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puzzles

 

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.

mathsdingbat18

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.

b

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.

 

TES collection number 1

TES collection number 2

code

Code breaking is a good activity to introduce problem solving skills and real world careers for mathematicians. 

Code Cracking worksheets

Marcus De Satouy video explaining codes

Counton website to generate different codes

Nice Morse Code Generator

Numberphile also have a good introduction to public key encryption using prime numbers.

csi

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.

IGCSE Number CSI

TES Collection of GCSE Number, Algebra, Geometry, Data Handling, KS3 mixed and Grade C GCSE Revision.

blockbusters

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.

Vectors IGCSE Blockbusters

KS3 Missing angles Blockbusters

Algebra Blockbusters

KS3 Sequences and Patterns

treasure hunt maths

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.

tarsia

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!

jeopardy

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

Year 7 Easy General Revision

Year 7 Hard General Revision

Year 8 Easy General Revision

Year 9 Hard General Revision

KS3 – Fractions, Decimals, Percentages (Levels 5 and 6)

KS3 – Shape (Level 5 and 6)

KS3 – Algebra (Level 5 and 6)

Key stage 4

Topic: GCSE Number

Topic: GCSE Algebra 1

Topic: GCSE Algebra 2 e

Topic: GCSE Stats and Probability

Topic GCSE Trig/Shape

Topic: GCSE Geometry

Topic: GCSE sets functions vectors

Topic IGCSE Matrices

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IB Maths Exploration Guide

IB Maths Exploration Guide

A comprehensive 63 page pdf guide to help you get excellent marks on your maths investigation. Includes:

  1. Investigation essentials,
  2. Marking criteria guidance,
  3. 70 hand picked interesting topics
  4. Useful websites for use in the exploration,
  5. A student checklist for top marks
  6. Avoiding common student mistakes
  7. A selection of detailed exploration ideas
  8. Advice on using Geogebra, Desmos and Tracker.

Available to download here.

IB Exploration Modelling and Statistics Guide


IB Exploration Modelling and Statistics Guide

A 60 page pdf guide full of advice to help with modelling and statistics explorations – focusing in on non-calculator methods in order to show good understanding. Includes:

  1. Pearson’s Product: Height and arm span
  2. How to calculate standard deviation by hand
  3. Binomial investigation: ESP powers
  4. Paired t tests and 2 sample t tests: Reaction times
  5. Chi Squared: Efficiency of vaccines
  6. Spearman’s rank: Taste preference of cola
  7. Linear regression and log linearization.
  8. Quadratic regression and cubic regression.
  9. Exponential and trigonometric regression.

Available to download here.

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