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Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-5
Featured UK Key Stage 3-5; US Grades 6-12
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Featured UK Key Stage 2; US Grade 3-5
Featured UK Key Stages 3 & 4; US Grade 6-10
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Science, Technology, Engineering and Mathematics
Making Algebra Rich
Stage: 1 and 2
Article by Lynne McClure
Published December 2014,June 2014.
In her article
'What's X Got to Do with It?'
Anne Watson describes how, even though algebra is only mentioned formally in the year 6 programme of study in the new National Curriculum, the roots of algebraic thinking can be traced back throughout the primary years. This feature brings together rich activities that support early algebraic thinking, and one or two that support the more formal algebra in year 6.
Balancing and the equals sign
Anne describes the importance of ensuring that = does not signify a calculating instruction ('makes') but does mean 'equivalent to'. The idea of both sides of an equation being worth the same is a fundamental concept but many children don't realise that 4 + 5 = 9 can be written:
4 + 5 = 6 + 3, 4 + 5 = 7 + 2, 4 + 5 = 11 - 2 or even 4 + 5 = 3 x 3.
This idea of
can be illustrated beautifully using a balance - you might choose to use the interactivity in
Getting the Balance
(KS1) to explore some whole class questions before tackling the challenge itself, and then invite your pupils to have a go at
Balance of Halves
Using symbols then letters
The idea of equivalence is important in missing number problems. They are initially used where we want children to recall and use a number fact, for example 6 + ? = 10, in which if you know your number bonds to 10, the answer is obvious. Later we want them to use a symbol as a place holder for an unknown quantity where the answer is
immediately obvious and we have to do some work to find a solution.
Heads and Feet
Plenty of Pens
(KS2) are both types of missing number problems
which encourage children to use personal representations (using objects or perhaps drawing) and then, if appropriate, to move into using symbols. And if you'd like your pupils to become more confident in using symbols, you could offer them
Shape Times Shape
, both of which are problems requiring chains of reasoning and offer excellent opportunities for children to communicate their thinking.
Generalising from a number of examples and stating a rule
Maths is shot through with patterns. The algebraic idea of finding a rule implies first noticing a pattern and then generalising it. In the early stages the generalisation will be a statement in words, later this may be refomulated into symbolic representation.
(KS1) is a well known elimination game (similar to one potato, two potato) for younger pupils. Can they predict what will happen if they start the rhyme in different places and what patterns do they notice? How can they record this - perhaps in words or maybe in a picture? In
(KS2) pupils are asked to make geometric patterns with sticks and predict how many they would need to continue the pattern. This idea of linking geometry with number is one that becomes more important as pupils' understanding progresses, as is finding elegant ways of recording which support pattern spotting.
On NRICH there are many more longer investigations which require children to conjecture, convince and prove, and using algebraic notation can often be helpful in the latter. For KS2 children you may want to revisit
(an old NRICH favourite) or
Up and Down Staircases
For even more algebra possibilities have a look at the Patterns and Sequences collections for
Algebra - generally
Trial and improvement
Multiplication & division
Addition & subtraction
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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