Download ATM Camborne Branch Enriching NUMBER 4th October

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: 23, 34, 45, 56,…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