1. Lead teacher day September 2009 In a range of meaningful contexts: Students learn about scale Michael Drake School of Education Policy and Implementation

2. Think of a thermometer (imagine a picture of a thermometer in your head) What did it look like?

5. Think how you would describe such a scale to someone who can’t see it Turn to the person next to you and describe the scale

6. What language did you use? Words like ‘gaps’, ‘places’, ‘skips’, ‘jumps’, and ‘spaces’ were used to refer to an interval. ‘Notches’, ‘dashes’, ‘ones’, ‘small ones’, ‘little things’, ‘things’, ‘bars’, ‘numbers’ and ‘arrows’ were used to describe marks. Some students referred to the same thing using a variety of terms in different questions. Others simply avoided naming what they were talking about…

7. So what language do you teach students to use when working with measuring instruments like thermometers? Are there any correct terms? So what message is being sent?

8. Now describe this one What can you tell me about this thermometer?

9. And this one

11. Now picture a graph

13. So what’s the message?… Measurement and graphing are both built upon the concept of a scale A scale is not a single object that students can learn about – it is a mathematical tool of great variability Its complicated…

14. So how do we get this incredible variety across? In MiNZC it was assumed that students would learn what they need to learn about scale by using scales “within a range of meaningful contexts” – that is while measuring and graphing

15. Student P Student P showed she could successfully locate and read whole numbers, fractions, and decimals on scales, using multiplicative thinking when appropriate. However, when plotting points she reverted to using a unit scale, even when this meant there was insufficient space on the grid to complete the task… “I haven’t really learnt about graphs and all that sort of stuff.”

16. What skills do students need to learn to be able to cope with scales (and measurement and graphing) successfully?

17. What do you have to do to accurately work out the temperature in degrees Fahrenheit? (Try it).

18. The gap between the numbers is 20 (e.g., 80 – 60 = 20) The large mark in the middle shows where 70 is Five marks between 70 and 80, so each is worth 2 (e.g., 5 × 2 = 10) So one mark below 80 is 78 ℉

19. Work out the height of the ball at the 5 seconds mark

20. NZC GM2-1 Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time. GM3-1 Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.

21. GM4-1 Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time. GM4-4 Interpret and use scales, timetables, and charts