Understand and use algebraic notation

Term 1 starting in week 3 :: Estimated time: 2 weeks

Given a numerical input, find the output of a single function machine
Use inverse operations to find the input given the output
Use diagrams and letters to generalise number operations
Use diagrams and letters with single function machines
Find the function machine given a simple expression
Substitute values into single operation expressions
Find numerical inputs and outputs for a series of two function machines
Use diagrams and letters with a series of two function machines
Find the function machines given a two-step expression
Substitute values into two-step expressions
Generate sequences given an algebraic rule
Represent one- and two-step functions graphically

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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.

Algebraic Notation Simplification using the normal conventions of algebra.

Writing Expressions Listen to the voice saying the algebraic expression then write it in its simplest form.

BIDMAS A self marking exercise testing the application of BIDMAS, an acronym describing the order of operations used when evaluating expressions.

Algebra Pairs The classic Pelmanism or pairs game requiring you to match equivalent expressions.

BIDMAS Video A reminder of the order of operations often referred to as BIDMAS, BODMAS or PEMDAS.

Connecting Rules If you are given the values of x and y which of these equations is correct?

Substitution Examples A projectable set of animated examples to help prepare pupils to do the Substitution online exercise.

Substitution Video Lots of examples of substituting values into algebraic expressions. This video is to help you do the online, self-marking exercise.

Substitution Substitute the given values into the algebraic expressions.

Collecting Like Terms Video If you have forgotten what collecting like terms means watch this video for a quick refresher.

Collecting Like Terms Practise your algebraic simplification skills with this self marking exercise.

Stable Scales Ten balance puzzles to prepare you for solving equations.

Brackets Levels 1 and 2 Learn how to remove brackets from simple algebraic expressions. This video is to help you do the online, self-marking exercise.

Brackets Levels 3 to 5 Learn how to multiply the terms inside a pair of brackets by the term outside. This video is to help you do the online, self-marking exercise.

Brackets Levels 6 to 8 Expand a pair of brackets using the clown's face method. This video is to help you do the online, self-marking exercise.

Brackets Levels 9 and 10 The final video showing how algebraic expressions containing brackets can be simplified.

Missing Operations Exercise Each box represents a missing operation (add, subtract, multiply or divide). What are they?

Brackets Expand algebraic expressions containing brackets and simplify the resulting expression in this self marking exercise.

DiceGebra An online board game for two players evaluating algebraic equations and inequalities.

Substitution Sort Order the algebraic expressions according to their value with the given substitution.

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".

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

5.5 Times Table

Write out the 5.5 times table as far as possible.

2nd Lesson

Connecting Rules

Give 20 rules connecting x and y given their values.

3rd Lesson

PYA

You have four minutes to write down as many equations as you can involving the given letters.

4th Lesson

Missing Lengths

Introduce linear equations by solving these problems about lengths.

5th Lesson

Sum of the Signs

Each traffic sign stands for a number. Some of the sums of rows and columns are shown. What numbers might the signs stand for?

6th Lesson

Sea Shells

A question which can be best answered by using algebra.

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.

White Rose Resources

End of block assessments provide a quick progress check at the end of each block of learning to make sure students have understood the content covered.