Category Archives: Number

160. TMNW 2 – Learning Wall 1

Leave a reply

Earlier this term, my colleague, J, and myself attended the rather brilliant #TMNorthWest at Calderstones School. We were particularly inspired by the idea of independent or ‘Help yourself’ learning walls. We’ve chosen this as our Departmental focus for the year and once we have trialled it, we hope to install a learning wall in every maths room.

The basic premise is that ideas and key points are collected in themed pockets, which students can go to whenever they require assistance or a hint on how to progress. The cards are numbered and indexed. The idea was introduced by Claire Gillies in the context of English lessons.

The self help cards were stored in hanging wallpockets:

image

Claire used the Kusiner wallpockets from Ikea.

There are six pockets in this particular product. We have chosen to split them into the following categories:
*Number
*Algebra
*Data
*Shape
*Using equipment
*Index

We designed our cards to have methods, misconceptions, Levels/Grades, a question with worked answer and possibly QR codes to useful videos.

Now, sitting and designing a self help card layout is easy. Completing them is a much bigger task! We have decided to start with KS3 and have selected key objectives from the Y7 scheme of work.

We also have GCSE classes who sat their exams last week and, quite frankly, need a break.

This sounds like fate …

The plan is that Year 11 students will take Y7 objectives and write self-help cards. Teachers will moderate/edit what they write.

Well, that’s our plan for a bit of independent student power. I’ll continue to post about our walls as they develop.

159. Firework Skills Fun

Leave a reply

On 5th November, I stumbled across the Skills Workshop website when I was looking for a quick Guy Fawkes Night resource. I found a nice Functional Skills task on planning a Bonfire Night party.

image

My Year 10 Foundation GCSE pupils really focussed on the task and actually asked for more lessons like this.

I used an activity based on units of alcohol, from this site, as an extension task.

image

We had some interesting conversations about how easy it is to exceed the daily allowances for alcohol consumption. PSCHE in a Maths lesson!

Have a browse of the website and see what you can find!

158. May I take your order, sir?

Leave a reply

Imagine getting your class to think about a number topic in a real-life context and subsequently having students leave the lesson feeling happy they could use this skill.

About as real as the square root of minus one? Not if you relate it to breakfast*

Image credit: ifood.tv

I wanted to make estimation more relevant for my class, a low ability Year 10. Outside my classroom I put a breakfast menu and my associate teacher took their orders** as they entered the classroom. I had put mini whiteboards on tables and I instructed the class to work out an estimate and the accurate total for their menu choice(s). The lesson had barely begun and the class were already talking about what they were doing (rather than Halloween antics the night before)!

Once everyone had arrived and settled down, I asked if anyone had underestimated and what this would mean – not enough money and doing the washing up!

I then asked each table how much their group order would cost. Would their overestimates cancel out their underestimates? Would the waiter get a tip? Meanwhile the associate teacher had added up the orders, so we could quickly check their calculations.

What if everyone paid £10? Would you have enough? How much tip would you be leaving? Would it cover a 10% service charge?

We followed up this task with some standard estimating questions.

Image credit: www.fudds.ca

The menus I used for the lesson are from a restaurant chain in California. The useful thing is there are no units of currency, so this works for different countries. It will work equally well with KS2 and KS3 pupils.

Download resource: Breakfast estimation (pdf)

BTW The students decided if the waiter wanted a tip, he should actually feed them first!

*Strongly suggest you use this before students have break or lunch time, or else they’ll be drooling in their next lesson.

**Unless you are providing food, please add the disclaimer that you are not feeding them.

157. Receipt for learning

Leave a reply

Do you ever really look at the bottom of your supermarket receipts?

This caught my eye today:

image

The bill is broken down into three bands of tax, the relevant amounts, VAT and total amount payable.

It would be quite an easy task to enlarge a receipt on a photocopier and blank out quantities. Don’t forget to blank out financial transaction details. You could work out percentages of amounts, reverse percentages or find missing percentages. It could be extended to percentage increase using multipliers. It also links to decimal calculations, rounding and money.

All this learning from a bit of paper from the supermarket*.

*Not all supermarkets do this, but there is usually some kind of tax reference.

153. Sequences Starter 2

Leave a reply

So, you’ve got term to term sequences sussed. Time to tackle Nth term!

This idea just sort of appeared in my sequences lesson.

