Definition of Numeracy
The following definition is used to underpin the National Numeracy Strategy:
Numeracy is a proficiency that involves a confidence and competence with numbers and measures. It requires an understanding of the number system, a repertoire of computational skills and an inclination and ability to solve number problems in a variety of contexts. Numeracy also demands practical understanding of the ways in which information is gathered by counting and measuring, and is presented in graphs, diagrams, charts and tables.
Principles
- To develop a standardised approach to numeracy which offers consistency to students from all curriculum areas.
- It is the responsibility of all teachers within the school to maximise opportunities for pupils to develop and improve their numeracy.
- All teachers to recognise the importance of developing a positive attitude towards maths.
- All teachers to ensure that children’s own informal strategies for finding solutions are valued.
Aims
- To maximise the potential of all pupils, regardless of their level of ability, by working together as a staff in an atmosphere of mutual support, to improve levels of numeracy in all curriculum areas.
- To ensure that all pupils develop the confidence to use their mathematics in a range of contexts within the school and so help to equip them to cope with the mathematical demands of everyday life.
Objectives
- To identify key mathematical skills and applications that occur in different curriculum areas within the school.
- To encourage staff and pupils to become more aware of situations in which they are drawing on their mathematical skills and experiences.
- To help staff to have realistic expectations of possible levels of mathematical proficiency among pupils of different abilities and to develop an awareness of possible difficulties and misconceptions in pupils’ application of mathematical skills.
- To ensure that staff and pupils value personal, non-formal mathematical skills and processes in addition to formal mathematical techniques and strategies.
The remaining objectives are in accordance with the attributes of a numerate pupil as identified by the National Numeracy Strategy:
- To encourage and assist pupils to calculate accurately and efficiently, both mentally and on paper drawing on a range of calculation strategies.
- To help pupils recognise when it is appropriate to use a calculator – and when it is not – and be able to use one effectively.
- To enable pupils to make sense of number problems, including non-routine problems, and recognise the operations needed to solve them.
- To encourage pupils to explain their methods and reasoning using correct mathematical terms.
- To assist pupils to judge whether their answers are reasonable and to develop strategies for checking their work where necessary.
- To encourage pupils to suggest suitable units for measuring and make sensible estimates of measurement.
- To assist pupils to explain and make predictions
from the numbers in graphs, diagrams, charts and tables.
GRAPH POLICY
Most data can be displayed in a variety of graphical forms.
Pupils need to be aware of the different types of graphs and to be able to
make choices about which type of graph would be appropriate to use in different
situations. A consistent use of graphs needs to be applied across the curriculum.
Language associated with graphs:
Discrete data – has a limited number of possible values. It may be non numerical e.g. types of pet, or numerical e.g. shoe size, number of words in a sentence.
Continuous data – can take an infinite number of possible values. For example, temperature or length, which can be measured to any degree of accuracy.
The x-axis, (the horizontal axis), is used in all graphs to plot the independent variable and the y-axis, (the vertical axis), is used to plot the dependent variable.
Drawing graphs:
- All drawings should be completed with a pencil.
- Points should be marked with small crosses.
- Axes should always be labelled.
- The graph should have a title.
- Straight lines on graphs should be drawn with a ruler.
- Non-linear graphs should be drawn freehand.
- If axes do not start at zero (compressed axes) a zigzag should be drawn at the beginning of the axes.
Mathematics National Curriculum Level:
| Graph Type | N.C. Level |
| Pictogram | Level 3 |
| Pie Chart | Level 5 |
| Bar Chart | Level 3 |
| Frequency Diagram (discrete data) | Level 4 |
| Frequency Diagram (continuous data) | Level 5 |
| Frequency Polygon | Level 7 |
| Line Graph | Level 4 |
| Conversion Graph | Level 5 |
| Scattergraph | Level 6 |
| Cumulative frequency Graph | Level 8 |
| Histogram | Level 9 |
PIE CHARTS
- Pie charts should include a ‘Key’
- A pie chart needs a title
- Suitable to illustrate discrete data
A Pie Chart showing the types of crops on 100 local farms
BAR CHARTS
- Used to illustrate discrete data
- A bar chart needs a title
- The axes need to be labelled
- Generally the vertical axis will be frequency but it is acceptable to draw a horizontal bar chart.
