Understand and use statistical problem solving process/handling data cycle
Design an experiment or survey
Design data-collection sheets distinguishing between different types of data
Collect data using various methods, including observation, controlled experiments, data logging, questionnaires and surveys
Extract data from printed tables and lists
Design and use two-way tables for discrete and grouped data
Look at data to find patterns and exceptions

An understanding of why data needs to be collected
Experience of simple tally charts
Experience of inequality notation and signs

By the end of the module the student should be able to:
• Design a suitable question for a questionnaire (1.3)
• Understand the difference between: primary and secondary data; discrete and continuous data (1.1)
• Design suitable data sheets for surveys and experiments (1.2)
• Understand about bias in sampling (1.4)
• Choose and justify an appropriate sampling scheme, including random and systematic sampling (1.4)
• Deal with practical problems in data collection, such as non-response, missing or anomalous data (in context 2.2, 4.4)
• Gather information from two-way tables

Carry out a statistical investigation of their own including, eg designing an appropriate means of gathering the data
Investigate into other sampling processes, such as cluster and quota sampling

Students may need reminding about the correct use of tallies
Emphasise the differences between primary and secondary data
Use Mayfield data as an example of secondary data
Discuss sample size and mention that a census is the whole population. In the UK, the census is every year that ends in ‘1’, so the next census is in 2011
If students are collecting data as a group, they should all use the same procedure
Emphasise that continuous data is data that is measured, eg temperature
Mayfield High data can be used to collect samples and can be used to make comparisons

1-2

Displaying data, charts and graphs

Draw and produce a wide range of graphs and diagrams
Interpret a wide range of graphs and diagrams and drawing conclusions

An understanding of the different types of data: continuous; discrete; categorical
Experience of inequality notation and symbol
Some basic fraction work for pie charts (link with Unit 2)
Use a protractor to measure and draw angles (link with Unit 2)

By the end of the module the student should be able to:
• Represent data as:
- Pictograms (2.1)
- Pie charts (for categorical data) (2.2)
- Bar charts and histograms (equal class intervals) (2.3, 2.4)
- Frequency polygons (2.6)
- Stem and leaf diagrams (3.6)
• Choose an appropriate way to display discrete, continuous and categorical data (2.1 - 2.6)
• Understand the difference between a bar chart and a histogram (2.3, 2.5)
• Compare distributions shown in charts and graphs (2.3 - 2.6)

Carry out a statistical investigation of their own and use an appropriate means of displaying the results
Use a spreadsheet to draw different types of graphs
Collect examples of charts and graphs in the media which have been misused, and discuss the implications

Clearly label all axes on graphs and use a ruler to draw straight lines
Stem and leaf diagrams must have a key
Show how to find the median and mode from a stem & leaf diagram
Angles for pie charts should be correct to within 2°
Make comparisons between previously collected data, eg Mayfield boys vs girls or Yr 7 vs Yr 8
Encourage students to work in groups and present their charts, eg display work in classroom/corridors
Use Excel graph wizard
Use Functional Elements questions, eg comparing rainfall charts, distribution of ages in cinemas etc

1-3

Averages

Calculate the mean for large data sets
Estimate the mean for large data sets from a table (with grouped data)
Find the (mode) median, mean and range of small data sets with discrete data
Compare distributions and make inferences
Compare distributions and make inferences, using the shapes of distributions and measures of average and spread

Knowledge of finding the mean, median, mode & range for small data sets
Stem and leaf diagram to find mode and median
Ability to order and find the mid-point of two numbers

By the end of the module the student should be able to:
• Find the mean of data given in an ungrouped frequency distribution (3.2)
• Find the mode, median and range for a small set of data (3.2, 3.5)
• Find the modal class for grouped data (3.8)
• Find the median by using , where n is the number of data (3.2)
• Find the mean from a frequency table by using ‘fx’ (extend table to extra columns) (3.7)
• Use the midpoint of equal class intervals to find an estimate for the mean of grouped data (3.9)
• Know the advantages/disadvantages of using the different measure of average (3.4)
• Compare data sets by using statistics like averages, range, and frequency polygons (3.5, 3.6)

Use statistical functions on calculators and spreadsheets
Use statistical software to calculate the mean for grouped data sets
Discuss occasions when one average is more appropriate, and the limitations of each average
Show how the mean can be affected by extreme values

Collect data from the class – children per family etc. Extend to different classes, Year groups or use secondary data
from the internet, eg ‘boys are taller on average but there is a much greater spread in heights’ (use data collected from earlier work done or use Mayfield High data)
Previous coursework tasks provide a rich source of data to work with, eg Second-Hand Car Sales
Students tend to select modal class, but identify it by the frequency rather than the class itself
Explain that the median of grouped data is not necessarily from the middle class interval and will almost certainly not be the one in the centre for an examination
Show a quick method for finding the middle value (for either the median of an even number of values or the midpoint for grouped data) by adding the two values and dividing the total by two

1-4

Scatter graphs and correlation

Draw a scatter graph
Interpret a scatter graph
Recognise correlation is a measure of the strength of association between two variables
Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’
Distinguish between positive, negative and zero correlation and using a line of best fit
Draw a line of best fit by eye, and understand what this represents

