# Key ideas

The key words for each of the chapters in The Language of Mathematics in Science: A Guide for Teachers of 11-16 Science are listed below (note that some terms appear in more than one section). These are the terms that appear in the glossary. This is then followed by a list of the section titles.

### Chapter 1 Collecting data

Key words: quantitative data, qualitative data, quantity, value, unit, resolution, scale, significant figures, range, variable, continuous, discrete, categorical, integer, experiment, survey, independent variable, dependent variable, control variable, factor, time series, raw data, primary data, secondary data.

1.1 Measuring and counting

1.2 Measurement, resolution and significant figures

1.3 Characteristics of different types of data

1.4 Naming different types of data

1.5 Where do data come from?

### Chapter 2 Doing calculations and representing values

Key words: unit, quantity, compound measure, base unit, derived unit, variable, decimal, fraction, significant figures, round, integer, recurring decimal, decimal place, mean, arithmetic mean, index notation, index, power, exponent, square, cube, square root, cube root, reciprocal, unit prefix, standard form, standard index form, scientific notation, power of 10, order of magnitude, approximation, estimate.

2.1 Calculations and units

2.2 Fractions and decimals

2.3 Rounding and significant figures

2.4 Calculating means

2.5 Index notation and powers

2.6 Dealing with very large and very small values

2.7 Approximations and orders of magnitude

### Chapter 3 Choosing how to represent data

Key words: variable, unit, raw data, categorical, discrete, continuous, factor, frequency, frequency table, grouped data, two-way table, pie chart, bar chart, grouped bar chart, stacked bar chart, independent variable, dependent variable, data point, horizontal axis, vertical axis, line graph, gradient, time series, scatter graph.

3.1 Using tables to collect and present data

3.2 Using tables to process data

3.3 Presenting data visually

3.4 Charts showing a quantity categorised by one factor

3.5 Charts showing a quantity categorised by two factors

3.6 Line graphs and scatter graphs: two related quantities

3.7 Bar charts and line graphs

### Chapter 4 Drawing charts and graphs

Key words: line graph, bar chart, scatter graph, independent variable, dependent variable, time series, axis, horizontal axis, vertical axis, x-axis, y-axis, origin, range, scale, tick mark, tick mark label, axis label, unit, data point, coordinate, x-coordinate, y-coordinate.

4.1 The important features of a chart or a graph

4.2 Choosing the axes

4.3 Choosing the range of each axis

4.4 Ranges and scales

4.5 Choosing a good scale

4.6 Labels and units

4.7 Plotting points and finding values

4.8 Reading scales

### Chapter 5 Working with proportionality and ratio

Key words: proportional, directly proportional, line graph, origin, gradient, slope, horizontal axis, vertical axis, x-axis, y-axis, x-coordinate, y-coordinate, rate, constant, constant of proportionality, reciprocal, inverse, inversely proportional, ratio, percentage, scale, scale drawing, scale factor, linear dimension.

5.1 Meaning of proportional

5.2 Proportionality and visual representation

5.3 Interpretation of gradient

5.4 Proportionality and algebraic representation

5.5 Proportional relationships in science

5.6 Ratios

5.7 Proportional reasoning and ratios

5.8 Percentages

5.9 Scale drawings and images

### Chapter 6 Dealing with variability

Key words: variability, random error, true value, uncertainty, population, sample, distribution, histogram, batch, class interval, frequency, average, mean, arithmetic mean, median, mode, spread, range, quartile, interquartile range, box plot, outlier, anomaly, probability, independent events, combined events, risk.

6.1 Where does variability come from?

6.2 Variability and measurement uncertainty

6.3 Variability in a population of individuals

6.4 Displaying larger sets of values

6.5 How big is a typical value?

6.6 How much do the values vary?

6.7 Comparing shapes of distributions

6.8 Are there any unusual values?

6.9 Basic ideas in probability

6.10 Estimating risks

6.11 Interpreting reports about risk

### Chapter 7 Looking for relationships: line graphs

Key words: line graph, variable, linear, linear relationship, non-linear, gradient, origin, intercept, proportional, rate, line of best fit, interpolation, extrapolation, outlier.

7.1 Types of relationship and shapes of line graphs

7.2 Developing a descriptive language

7.3 Gradients and rates of change

7.4 Lines of best fit: linear relationships

7.5 Interpolation and extrapolation on a line graph

7.6 Origin and intercepts: the meaning of where a fitted line starts

7.7 When a straight line does not fit all the points

### Chapter 8 Looking for relationships: batches and scatter graphs

Key words: population, sample, random sample, batch, variability, stem-and-leaf diagram, histogram, box plot, median, quartile, range, interquartile range, outlier, percentile, scatter graph, variable, correlation, line of best fit.

8.1 Different kinds of relationship

8.2 Populations and samples

8.3 Analysing a batch of data

8.4 Dealing with more than one batch of data

8.5 Comparing batches of data

8.6 Judging whether a difference is significant

8.7 Relationships between variables: scatter graphs and correlation

8.8 Drawing a line of best fit on a scatter graph

### Chapter 9 Scientific models and mathematical equations

Key words: equation, algebraic equation, formula, expression, variable, constant, coefficient, brackets, order of operations, subject of a formula, proportional, directly proportional, constant of proportionality, linear relationship, linear equation, inversely proportional, exponential relationship, inverse square relationship, line graph, rate, intercept, gradient, tangent, area under the line (on a graph).

9.1 Equations, formulae and expressions

9.2 Variables, constants and coefficients

9.3 Operations and symbols

9.4 Calculations using formulae: order of operations

9.5 The real-world meaning of a formula

9.6 Rearranging formulae involving addition and subtraction

9.7 Rearranging formulae involving multiplication and division

9.8 Rearranging other formulae

9.9 Calculations without formulae

9.10 Use of ‘calculation triangles’

9.11 Mathematical equations and relationships in science

9.12 Graphs of quantities against time: gradients

9.13 Graphs of rates against time: area under the line

### Chapter 10 Mathematics and the real world

Key words: mass, weight, area, volume, square, cuboid, cube, scale drawing, scale factor, linear dimension, cross-sectional area, surface area, surface area : volume ratio, radius, diameter, circumference, scalar, vector, distance, displacement, speed, velocity, gradient, distance–time graph, displacement–time graph, speed–time graph, velocity–time graph, area under the line (on a graph).

10.1 Mass and weight

10.2 Length, area and volume

10.3 Scale factor, cross-sectional area and surface area

10.4 Circles and spheres

10.5 Scalars and vectors: distance and displacement

10.6 Movement of objects: speed and velocity

10.7 Gradients of lines on speed–time and velocity–time graphs

10.8 Area under the line on speed–time and velocity–time graphs