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ATM Camborne Branch Enriching ALGEBRA 4th October 2008 1. Generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence). Silent starter: 23, 34, 45, 56,…n? Given a rule: learners have number cards – is their card in the sequence? Pictorial – practical ideas – then to graph or 100 square to illustrate Link to y=mx+c 2. Use simple formulae from mathematics and other subjects, substitute positive integers into simple linear expressions and formulae and, in simple cases, derive a formula Series of practical experiments e.g. Hooke’s law where learners change the values of the variables and make hypotheses about the relationship For various mobile phone tariffs convert to a formula and test it on learners’ own data For car or machine hire convert charges to a linear formula, or at least a piecewise linear formula 3. Simplify linear algebraic expressions by collecting like terms; begin to multiply a single term over a bracket Problems in the context of algebraic ‘pyramids’ Use shapes for variables to help establish the ‘rules’ Cards and/or colour to group ‘like’ terms Kinaesthetic – use students as variables (their characteristics or …) Envelopes or boxes to represent the contents of brackets to emphasise the idea that all inside are multiplied Show it with numbers rather than letters to start off Treasure hunt games for practice Tarsia activities to practice 4. Construct and solve linear equations with integer coefficients Clouding the picture Problems like ‘Gerald has n cubes and Samantha has three times as many….’ Or use sweets or money for engagement Age puzzles: ‘My age, my son’s age and my grandson’s age add to 91. My age is twice my son’s age and his age is 4 times is son’s. How old am I?’ 5. Plot the graphs of simple linear functions History of Cartesian coordinates – Descartes, and notion of graphs Research what do the words mean – linear, function Investigate using graphical calculators or AUTOGRAPH Real-life – temperature conversion Link to number sequences Focus on axes and scales and coordinates to ensure secure foundation 6. Solve simultaneous linear equations algebraically Start with a word problem (cows and chickens) and solve in pairs and consider the strategies used, moving on to algebra Graphical solution can be explored with graphical calculators or AUTOGRAPH Sort the steps in the solution into the correct order Mathematical Team games book (Tarquin) has activities Practice using treasure hunt, Tarsia, Enhance understanding using posters and creating own problems 7. Use multipliers to calculate exponential growth Simulate radioactive decay using dice throws and see how many are left after each time period. Model using multipliers Auntie’s will/pocket money – compare returns using different systems Game of life simulations Rice on a chess board Folding paper lots of times – thickness? Debt for LEDC’s and compound interest Maths4real video Bacterial growth 8. Rearrange a formula Group versions of the same formula – matching activity Do it with numbers first to establish basic ideas 9. Given values for m and c, find the gradient of lines given by equations of the form y = mx + c Learners work on paper (in pairs) writing down things like (2,1), (2,3), (2,10)… What do you notice? Learners create their own pairs. Explore using graphical calculators and graph-plotting software Puzzles like ‘match the graph’ or ‘match the screen’ Place 2 points on the graph and then ‘shoot through the goalposts’ What does the equation tell you about the line? Can you draw it straightaway? Given any straight line can you write down its equation? 10. Solve a quadratic equation by using the formula Mnemonic: A negative Boy wasn’t sure about going to a Radical party. He was too SQUARE and turned down 4 Awesome Chicks. It was all over when he got 2 Angry. Engage by starting from number problems. Impossible to solve many without rule. 11. Completing the Square Use diagrams to show what is happening Matching activities