of cereal (Weetabix) from Asda:
image

The first one says 72 biscuits for £5.68

image

The second one says £3 for 48 biscuits.

Put the price and number of biscuits per pack on the board and ask students what they think. Once they’ve discussed it you could ask whether they thought that kind of pricing happened in real life.  Then you can pull the starter together by projecting these pictures onto the screen/board.