The big mathematical content picture – algebraic thinking Michael Drake SNP national resource coordinator

What is algebra? Think… Discuss in pairs…

Try this problem What do you notice? Does this always work? Explore…

Algebraic thinking can be defined as what happens when “students demonstrate they can use and understand principles that are generally true and do not relate to particular numbers.” Algebra arises throughout mathematics whenever generalisations are made. This may be when a student is looking at how a simple pattern is being created by adding threes, or recognising that it is quicker to find the area of a rectangle by multiplying the number of rows by the number of columns, instead of skip counting or counting squares Algebraic Thinking

Algebra is a language The language is based on symbols Students need to learn how to use this language. If they are not taught how to use this language – they will make their own sense of the symbols

The equals sign = =  + 3 x = 3 What does the equals sign mean in each of these situations?

John has 54 marbles. He buys another packet of them and ends up with 83 marbles. How many marbles were in the packet?  = 83

What generalised understandings do children need to be able to solve this problem? What understandings of the language do students need to have?

It’s a race… Have a clean piece of paper and a pen at the ready Add up all the numbers from 1 to 100 Set… Lolly for the winner…

How do we use letters in mathematics? 1)A letter can be used to name something In the formula for the area of a rectangle, the base of the rectangle is often named b 2)A letter can be used to stand for a specific unknown number that needs to be found In a triangle, x is often used for the angle students need to find 3)A letter is really a number evaluate a + b if a = 2 and b = 3 4)A letter can be used as a variable that can take a variety of possible values 5)In the sequence, (n, 2n+1), n takes on the values of the natural numbers – sequentially

The development of formulae Area = base × height A = b × h A = bh 5cm 3cm A = 5 × 3 A = 15cm 2

Equations Sian has 2 packs of sweets. She eats 6 sweets and is left with 14 sweets. How many sweets are in a pack? How did you solve this?

When is a problem a number problem – and when it is an algebra problem? 6 +  =  =  = 4½ 57 + x = 83

Ameeta has 3 packs of biscuits, and 4 extra loose biscuits. Sam has one pack of biscuits and 16 loose biscuits. If they both have the same number of biscuits, how many biscuits are in a pack? Can you draw a picture to show the problem?

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Materials Imaging Property of numbers Generalisation from numbers

What is algebra?