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.
Calling all creative thinkers!
What mathematical questions could you set from this picture?
Here are a few to start you off:
1. Sequences – do the increasing number of chocolates in each layer form a sequence (in 2D, in 3D)? If so, what is the general term? Is it geometric or arithmetic?
2. Series – if it is an arithmetic sequence, can you find the sum of a finite number of layers? Which layer would have the 1000th chocolate?
3. Geometry – what shape must the layers be in order to form this structure? Is there a pattern to the layers? Could you stack these in a different way to form an equally stable structure?
4. Money – if a standard box holds 12 chocolates, how many boxes would a 2D or 3D version of this require? What is the cost? What if they came in a larger box? Could you save money?
5. Health – how many calories are there in the tower? How far would you have to run to burn off the calories? How many ‘average’ meals is it equivalent to? How many fastfood burgers? How sick would you feel after all that chocolate?!
Instead of setting a question, why not ask your students or even your trainee teacher what questions they can come up with?
Here’s a quick post for all those of you teaching Arithmetic Sequences. Whether you are teaching Level 3 Algebra or the C1 A-Level module, the jump from GCSE Nth term to the form ‘a + (n-1)d’ can be unnecessarily tricky. To help with this I’ve written a starter booklet for Arithmetic Sequences. You can download it here:
Introduction to arithmetic sequences
By the way, if your students confuse the vocabulary ‘sequence’ with ‘series’ get them to think about television. A normal television series ends, so an arithmetic series must end too!
I like to encourage students to discover rules and formulae for themselves. It’s important that students understand where the maths comes from so they can apply their skills effectively. They also don’t have to rely on remembering a rule (which they may forget when they are stressed).
Image credit: http://www.ck12.org/geometry/Surface-Area-and-Volume-of-Cones/
This resource is a neat and effective way to investigate the surface area of a cone through measuring circles and creating a 3D shape. Students get a physical feel for how the dimensions fit together. Throughout the lesson I let students choose their degree of accuracy in cutting, measuring and calculating. Of course, when we discussed the ‘solution’ at the end of the session it was impossible for me to put one correct answer on the board. So I generalised using a and b for the radii – explaining that everyone could check their method in general terms. The lovely ‘penny drop’ moment happened when my a’s and b’s suddenly became a general rule. I’d conned the class into using algebra because of the accuracy issue.
Download the worksheet and answers here: Surface_area_of_a_cone
Hint: Copying onto coloured paper or card makes this activity stand out in their notes.
I’ve been using this idea since I first started teaching and I’ve finally got around to typing it up!
Image Credit:http://coachandhorsesn16.com/eat/fish-n-chips/
I introduce order of operations by creating an imaginary Chip Shop. I usually read out orders and get the students to write down what they think they are on whiteboards. Note that when you read out the orders, the punctuation doesn’t give any hints.
This activity always prompts a ‘discussion’ as to who is correct. The misconception of what an order could mean links nicely with the misconception when working out 2 + 3 x 4. You could also adapt the idea for writing algebraic expressions.
A presentation, with questions, is downloadable in three different formats here:
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.
I love the worksheets produced by danwalker on TES resources. Basically a set of results are combined to make a numerical code. You could have a ‘Kilner’ stye jar with a changeable combination padlock and a prize locked inside as motivation.
Image credit: www.waragainstwork.com
I’ve started using this style of activity with sleepy sixth formers, unmotivated low ability Year 10 and excitable Year 9s. Dan Walker has released the following activites on TES resources:
I’ve now created a Code sheet for Number Patterns. It covers term to term rules, using an Nth term rule, finding an Nth term and finding a specified term.