## Key mathematical activities & Teaching Points

### Key mathematical activities

• breaking a task up into component parts
• making reasonable estimates on a scale which is convenient and understandable
• stating assumptions, documenting sources of information, and explaining and justifying solutions

### Key teaching points

• Don't allow pupils to bury themselves in computational 'busy work'
• large tasks need to be broken into component parts
• measurement accuracy depends on the purpose of the measurement, and the closeness of the result [if you use crude measures and the conclusions are not crystal clear, you have to do everything again, carefully!]
• it is a good idea to solve the problem in two (or more) different ways - if you get similar answers, you can be more confident than if you used just one approach
• it is a good idea to produce bounded estimates - make assumptions that are at the low end, and at the high end, and look at the difference. This will show you how sensitive the PE is to the assumptions that have been made
• look out for problems when pupils have to change units (e.g. gallons of diesel to metric tonnes!)
• look out for problems when students are using very large numbers
• you could encourage them to round intermediate values in calculations
• to get a sense of scale, it is often helpful to convert large numbers with lots of zeroes into numbers of thousands, millions or billions
• so, combining the two ideas above, if a pupil works out heart beats using 70 beats per minute, you might see 70 x 60 x 24 =108,000 beats per day [encourage pupils to keep track of what the numbers mean]. Talking about this as 100 thousand helps make sense of it. Then multiplied by 365 gives about 35 million [or 40 million] heartbeats in a year and about 500 million [ half a billion] for a 14 year old.