Cross Curricular Numeracy
Some Pointers from the Maths Department
All students should have a calculator with them in every lesson. Where appropriate, do encourage them to use calculators, so that they realise that they are an item of equipment they should have in school every day.
Do feel free to liase with maths staff about any subject needs you have – we are happy to try and teach skills in maths ready for you to use them in your subject.
Number Work
Numbers Many students do not understand big numbers. Try to write numbers in both word and digit form, for example for the population of the UK, 57 million and 57 000 000. Help them to appreciate and read the numbers by using column headings:
|
Ten Millions |
Millions |
Hundred Thousands |
Ten Thousands |
Thousands |
Hundreds |
Tens |
Units |
|
5 |
7 |
0 |
0 |
0 |
0 |
0 |
0 |
From primary school onwards they will have done work on rounding. Discuss with them the level of accuracy that has been used and hence the actual size the population could be. For example if the figure is 57 million to the nearest million, the true value could lie anywhere between 56 500 000 and 57 499 999.
Percentages In year 7 we concentrate on non-calculator methods, finding 50% by halving, 25% by dividing by 4 (halve and halve again), 10% by dividing by 10. We find other percentages by reference to these e.g. 15% is 10% + 5% (i.e. 10% plus half of 10%). From year 8 we use calculator methods, particularly with the more able, but methods will vary with year group and ability. For example to solve: Last year there were 145 voles in a colony. If the population increases by 3% per year, how many will there be this year?
Most would work out 1% of 145 is 145 ¸ 100 = 1.45
so 3% is 1.45 x 3 = 4.35
This gives 145 + 4.35 = 149.35 voles,
i.e. 149 as you can only have whole numbers of voles.
Higher ability students would say 3% is 0.03 as a decimal
so 3% of 145 is 0.03 x 145 = 4.35 etc.
Top set year 9 onwards might work out that there will be 103% of voles
so 1.03 x 145 = 149.35 etc.
Students struggle with questions
of the type: 345 people out of the 1200 people in the town were factory
workers. What percentage is this? The method is the same for all groups:
and this would
usually be solved using a calculator. Some of the more able students would be able to cancel this
down and solve it on paper.
Probability
In maths we express probability in fractions or decimals, in preference to percentages. It is not acceptable to write probabilities as 1 in 10 or 1:10. It is important to stress that probabilities add to 1 (for mutually exclusive events), for example if the probability of rain is 0.72, the probability of no rain is 0.28.
Space, Shape and Measures
Students need to know about both metric and common imperial units. Our students are very weak at associating units with measurements, and at estimating measurements (for example recently every student in a lower set in year 8 wrote down that a wedding ring was about 5 cm in width, rather than 5 mm). Many students do not know which units are for lengths, capacities or masses, and do not know which ones are metric and which imperial. They also struggle to convert between units, both within the metric system and, less importantly, but still in the National Curriculum, between metric to imperial. Please emphasise units wherever possible and get them to estimate lengths, masses and capacities. For example in PE “How far have you just run?” “What fraction of a kilometre is that?” “Roughly how many yards is that?”
Common metric to imperial conversions that are important are:
5 miles is about 8 km (or 1 mile is 1.6 km)
1 inch is about 2.5 cm
1 kg is about 2.2 pounds
1 pint is about ½ a litre
1 gallon is about 4.5 litres
Handling Data
Line or Scatter Graphs Many students make mistakes over the scale – they write the numbers ‘in the gaps’ not on the lines, and do not space the numbers evenly, especially near the origin. Graphs of this type should be drawn on graph paper for accuracy.
Bar Charts Bar charts are preferable to pie charts if the actual numbers of people, cars etc. in the different categories are important. For qualitative and discrete data (non-number data and data that can only take certain values, such as occupations, colours, shoe size) the bars should not touch, and labels explaining each bar should be put in the centre of the bar, as shown in figure 1. For continuous data (data which can take any value, such as the height of plants in a wood) the bars do touch and the scale should be linear, as shown in figure 2.
Pie Charts Pie charts are preferable to bar charts if a comparison of the proportion of people, cars etc. in the different categories is important, not the actual numbers. In maths we always draw pie charts using angles, not percentages, and this skill is largely taught in year 8. For example to draw a pie chart to illustrate this data on the ages of child workers in a factory:
| Age in years |
Number of Workers (Frequency) |
Angle |
Angle (to nearest whole number) |
|
10-11 |
8 |
8 x 5.29 = 42.442 |
42 |
|
12-13 |
12 |
12 x 5.29 = 63.5 |
64 |
|
14-15 |
17 |
17 x 5.29 = 90 |
90 |
|
16-17 |
31 |
31 x 5.29 = 164.1 |
164 |
TOTALS |
68 |
|