Let’s Think Secondary Maths, Lesson 2 – Organising teams
Overview
Thinking Strands: Number and Algebra
Learners are challenged to build upon the notion of number carriers they first encountered in
Roofs. The basis of the lesson is the systematic organising of teams to play in a league (see video
tutorial for details of this due to the ambiguity built into the lesson) to find the total number of
games played. In organising teams the move towards the use of expressions comes from the
systematic recording/listing of the matches played. The rule developed allows the expression for
any number of teams to be written.
Aims
 To recognise the need for systematic listing to spot patterns.
 To express patterns using the ‘nth’ term and to make predictions based upon this.
 To explore the use of algebraic symbols in a range of expressions derived from everyday
scenarios.
Vocabulary
Systematic. symbol, expression, algebra, rule, number carrier/holder/variable.
In-school resource preparation
Materials – Supplied
 Resource Sheet A: Netball game (Hook)
 Resource Sheet B: Algebra stories (not produced yet).
Materials – Not supplied
 Large sheets of paper, felt pens.
Overview of Activities – please see video tutorial for full details of how to develop this lesson
with your class.
Hook: This activity can be introduced in a variety of ways (the netball illustration provides a
backdrop for the narrative that flows through the lesson). The main task involves the pupils
having to work out the total number of games played if 3 schools each play each other and each
has to play at home. The ambiguity of not saying whether it is a league or a knock-out
tournament challenges the learners to articulate their reasoning and to show their methods. The
video tutorial highlights how to manage this aspect of the lesson. This aspect ends with the
realisation that 3 schools will play 6 games – please ensure that a range of methods of showing
this are present for use in activity 1.
Activity 1: Here the class is challenged to use a new method to show how many games will
be played if another school is now added. This can be done as a whole class or in pairs. With 5
schools groups of learners can be challenged to come up with the ‘best’ method of showing how
many games are played. At this point you may wish to allow them to work on showing 6, 7, 8, 9
or lots of schools. The important point to stress is that there must be a significant period of
sharing and debate as pupils air their methods and realise the need for systematic recording to
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highlight the moment when the penny drops i.e. ‘you don’t play yourself’, ‘it’s always one less’.
The board/class/large sheets of paper must show a range of methods from simple listing, to
highly systematic recording, to repeated addition, to multiplication to facilitate the move towards
using expressions by the majority of learners (the video tutorial highlights the way this can be
done).
The move to generalised number is managed in a similar way to that in Roofs i.e. starting with 10
schools the method to calculate number of games can be shown (10 x 9) until the numbers
involved become too large to practically manage without using the multiplication method ie n x
n-1. At this point reference can be made back to the use of number carriers and their role in
expressing patterns. It may be helpful to stress that we are using expressions to generalise the
rule.
Activity 2: Use the ‘algebra stories’ note sheet to encourage the learners to develop their
understanding of expressions. You may wish to use this activity to explore the use of symbols to
stand for numbers and the more formal use of letters within mathematics. This should develop
naturally as a consequence of the ideas that come from the note sheet and should not be used to
formally teach the use of x and y within formal mathematics notation.
End of activity reflection: learners can share and reflect upon and share their own ‘algebra
stories’ as they discuss the way we use symbols in expressions and equations to stand for
‘any number’.
Notes
During joint planning ensure you:
Many pupils are familiar with the term ‘algebra’ without understanding the role of number
variables and expressions. Many are comfortable with solving simple equations where the
‘unknown’ is fixed – here we are seeking to develop and this often leads them into a simplistic
way of thinking about algebra using 1 to 1 correspondence. Think carefully about how to allow
the learners to explore this concept themselves without leading them or reinforcing thee
misconceptions to bring to the secondary maths classroom.
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