Lesson 3 Number lines galore

# Episode 1

Reasoning Resources: Worksheet 1 photocopied on to card and cut into strips A, B, C
Introduction
Different classes need different starters for this, avoiding mental calculations.

Warm-up should lead to the main activity on the size of numbers on the number line.

Halving methods.

Visual estimation.
For younger classes start briskly with questions about ‘numbers you like, ‘lucky and unlucky numbers for you’ and then most importantly ‘easy numbers: Focus attention on the 10s and 5s, posing a question like; What is special or useful about these? Switch to how these numbers are useful on the number line, or rulers.

For other classes start with a question such as; How do you imagine numbers organised in your mind? This would focus pupils’ attention on how different people have different images of the number line.

These images may be influenced by special groups of numbers, like the ‘teens’ which are pronounced differently from the others, and 10s and 100s etc.

Another possible starter is to ask the class to imagine a number line starting from zero or ground level going up to the ceiling, and what number would it be at the ceiling. This should lead to discussion on scale, and to extending the line above the ceiling, and below the floor.
Pair and small group work
The need for two reference points on a number line to find the scale and therefore any other number.

Confidence to estimate
positions to be developed. The proportional scale does not need to be very accurate.

The number line is of infinite extension in the mind.
In short rounds, each of about 5-6 minutes, the pupils work in pairs and groups. Give out strip A from Worksheet 1, with a number line 0-30. Ask the pupils to place 15,8, and 24. In discussion pupils share their ways of finding the half-way, e.g. by folding, or using fingers etc. They talk of ways of estimating +10 positions, and possibly finding the size of the unit scale. Encourage rough work and estimation, rather than ruler- type accuracy.

Give out strip B from Worksheet 1. Ask; What could the other marker be? After discussion ask the class to choose a sensible number for it, e.g. 100 or 60 etc, and ask why they chose that one. They are now to place the same three numbers on it.

Give out strip C and ask them the same questions. 24 cannot be placed on the number line, which only goes up to 20. Discuss how the number line continues infinitely. Stick the number line to the board and ask pupils to place 24, off the end of the strip and on the board.

Ask the class how they would find any number on any number line; what are the minimal requirements, and how would they go about it. What other numbers can be placed on the number line?