The big mathematical

content picture – algebraic thinking

Michael Drake

SNP national resource coordinator

What is algebra?

Think…

Discuss in pairs…

• Try this problem

1000- 647

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

7 + 8 + 9 =

4 + 5 = + 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 - 54 54 + = 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 somethingIn 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 foundIn a triangle, x is often used for the angle students need to find

3) A letter is really a numberevaluate 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 × heightA = b × hA = bh

5cm

3cm

A = 5 × 3

A = 15cm2

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 + = 10

57 + = 83

3.64 + = 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?

4

16

Materials

Imaging

Property of numbers

Generalisation from

numbers

What is algebra?