After a secondary numeracy INSET course the following information was bought together as a starting point for further development. It should be noted that the information here was collected by mathematics teachers on the course and thus should only be considered as a first draft of the mathematical ideas in other National Curriculum subjects. The material has not been looked at by other subject specialists so should only be considered a starting point for further discussions.
I have not taken the time to format the text to give it a "finished" look because in my experience this encourages stray copies of the material to be snapped up by others and used as a definitive document.
MATHEMATICS IN THE HISTORY NATIONAL CURRICULUM
Key Stage 3
Pupils should be taught:
1. Chronology
a to place the events, people and changes in the periods studied within a chronological framework;
b to use dates and conventions that describe historical periods and the passing of time.
4.Historical enquiry
a to investigate independently aspects of the periods studied, using a range of sources of information, including documents and printed sources
b to ask and answer significant questions, to evaluate sources in their historical context, identify sources for an investigation, collect and record information relevant to a topic and reach conclusions.
5. Organisation and communication
a to recall, select and organise historical information, including dates and terms;
Pattern, symmetry - rotation, line, tiling, tessellations.
Shape, spatial awareness
Perspective
Manipulation of true through colour etc ... (art techs)
Enlargement
Views
Design skills - modelling
- measurement
- scale
- lengths/units req
Materials - costing, time management
Logical thinking - ordering (flow charts)
Systems and controls - combination / perm
input / output
Design skills - tolerences +/-
5 mat + comp cut & shape
nets
Geography
KEY STAGE 3 PROGRAMME OF STUDY
GEOGRAPHICAL SKILLS
2. In investigating places and themes, pupils should be given opportunities to:
a. identify geographical questions and issues and establish an appropriate sequence of investigation;
b. identify the evidence required and collect, record and present it;
c. analyse and evaluate the evidence, draw conclusions and communicate findings.
3. Pupils should be taught to:
b. undertake fieldwork, selecting and using appropriate techniques and instruments to measure and record accurately, eg land use survey, data logging;
c. make maps and plans at a variety of scales, using symbols, keys and scales, eg an annotated sketch map showing key features drawn from an OS map;
d. use and interpret maps and plans at a variety of scales, including Ordnance Survey 1:25,000 and 1:50,000 maps, the work should include using six-figure grid references, following routes, identifying relief and landscape features, drawing cross-sections, and using maps in decision-making exercises;
e. make effective use of globes and atlases to find appropriate information, and to locate places studied, places that are in the news, and the points of reference specified on Maps D, E and F (pages 15-17);
f. select and use appropriate graphical techniques to present evidence on maps and diagrams, eg pie charts, choropleth maps;
g. select and use secondary sources of evidence - photographs (including vertical and oblique aerial photographs), satellite images and other sources, eg census data, visits to school by representatives of local interest groups - to inform their studies;
Thematic Studies
9. Weather and climate\In studying how and why weather and climate vary, pupils should be taught:
a. how weather and climate differ;
11. Populatio\\In studying population distribution and change, pupils should be taught:
a. about the global distribution of population;
12. Settlement\In investigating the characteristics of settlements and the impact of change, pupils should be taught:
a. the reasons for the location, growth and nature of individual settlements;
b. how the types and variety of goods and services provided in settlements of different sizes vary;
c. how changes in function of settlements occur and how these changes affect different groups of people, eg how a decline in village services affects car owners and non-car owners;
d. about types and patterns of urban land use, how conflicts can arise over the use of land, and how they can be addressed.
1. Games
Scoring systems specific to different games. Scale measurement, size of courts, pitches etc. Time duration of games.
Application of number - scoring systems +/-
2. Gymnastics
Rotation, symmetry, measurements, distance, height
3. Dance
Rotation, symmetry, number work ... division, subtraction, multiplication addition.
4. Athletic activities
Conversion if imperial - metric weights, distances etc
Time :- use of decimal place - 10th, 100th seconds
Angles, quadrants - shot, discuss, javelin, hammer
Heartbeat - pulse - calculations for fitness - ratios percentages
Taking data from performances, analysing :- ratios, split times, distances, percentages.
5. Outdoor
Weights - rope strain - load bearing
distances - m/km - yds miles etc
co-ordinates - mapping
bearings - direction
average - mean time, mode, median, bar charts graphs.
Collecting data and analysing
Nutrition :- weights, percentages, ratios, bar charts, graphs, frequency graphs
6. Swimming
Distance
Time
Speed
Average - mean, mode, median, bar charts, graphs
Capacity - lung - litres, cc
Science
Key Stage 3
4. Communication
b use SI units;
c present their ideas through the use of diagrams, graphs, tables and charts, using appropriate scientific and mathematical conventions.
Experimental and Investigative Science
1. f to decide how many observations or measurements need to be made and what range they should cover;
2. b to make observations and measurements to a degree of precision appropriate to the context;
c to make sufficient relevant observations and measurements for reliable evidence;
d to repeat measurements and observations when appropriate;
e to record evidence clearly and appropriately as they carry out the work.
