Lesson 3 Number lines galore

# Episode 2

Reasoning Resources: Worksheet 2
Rather than treating the number line for ordering numbers and operations, it is now an equal interval scale.

The scale, with its easy large numbers such as 10s, helps in ‘seeing’ answers and checking.
Give out Worksheet 2 with empty number lines with a single mark for the zero. Ask pupils to place some marks in a scale so that they can have numbers up to 50, and to place the same three numbers 15, 8, 24. Scales do not have to be marked accurately. There should be a discussion of the numbers ‘below’ 0 to make sure pupils are clear on how to place negative numbers on a number line.

Now they should use the line to show how to find the answers to the subtractions: 15 ~ 24 and 24 - 8.

In the sharing phase pupils should first look at how they decided on the scaling, somewhat similar to the discussion on strip B in Episode 1. Then focus on the different ways the 10 markers are used for the subtraction.
Two meanings of subtraction: difference and going down.

The inversion of addition and subtraction. Likely methods are to:

• Go down in 1s to the nearest 10, then in 10s, then in 1s again
• Go down in 10s then in 1s
• Go up in similar ways.
• In subtracting the larger number you first subtract the smaller one to zero, then go down the difference. The more confident pupils should try subtracting the larger number from the smaller, and explain what is similar and what is different about the answers, and why. In the ‘going down’ sense of subtraction you first go down to zero, then further down, ending at a negative number as a position. In the ‘difference’ sense, however, subtracting larger numbers from smaller ones appears much more similar to subtracting smaller ones from larger ones.

Whole class reflection

• Why is this visual way better than the written algorithm?
• Why is going up possible for subtraction questions?