- The bars MUST be of equal width
A Bar Chart showing hours of sunshine in a week
BAR LINE GRAPH
- Exactly the same as a bar chart but with bars made from lines!
FREQUENCY POLYGON
- A line graph drawn over a frequency distribution for grouped data joining the mid points of the columns with straight lines
- The frequency distribution does not need to be shown under the frequency polygon
Weights of pupils in 8A
LINE GRAPH
- A line graph is a series of points joined together with straight lines
- A line graph must have meaning i.e. a continuous change is occurring
A graph to show Jane’s
temperature on Monday
HISTOGRAM
- A histogram is used for representing continuous data where class intervals are of differing sizes
- The area of each bar represents the frequency
- The frequency density is always plotted on the vertical axis
| Time in minutes | Frequency (f) | Class Width (m) | Frequency Density (f/w) |
| 40 | 28 | 20 | 28/20 = 1.4 |
| 60 | 43 | 10 | 43/10 = 4.3 |
| 70 | 58 | 10 | 58/10 = 5.8 |
| 80 | 40 | 10 | 40/10 = 4.0 |
| 90 | 34 | 10 | 34/10 = 3.4 |
| 100-120 | 18 | 20 | 18/20 = 0.9 |
A Histogram showing the time spent on homework
by 221 pupils
SCATTERGRAPHS
- A scattergraph shows how two statistical quantities might be related
- Points are plotted on a set of axes using small, neat crosses
- Any trend, (correlation), is observed
- A line of best-fit can be added in order to estimate unknown values based on the evidence provided by the known data
POSITIVE CORRELATION:
The points follow a line with positive gradient (uphill)
NEGATIVE CORRELATION:
The points follow a line with negative gradient (downhill)
NO CORRELATION:
The points are scattered with no obvious trend
| Numeracy Glossary | |
| acute | An angle between 0° and 90° |
| area | A measure of surface. Area is usually measured in square units e.g. square centimetres (cm2), square metres (m2) |
| average | There are three different averages: Mean – calculated by adding up all the data values and dividing by the number of data items Median – the middle value when all the data is arranged in size order Mode – the most popular or frequently occurring data value |
| capacity | A measure of the volume of fluid a solid
can contain. Units include cubic centimetres (cm3) and cubic metres (m3). A litre is equivalent to 1000cm3 |
| circumference | The length of a circle i.e. its perimeter |
| congruent | Describing two or more geometric shapes that are the same in every way except their position in space |
| co-ordinate | An ordered pair of numbers defining the position of a point written in the form (x,y) |
| degree | A unit of measurement for angles/turns |
| diameter | Any line joining two points on a circle and passing through its centre |
| equation | A mathematical statement showing that two expressions have equal value e.g. 7 – 2 = 4 + 1 |
| equilateral | Having sides of equal length |
| expression | A mathematical form expressed symbolically e.g. 7 + 3, a2 + b2 |
| factor | A number that will divide exactly into
a given number e.g. 1, 2, 3, 4, 6 and 12 are all factors of 12 |
| function | An algebraic rule linking two variables |
| gradient | The steepness of a slope |
| index | The ‘power’ or number of times
a number multiplies by itself e.g. 43 = 4 x 4 x 4 |
| integer | Any positive or negative whole number and zero |
| isosceles | A triangle in which two sides have the same length and consequently two angles are equal |
| obtuse | An angle between 90° and 180° |
| perpendicular | A line or plane that is at right angles to another line or plane |
| prime | A whole number greater than 1, which has exactly two factors |
| product | The result of multiplying one number by another |
| quadrilateral | A polygon with four sides |
| radius | The distance from the centre to any point on the circle |
| reflex | An angle between 180° and 360° |
| root | The number that multiplies by itself a
given number of times to give a particular answer e.g. the square root of 144 = 12 because 122 = 144 |
| scale | a) A degree of enlargement b) A measuring device usually consisting of points on a line with equal intervals |
| square | a) A shape with four equal sides and four
right angles b) To multiply a number by itself |
| substitute | To replace a variable in a function by a given value |
| sum | The result of one or more additions |
| translate | To move (slide) a shape so that each point moves the same distance and direction |