Algebraic representation
Term 3 starting in week 9 :: Estimated time: 1 weeks
- Draw and interpret quadratic graphs
- Interpret graphs, including reciprocal and piece-wise
- Represent inequalities
For higher-attaining pupils:
- Investigate graphs of simultaneous equations
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Activities for pupils
Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.
Completing the Square Practise this technique for use in solving quadratic equations and analysing graphs.
DiceGebra An online board game for two players evaluating algebraic equations and inequalities.
eQuation Generator An unlimited supply of linear equations just waiting to be solved. Project for the whole class to see then insert the working in your own style.
Factor Trees Create factor trees to find the prime factors of the given numbers.
Inequalities Check that you know what inequality signs mean and how they are used to compare two quantities. Includes negative numbers, decimals, fractions and metric measures.
Quadratic Equations Solve these quadratic equations algebraically in this seven-level, self-marking online exercise.
Quadratic Equations Video Learn the common methods of solving quadratic equations by factorising and by using the quadratic formula.
Three Ways Find three different ways of multiplying four different digits together to get the given target number. There are nine levels for this online challenge.
Using Graphs Use the graphs provided and create your own to solve both simultaneous and quadratic equations.
Words and Concepts Fill in the missing words to show an understanding of the vocabulary of equations, inequalities, terms and factors.
Writing Expressions Listen to the voice saying the algebraic expression then write it in its simplest form.
Click on a topic below for suggested lesson Starters, resources and activities from Transum.
- Algebra Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas. If this topic were split into four sub topics they might be: Creating and simplifying expressions; Expanding and factorising expressions; Substituting and using formulae; Solving equations and real life problems; This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".
- Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.
Lesson Starters
Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.
1st Lesson
Think Back
A problem which can be answered by forming an algebraic equation then solving it.
2nd Lesson
Simultaneous Occasions
A problem which can best be solved as a pair of simultaneous equations.
3rd Lesson
Rail Weigh
Use the weights of the trains to work out the weight of a locomotive and a coach. A real situation which produces simultaneous equations.
Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.
