# 245. Fair share

I spotted this ‘Expert Tip’ whilst flicking through a supermarket magazine:

Image credit: tesco.com/foodandliving

Question
If this cake has a diameter of 18cm (7in), is this a fair way to split it between guests? Can you prove your result in general terms?

Of course, this assumes that the icing on the side doesn’t count in the diameter or guest preference.

# 237. Quick Starter

Don’t you just hate it when students forget basic key skills? Especially those at the higher end of Year 11 or studying A-Level, who should have a better core knowledge. What if there was a magic tool which began to address this issue?

Skills required

• Comparing fractions
• Trigonometric ratios
• Simplifying surds
• Rationalising surds
• Pythagoras

Equipment

You will not need:

• Worksheet
• Powerpoint
• Printer
• Laminator
• Calculator

Magic Tool

• One board, with pen

Activity

Quite simply draw theĀ four diagrams below on the board and ask the following questions:

1. Which has the largest sine ratio: A or B?
2. Which has the largest cosine ratio: C or D?
3. Which has the smallest tangent ratio: A, B, C or D?
4. Extension: Calculate the missing angles and areas (Calculator allowed)

It takes moments to draw the questions on the board, but the discussion can take some time and addresses several basic skills. You can change the numbers to adjust the level of challenge.

# 235. Which witch is which?

Whether you are on half term holiday this week or next, I’m sure you’ll have time for this little number skills starter.

Image Credit: Jill Murphy, ‘The Worst Witch’ – a children’s classic, which I highly recommend.

Can you help Wanda, the Grand High Witch, to find the local reporter hiding at her Halloween Girls Night Out? Solve the number problems and unveil the imposter.

Which witch is which? (pdf)

This starter or homework activity includes order of operations, factors, prime numbers, addition and multiplying (written method).

Happy Halloween!

(Updated: 1st Nov 2017)

# 224. No Nonsense Negatives

Ever had a simple idea for a starter which your class just flies with? It happened today for me:

Background
In the previous lesson students understood the meaning of ‘y=mx+c’, but struggled to rearrange equations in this form. With this in mind, I went back to the basics of manipulating calculations.

Starter question 1
Make as many calculations as you can only using the numbers 2, 3 & 5 (once each) and any symbol you like. The obvious answer is 2+3=5.

Starter question 2
Make as many calculations as you can only using the numbers 3, 6 & 18 (once each) and any symbol you like. The obvious answer is 3×6=18.

The Extension
Most groups quickly found three solutions for each question. Some even used inequalities. To extend their understanding I suggested that they could use as many of each symbol as they wished – would a sprinkling of minus signs increase the number of results?

Results
The following pictures show the ideas my class came up with. I was using lolly sticks to randomly pick students and no one wanted to be the first to not give an answer.

Followed by:

We discussed the rearrangements and linked them to rearranging equations. They appreciated that one equation could be written in many different ways. This activity would work equally well to consolidate negative numbers.

# 183. New Year Resolutions

Why not get your students to make a New Year’s Resolution?

Image credit: someecards.com

There are so many little things that we remind students about, so how about getting them to take responsibility?

Start by discussing what they think you nag them about. When students peer review, what annoys them about each other’s work? Extend the conversation to include why these things are important.

Now the tricky bit: making the resolutions.

Get your students to pick two targets – an achievable one and a challenging one. They should be carefully worded and give a reason.

Example
I will show my working out so that I can get all the marks I deserve.

The resolutions should be clearly written on their books (maybe on the front cover?) and a copy should be handed in to you – hand out small sheets of paper for this.

The Future
We all know that resolutions often don’t last. So how can you support your students?

There was a reason why the students handed in a copy of their resolutions. Put them in a jar or box on your desk. Once a week, make your starter a resolution reflection. You could just give your students time to self evaluate or discuss their progress in pairs.

Alternatively you could dip into the resolution jar and pick out a resolution. You could generally discuss that resolution or ask who has a similar resolution and find out how they are getting on.

The key thing is to revisit and also recognise the progress students are making with their resolutions. They’d also make a nice talking point for Parents Evening.

The Twist
If you are asking your class to make a resolution, what would yours be?

Update
Kev Lister’s blog

# 151: TMNW 1 – Puzzle maker

As promised, I’ve been trying out ideas from TeachMeet North West at Calderstones School. Here’s the first post:

My colleague J had mentioned Discovery Puzzlemaker last term, but I’d not had time to try it out. Then Fiona Bate @fibate used it as part of her presentation on ‘Profound thinking in the classroom’.

How I used Puzzlemaker
I decided to test this out on my Year 9 students – they are a bright bunch and there are a lot of them. I put out tile puzzles on sheets of A5 and the class settled to the starter task, after they’d got their books out. There were lots of different strategies and eventually everyone cracked the code – the formula for the area of a circle.

Blank puzzle

Different strategies

The funniest part was later in the lesson. A student put his hand up and said he couldn’t remember the rule for the area of a circle. More than one of his peers pointed out he’d just spent ten minutes cracking a code where the rule was given and it was still on his desk in front of him!

Lesson Objectives
Luke O’Hanlon @funkwalkee did a presentation on ‘Ways to engage with Learning Objectives’. This linked nicely with using Puzzlemaker to discover the aim of the lesson, as well as encourage independent learning and problem solving. Once the class had cracked the code they knew what they’d be doing that day.

Puzzlemaker

As you can see, Discovery Puzzlemaker is a really useful tool. I’m going to use some of the larger puzzles as homework tasks for my lower ability classes as I can tailor them to their specific needs. I’m starting with the ‘Hidden Message’ task to reinforce circle vocabulary.

Thank you to J, Fiona and Luke for sharing this site/their ideas.

# 136. Quiz-Its

Here’s a simple starter/revision activity. All you need is Post-it notes.

Hand out Post-its as the class arrive.

Once they have got their things out they each write four questions on a topic of your choice. Encourage them to make the questions challenging. Once that’s done tell them they need to write the answer lightly in pencil on the back.

Stick all the Post-its on a table or wall.

Everyone then collects a Post-it (or Qwiz-it) to answer (not their own).

Once they’ve answered, they can check their answer. If the answers don’t match, who is correct? Why?