Pupils should be taught:
3. Analysing evidence and drawing conclusions
a to present qualitative and quantitative data clearly;
b to use graphs appropriate to the results obtained;
c to use lines of best fit where appropriate;
conclusions
d to identify trends or patterns in results;
e to use results to draw conclusions;
Life Processes and Living Things
5. c how food chains may be quantified using pyramids of numbers;
Materials and their Properties
1. Classifying materials
solids, liquids and gases
a to recognise differences between solids, liquids and gases, in terms of properties, eg density, compressibility, ease of flow, maintenance of shape and volume;
b a simple model of solids, liquids and gases, in terms of the arrangement and movement of particles;
g that compounds have a definite composition, and to represent compounds by formulae;
2. b that solutes have different solubilities in different solvents and at different temperatures;
c that different materials change state at different temperatures;
Pupils should be taught:
e how materials expand and contract with changes in temperature, and that the forces that result are sometimes considerable;
g that the rock cycle involves sedimentary, metamorphic and igneous processes that take place over different timescales;
h that rocks are classified as sedimentary, metamorphic or igneous on the basis of their processes of formation, and that these processes affect their texture and the minerals they contain;
chemical reactions
i that when chemical reactions take place, mass is conserved;
c how to measure current in series and parallel circuits;
a how to determine the speed of a moving object;
b the quantitative relationship between speed, distance and time;
c that unbalanced forces change the speed and/or direction of moving objects;
h the quantitative relationship between the force acting normally per unit area on a surface and the pressure on that surface;
3. Light and sound
c that light travels much faster than sound;
Key Stage 4
(Double)
4. Communication
a use a wide range of scientific and technical vocabulary and conventions, and to use diagrams, graphs, tables and charts to communicate information and to develop an argument;
b use SI units;
c present scientific information in symbolic or mathematical form.
1. f to consider the number and range of observations or measurements to be made;
2. b to make observations and measurements to a degree of precision appropriate to the context;
c to make sufficient relevant observations and measurements for reliable evidence;
d to consider uncertainties in measurements and observations;
e to repeat measurements and observations when appropriate;
f to record evidence clearly and appropriately as they carry out the work.
Pupils should be taught:
3. Analysing evidence and drawing conclusions
a to present qualitative and quantitative data clearly;
b to present data as graphs, using lines of best fit where appropriate;
c to identify trends or patterns in results;
d to use graphs to identify relationships between variables;
e to present numerical results to an appropriate degree of accuracy;
4. Evaluating evidence
a to consider whether the evidence collected is sufficient to enable firm conclusions to be drawn;
b to consider reasons for anomalous results and to reject such results where appropriate;
c to consider the reliability of results in terms of the uncertainty of measurements and observations;
d to propose improvements to the methods that have been used;
e to propose further investigation to test their conclusions.
5. c how food chains may be described quantitatively using pyramids of numbers and pyramids of biomass;
3. a that the periodic table shows all elements, arranged in order of ascending atomic number;
l that there is great variation in the rates at which different reactions take place;
m how the rates of reactions can be altered by varying temperature or concentration, or by changing the surface area of a solid reactant, or by adding a catalyst;
that reactions can occur when particles collide;
1. Electricity and magnetism
energy and potentialdifference in circuits
a how to measure current in series and parallel circuits;
e how to make simple measurements of voltage;
f the quantitative relationship between resistance, voltage and current;
h that voltage is the energy transferred per unit charge;
i the quantitative relationship between power, voltage and current;
m how measurements of energy transferred are used to calculate the costs of using common domestic appliances;
electric charge
about common electrostatic phenomena, in terms of the movement of electrons;
p the quantitative relationship between steady current, charge and time;
v the quantitative relationship between the voltages across the coils in a transformer and the numbers of turns in them;
w how electricity is generated and transmitted.
2. Forces and motion
force and acceleration
a how distance, time and speed can be determined and represented graphically;
c the difference between speed and velocity;
d about acceleration as change in velocity per unit time;
f the quantitative relationship between force, mass and acceleration;
l how the volume of a fixed mass of gas at constant temperature is related to pressure.
3. Waves
characteristics of waves
e the meaning of frequency, wavelength and amplitude of a wave;
Pupils should be taught:
f the quantitative relationship between the speed, frequency and wavelength of a wave;
4. Communication
a use a wide range of scientific and technical vocabulary and conventions, and to use diagrams, graphs, tables and charts to communicate information and to develop an argument;
b use SI units;
c present scientific information in symbolic or mathematical form.
2. b to make observations and measurements to a degree of precision appropriate to the context;
c to make sufficient relevant observations and measurements for reliable evidence;
d to consider uncertainties in measurements and observations;
e to repeat measurements and observations when appropriate;
f to record evidence clearly and appropriately as they carry out the work.
Pupils should be taught:
3. Analysing evidence and drawing conclusions
a to present qualitative and quantitative data clearly;
b to present data as graphs, using lines of best fit where appropriate;
c to identify trends or patterns in results;
d to use graphs to identify relationships between variables;
e to present numerical results to an appropriate degree of accuracy;
p that changes of temperature often accompany reactions;
2. Forces and motion
force and non-uniform motion
a how distance, time and speed can be determined and represented graphically;
5. Energy resources and energy transfer
a that differences in temperature can lead to transfer of energy;