Equipment
Giant playing cards (or numbers on two different colours of A5 card)
Numbered headbands (I made crowns out of corrugated border card)

Set Up
1.Lay out one coloured set of cards on a table or the floor – these are the ones we needed in class. We started with all the cards in the suit.

image

2. Issue headbands to four pupils.

image

3. Pupils stand in number order.
4. Give each pupil a different. coloured card from a sequence to hold facing them.

image

Task
1. Explain that each person represents a term in a sequence, given by the headband.
2. Pupil 1 turns around their card – Red 3.
Question: What is the next number?
Answer: Don’t know
3. Pupil 2 turns around their card – Red 5.
Question: What is the next number?
Answer: Might predict 7
4. Pupil 3 turns around their card – Red 7.
Question: What is the next number? Why?
Answer: 9, add 2.
5. Reveal the last number – Red 9.
6. What is the pattern? Add 2 Which multiplication table has the same pattern? Twos
7. Give each pupil in the sequence the appropriate number from the two times table.
Question: How do you turn the two times table into the sequence?
Answer: Add 1
8. How do you get from the headband to the sequence?
Headband x 2 + 1 = sequence

image

9. What about a headband with 10 on it? Or 100? Or a mystery number?
10. Try this with other sequences and develop the idea of Nth term.

Outcome
I used this as a plenary for a term to term sequences lesson with a shared class. In the following lesson my colleague, D, used this idea to develop the concept of Nth term with another class. He wanted to make something for the pupils to have in their book to remember this. This is what he came up with: Handout for sequences intro (pptx) or How to for sequences(docx). I’m currently trying out hosting my own resources, rather than using TES resources – so we’ll see how effective this is.

152: Sequence Starter 1

Leave a reply

So many people have the preconcieved notion that there is only one right answer to a maths question. This is such a silly idea – they just haven’t had the right question!

Here is a simple starter for introducing term to term sequences.

Equipment
Classroom whiteboard or large sheets of paper
Imagination

Task
Write down the next three terms in the sequence 1, 2 … and the rule used.
Eg: 1, 2, 3, 4, 5, …      Add 1
Note: Rules should be one short sentence.

Outcome
My Year 7 were frustrated that I’d given them the obvious answer and was asking for more. After a few minutes adjusting their expectations, they went for it. Some methodically wrote down rules, some abbreviated rules to symbols, some wrote rules and didn’t check them. Some didn’t write rules at all.

I randomly picked pupils to share their ideas on the board. I did the writing as I wanted to control the wording of rules and half of them can’t reach the top of the board.

image

Their sequences were brilliant and very creative. The stumbling block was the rules. They didn’t always work for every term of the sequence. This gave other pupils the opportunity to develop their ideas by improving or adjusting the rules to fit the sequences. We also discussed how many terms you need to make a unique sequence. By the end of the discussion we only had one sequence without a rule. I was really impressed by their numerical skills!

In the subsequent classwork, their solutions were precise and well explained.

We finished with this brain teaser:
1,2,5,10,20,50,100 …

It’s UK currency:
1p,2p,5p,10p … etc

148. Ordering Decimals

Leave a reply

Here’s a mini-investigation on ordering decimals, suitable for Year 6/7 (maybe even Y5 too)!

Equipment
Exercise book (or equivalent)
Pen/pencil
Felt tip pen
Sheet of paper: A4 or A5
Scissors

Activity
1. Fold the paper into 8 and cut along the fold lines. This will give you some spares, just in case.
2. Clearly write 0 and a decimal point onto two pieces with felt tip pen.
3. Choose two different digits and write them down – you now have four activity cards.
4a. What is the biggest number you can make? Arrange it on the desk. (The decimal point can’t be at the end of the number)
4b. Discuss what you notice about the digits and size.
5a. What is the smallest number you can make? Arrange it on the desk (The decimal point can’t be at the start of the number).
5b. Discuss what you notice.
6. What other numbers can you make? There are 12 possible ways to arrange the four cards (according to my class). Encourage the class to be logical and record their answers carefully.
7. Arrange the numbers in order from smallest to biggest.

Activity 2
Add another digit and investigate. My class insist there are 52 possible numbers – I’m waiting for a reasoned justification of this.

What happens if you duplicate a digit?

Follow-up Activity
After completing either activity, ask the class to find the numbers in their lists which are closest to 0, 1, 10 & 50. This helps consolidate their understanding of place value. I asked my class to write their answers on the board. We then discussed the accuracy of their answers.

image