Let's Think Secondary Science

Let’s Think Secondary Maths, Lesson 1 – Roofs

Overview

Thinking Strands: Number and Algebra

Learners are challenged to describe the number patterns associated with trapezia drawn upon triangular dotty paper. The two-part nature of the rule is explored prior to extending the number patterns towards the ‘nth’ term. The idea of a number variable or carrier is used to focus the learners on the fact that letters can be used to ‘stand for’ any number. There are several possible extension activities that build upon the idea of an expression this activity introduces.

Aims

v To familiarise the learners with the idea of rules and relationships derived from number patterns.

v To express patterns using the ‘nth’ term.

v To introduce the term number holder/carrier as a label to introduce the concept of generalised number.

Vocabulary

Trapezium, expression, algebra, rule, number carrier/holder/variable.

In-school resource preparation

Materials – Supplied

v Resource Sheet A: Drawing on the sand (Hook)

v Resource Sheet B: Number holder image (not produced yet).

Materials – Not supplied

v Triangular dotty paper.

Overview of Activities – please see video tutorial for full details of how to develop this lesson with your class.

Hook: The image presents the idea of a child drawing shapes and making up a new name to describe what it looks like rather than its true mathematical name. It should get the learners thinking about what the shape actually is – a kite. They can then do the same by drawing 4-sided shapes, on the dotty paper, and naming them.

Activity 1: To move into the first part of the lesson encourage the pupils to share their shape names and then ask their peers if they can say what the shape is. Engineer the feedback so you end this phase by discussing those who have drawn trapezia and, if it is not forthcoming, name this shape as a roof. Clarify the parameters of a roof and show how to derive the number code. They can now draw their own roofs and share the number patterns. You may wish to write several roofs or not-roofs on the board from them to try.

Agree which number codes represent roofs and not-roofs (see video for details of how to manage this part and subsequent episodes) and then pose the question about how to come up with a rule to describe the number patterns. Grasping the nature of the two-part rule is the first main thinking focus of this lesson. The class should vote on the ‘best’ rule regardless of how many are aired so that you can use counter examples to challenge them to consider that when describing roofs they need to use a two-part rule.

Activity 2: This is a shorter section and sees the learners move towards generalised number. And involves the whole class working together with times of small group discussion to allow for times of reflection. Building on from their verbalisations of the two-part rule you can now use larger and larger numbers to complete the code starting with the first two numbers i.e. 14, 12, …., ….. This needs to be done slowly so the numbers become very large and that you run out of space as you struggle to write down the 4 numbers. At this point, usually when millions are involved, pose the question, ‘How can we carry on the pattern to save space?’ Time must be given to allow the learners to process this and also to formulate their response. The aim here is to familiarise learners with the idea that letters/shapes can stand for any number and to avoid 1 to 1 correspondence i.e. b = 2 because it’s the second letter of the alphabet.

End of activity reflection: Introduce the term number carrier/holder or variable for more able

learners and encourage the pupils to reflect upon this and share their insights. Use the ‘Reflective prompt sheet to facilitate this. Use Resource sheet 2 to support this phase of the lesson.

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.