Folding Fractions

Skills Practiced:

• Spatial reasoning
• Fractions of shapes
• Multiplication of Fractions
• (Potentially) Pythagoras

Material:

• Paper cut in to squares
• Display Board

Instructions

• Each student gets a square piece of paper.
• Ask if anyone can fold the square into a shape that is 1/4 of the original size. Ask them to explain how they know that it is exactly 1/4.
• Project the fractions on the picture below on to the board.

• Students aim to make those fractions from the original square.
• Every time they get an answer, they must convince their partner that it is correct before they put their name on it and blue-tack it to the board. Multiple different answers are allowed for each fraction
• Below this (or on another board(, students put up any other fractions they can find.

Example work

Extensions and Variations:

• Find the same fractions as above, but now your final shape must be a square.
• https://www.youcubed.org/task/paper-folding-fun/ 

Interactive: Polyrhthmic fractions

I've been coding again! See my latest maths game below...

I was inspired by how some of favourite musicians (Joanna Newsom)
overlap simple rhythms containing quarter, sixth and eighth notes and make something that is subtly complex and interesting. The above version is a much more advanced version of these polyrhythms.

I thought that this was an interesting way to look at how fractions add up. I also wanted the game to be a little more informal and sand-boxy than the last, so it allows you to try things out and see what works. Have a play:

 

Direct students to a fullscreen version with this memorable address: thedrummer.rocks.it

Its not perfect. Some of the problems are solvable, others aren't (because my original file has corrupted!!!)

• there's no way to tell which achievements you've done (i was implementing this when the file corrupted)
• you can't save and share your beats, which would have given an incentive to make a good one.
• the tradeoff with it being informal and intuitive is that its gamable and you can get away with using little fraction knowledge - I would solve this by having a worksheet of questions to answer (but only once people have already got in to playing the game). It feels like a cheap cop-out though. What could I have done to make it organically more challenging/rigorous? I would love your thoughts on this.

Lesson Sketch: mathematics of a cake sale

Intro:

There is a cake sale coming up and you plan to sell these flapjacks:

How much should you charge for one? Why? Will that make me a profit? How do you know? How much profit would I make? How could I work it out?

Main:

Give pupils the recipe: http://allrecipes.co.uk/recipe/3846/apricot-oat-flapjacks.aspx and either a table of prices or access to a supermarket website, such as http://www.tesco.com/
Pupils work out how much it costs to make a batch of 8 flapjacks and the profit they could make on each one sold.

Extension:

What are the most expensive parts of these flapjacks? Try to replace some things in the recipe with something similar in order to make the total cost lower. How much profit would you make now? How cheap could you make them?
Can you find a different cake recipe that would be cheaper to make?

Further Discussions:

This cake is slightly cheaper to make than the flapjacks:

Should I make these instead of the flapjacks? Why? Why not? What other considerations should I be making apart from price? (Time, effort, equipment needed, etc.)

You may discuss how some people factor time as money using a basic wage.