# 198. You sunk my rectangle!

How about a game of ‘Battleships’ with a graphical twist? My Year 7 class loved playing this game and we developed understanding without resorting to tediously drawing out lots of graphs.

Objective

To be able to draw and label lines parallel to the x or y axes ie x=1, y=3

Equipment

• Squared paper
• Pencil
• Coloured pens or pencils
• Ruler or straight edge

Preparation

1. In pairs, agree the size of a set of axes and draw two identical sets each. Negative axes can be used as an extension.

2. On one set of axes draw a rectangle, making sure the edges are on whole numbers.

3. Extend the edges of the rectangle to give you two horizontal and two vertical lines. Label the lines accordingly. You are now ready to play!

Playing the game

1. Players take it in turns to guess a straight line eg x=3. Their partner says ‘Hit’ if it is the edge of their rectangle and ‘Miss’ if it isn’t. This information is recorded on the players second grid so they can keep track of their guesses.

2. The game continues until a rectangle is revealed:

3. The player must then label where the lines intersect. The losing player may find it useful to continue guessing.

Extension: What do thy notice about the co-ordinates and the equations of their lines?

4. What is the area of the rectangle?

Extension: Is there a link between the co-ordinates and the area?

# 197. £40.95

Today we have a discussion starter question for you, inspired by a trip to the shops.

My shopping cost £40.95 today. What is the smallest number of coins required to make this amount?
If I paid with two £20s and a £10 note, what is the most efficient change?
Why would someone pay £41.05, as opposed to £41?

I purchased 17 items, do you have enough information to calculate the mean?
The most expensive item was £10, the cheapest was 45p. What does this allow you to calculate?
Two luxury items cost £9 in total. If I hadn’t bought these, what would the mean have been? Does this effect the range?

When I paid I was given this voucher:

What would the shopping have cost somewhere else?
What would the mean cost per item be after this discount?
What percentage discount is this?

You could also use this as a discussion starter about the number skills you use when you go shopping.

# 196. Gadget of the day 6

It’s been a while since I’ve had a gadget of the day. Today is more of a stationary item of the day. I’m a fan a moleskine books and the number of index markers mine have hanging out of them is a standing joke.

Now I’ve discovered Leuchtturm 1917 books.

Just like basic moleskine books they come in plain, lined and squared paper versions. Just like moleskine they are hardback, have an elastic closure and wallet in the back cover.

Unlike moleskine books, they have a blank index and every page is numbered. This makes finding specific notes really easy and doesn’t require excessive sticky tabs. You can also get pen loops, so you don’t lose your favourite pen. I definitely think my notes look more professional/organised now: Left has 17 sticky tabs, right has an index.

You can purchase both moleskine and Leuchtturm books from most big stationers or online.

# 195. Marshmallow Maths

It’s our first birthday at the MathsSandpit and this post is party themed. Remember a few years ago, when chocolate fountains were the ‘in thing’ at celebrations and parties. The healthy guests stuck to strawberries drenched in chocolate. The unhealthy went for marshmallows on sticks and … well … all I’ll say is Geraldine Granger (Vicar of Dibley – Chocolate Fountain)

I’m trying to decompartmentalise the maths in my students heads. They struggle to see the links between different topics. So I introduced ‘Marshmalllow Maths’ – they were intrigued/hungry as soon as I mentioned it.

Equipment

• Cocktail sticks
• Pink and white marshmallows

Step 1

Step 2

What mathematical characteristics do the marshmallows have? I’ve summarised my classes’ responses below:

Two marshmallows lead to ratio, percentages, fractions, decimals and probability. The links between these topics start to emerge.

Step 3

How have the ratios, fractions, decimals, percentages changed?

Step 4

Make another 1:2 ratio marshmallow, identical to the previous one. How have the mathematical facts changed? In fact although the numbers have changed, the proportions have stayed the same which is proved when you simplify the numbers. Physically you can prove it by stacking the structures on top of each other – from above it looks like the original structure.

At this point I went cross-curricular and discussed the similarities between the marshmallow structure and water (H20). I was going to label the marshmallows with H and O, but my food-colouring pen wasn’t working. My logic was that water always has hydrogen and oxygen in the same ratio – this means we know we can drink it. If the ratio suddenly changed to H2O2, we would be in trouble! As far as I can remember H2O2 is hydrogen peroxide and is better for bleaching than drinking. This actually got the idea across quite well – no-one tried to fudge their ratios.

Step 5

I then allowed the class to make their own simple structures using their own piles of marshmallows. They had to make at least three identical structures, work out the related maths and prove that their numbers could be simplified to the basic form. In doing so they also looked at converting ratios to fractions and also found fractions of amounts.

Step 6

Eat marshmallows (whilst doing some related questions).

Optional: Step 7

Calculate the percentage increase in body mass on results day! It was marshmallows today, a chocolate prize for cracking a code earlier in the week and they say they learn better when they eat. I think it’s all a ploy to scrounge more food … but if it works … maybe fruit next time!

# 194. Valentine’s Stand up

If you haven’t seen Matt Parker’s cool valentine’s maths activity, you are missing out: Valentine Hearts

# 193. Resource of the Week – Reflective Detentions

This splendid resource by ealdor, on TES Resources, was recommended on Twitter last year. It is a Reflective Detention sheet. Pupils spend time in detention reflecting on what they did, why it wasn’t appropriate and what they will do to improve. The teacher then keeps the sheet as a record of the event. They can then be referred to at Parents Evening and in Departmental/Pastoral interventions.

Image credit: teachers.saschina.org

Personally I have used these sheets since September and they have provided me with a constructive talking point at Parents Evening. In fact, one parent described them as handwritten confessions that their child couldn’t talk their way out of. Thank you ealdor!

# 192. It’s a stick up!

Just a quick picture to share today. My colleague, D, went to the same TeachMeet as me and was equally impressed by the use of gaffer tape in the ‘Big Maths’ presentation.

Today his class were doing box plots and took the idea of averages even further. They made a vertical box-plot on a wall of the class heights. Brilliant!

I’m sure this idea has lots of potential.