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This is a really nice puzzle we looked at at the IB HL workshop:
When x = 1, y = 1, when x = 2, y = 2, when x = 3, y = 3 but when x = 4, y does not equal 4. Find a sequence which describes these points.
There are an infinite number of answers, though not necessarily easy to find!
If you are interested in the solutions, the answer is written below in white text, highlight to reveal!
Answer:
Two possible ways of tackling the problem –
1) as a polynomial – if y = (x-1)(x-2)(x-3) + x this satisfies the original question – as the brackets all cancel to zero for 1,2,3 but will remain for x = 4 onwards.
2) modelling as a function with absolute value. Notice that -(abs x ) will satisfy the correct shape – ie a linear increase and then divergence from this. By transformations therefore we can get -(abs(x-3) ) +3. This fits the graph for y=x for 1,2,3 before altering for y=4.
Maths Dingbats are great for lesson starters and for using in quizzes – I’ve uploaded about 50 to this website here. These one all use some maths terms to generate the answer
There is a big powerpoint file with about 50 more here. These ones all give a maths related word as the answer.
and there are some great Pi-related Dingbats, here and here. A good resource for Pi Day and throughout the year.
Bingo works great as a starter and plenary activity. It’s surprising how much students enjoy this game. Even better, there are so many ready created games on TES, you’ll never even have to make your own.
Code breaking is a good activity to introduce problem solving skills and real world careers for mathematicians.
Marcus De Satouy video explaining codes
Counton website to generate different codes
Numberphile also have a good introduction to public key encryption using prime numbers.
Maths CSI is a really good revision resource from Laura Rees Hughes – students work in groups to solve clues, eliminate suspects and arrive at the culprit.
Another variation on a gameshow theme – Maths Blockbusters is a good way of introducing competition into the class. It works well splitting the class (say) girls versus boys – with all pairs of students given whiteboards. When it’s the boys’ question, all the boys must raise their whiteboards with the answers. Any incorrect answers and the girls get a chance to steal. First team all the way across wins.
There are a real variety of treasure hunt resources on TES – and these are great for adding a bit of momentum to a lesson.
1a) Find the Treasure is a IGCSE activity for using loci and constructions to find the buried treasure.
1b) Loci and constructions to find the murderer from map instructions.
2) Pirate Treasure Hunt is an IGCSE activity testing using and applying SOHCAHTOA to word problems.
3) Round the classroom treasure hunts are a good way of getting students off their seats. There are a large number of KS3, IGCSE and IB resources listed on TES.
Maths Tarsia are one of the best group activities for maths – there are already a large number of Tarsia puzzles on TES Secondary Maths Resources but most of these relate to A level rather than IB. I’ve uploaded a few more specifically for IB here . There include:
HL or SL:
Binomial distribution
Probability
Normal distribution
HL:
Differentiation
Poisson distribution
Studies:
Financial maths
Functions
I will add to these throughout the year!
One of my favourite resources is Jeopardy. For those not familiar with the game (I think it’s American), it’s a gameshow, where you get to choose questions of different levels of difficulty, from a range of categories. I downloaded the template from TES – it’s a ready-made powerpoint which you can click on to take you to relevant questions, and then another click returns you to the home screen. The class can be split into teams, each team given a whiteboard and (say) 2 minutes to answer a question. Teams with the correct answer get those points for their teams. The challenge round adds a bit more excitement – and you can add any general questions or puzzles – such as dingbats or memory challenges (memorise pi to 10 places etc). Here is a screen capture of the initial powerpoint slide:
I’ve uploaded a large number of these to TES (mostly IGCSE at the moment – but some IB and KS3 too)
IB
Maths Studies Revision of Triangles, Sets, Geometry and Logic
Maths HL Trigonometry (geometrical shapes)
Key stage 3
KS3 – Fractions, Decimals, Percentages (Levels 5 and 6)
Key stage 4
Topic: GCSE Stats and Probability