Plotting coordinates
An understanding of the concept of a variable
Recognition that a change in one variable can affect another

By the end of the module the student should be able to:
• Draw and produce a scatter graph (4.4)
• Appreciate that correlation is a measure of the strength of association between two variables (4.5)
• Distinguish between positive, negative and zero correlation using a line of best fit (4.5)
• Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’ (4.5)
• Draw a line of best fit by eye and understand what it represents (4.6)
• Use a line of best fit to interpolate/ extrapolate (4.7)

Vary the axes required on a scatter graph to suit the ability of the class
Carry out a statistical investigation of their own including; designing an appropriate means of gathering the data, and an appropriate means of displaying the results
Use a spreadsheet, or other software, to produce scatter diagrams/lines of best fit
Investigate how the line of best fit is affected (visually) by the choice of scales on the axes

Mention that the line of best fit should pass through the coordinate representing the mean of the data
Clearly label all axes on graphs and use a ruler to draw straight lines
Warn students that the line of best fit does not necessarily go through the origin or ‘corner’ point of the graph

1-5

Probability

Use and understand the vocabulary of probability and probability scale
Listing all outcomes for single events, and for two successive events, in a systematic way
Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1
Compare experimental data and theoretical probabilities
Understand that if they repeat an experiment they may, and usually will, get different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics

Understand that a probability is a number between 0 and 1
Know how to add simple fractions and decimals (link with Unit 2 topics)
Recognise the language of statistics, eg words such as likely, certainty, impossible, etc

By the end of the module the student should be able to:
• Mark events and/or probabilities on a probability scale of 0 to 1 and/or express probability in words (5.1)
• List all the outcomes from mutually exclusive events, eg from two coins, and sample space diagrams (5.5)
• Write down the probability associated with equally likely events, eg the probability of drawing an ace from a pack of cards (5.2)
• Know that if the probability of an event occurring is p than the probability of it not occurring is (1 – p) (5.3)
• Find the missing probability from a list or table (decimal or fractional values) (5.3)
• Find estimates of probabilities by considering relative frequency in experimental results (including two-way tables) (5.6)
• Know that the more an experiment is repeated the better the estimate of probability (5.6)
• Add simple probabilities (5.3)
• Estimate the number of times an event will occur, given the probability and the number of trials (5.8)

Experiments with dice and spinners or ICT simulations show how a larger number of trials leads to more accuracy
Show sample space for outcomes of throwing 2 dice. Stress that there are 36 outcomes (students will initially guess it’s 12 outcomes for 2 dice)
Show that P(Double 6) can be found by seeing that there is only 1 outcome from 36 in the
sample space or by P(6) P(6) = =

Students should express probabilities as fractions, percentages or decimals
Probabilities written as fractions do not have to be cancelled to the simplest form

1-6

Integers

Order integers
Approximate to specified or appropriate degrees of accuracy
Add, subtract, multiply and divide any integer
Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations
Use calculators effectively and efficiently
Use standard column procedures for multiplication of integers
Multiply or divide any number by powers of 10

The ability to order numbers
Appreciation of place value
Experience of the four operations using whole numbers
Knowledge of integer complements to 10
Knowledge of multiplication facts to 10 ´ 10
Knowledge of strategies for multiplying and dividing whole numbers by 10

By the end of the module the student should be able to:
• Understand and order integers (1.1)
• Add, subtract, multiply and divide integers (3.1)
• Understand simple instances of BIDMAS, eg work out 12 ´ 5 – 24 ¸ 8 (3.1)
• Round whole numbers to the nearest, 10, 100, 1000, … (1.5)
• Multiply and divide whole numbers by a given multiple of 10 (1.1)
• Check their calculations by rounding, eg 29 ´ 31 » 30 ´ 30 (3.10)

Check answers by reverse calculation, eg if 9 ´ 23 = 207 then 207 ¸ 9 = 23
Estimating answers to calculations involving the four rules
Directed number work with two or more operations, or with decimals
Encourage effective use of a calculator

Present all working clearly
Show what is entered into your calculator, not just the answer

1-7

Decimals

Use decimal notation and recognise that each terminating decimal is a fraction
Order rational numbers
Approximate to a given number of significant figures (and decimal places)
Estimate answers to calculations

Integers
The concepts of a fraction and a decimal

By the end of the module the student should be able to:
• Put digits in the correct place in a decimal number (1.1)
• Write decimals in ascending order of size (5.5)
• Approximate decimals to a given number of decimal places or significant figures (3.10, further
content in Unit

Use decimals in real-life problems eg Best Buys and other Functional Elements
Use Functional Elements examples such as entry into theme parks, costs of holidays and cost of sharing a meal
Money calculations that require rounding answers to the nearest penny
Multiply and divide decimals by decimals (more than 2 decimal place)
Round answers to appropriate degrees of accuracy to suit the context of the question

Advise students not to round decimals used in calculations until the final answer is to be declared
Link decimals to statistics and probability, eg the mean should not be rounded, all events’ probabilities add up to 1
Also link decimals to converting units and compound measures (Unit 1 and 2)

1-8

Fractions

Understand equivalent fractions; simplifying a fraction by cancelling all common factors
Order fractions by rewriting them with a common denominator

Multiplication facts
Ability to find common factors
A basic understanding of fractions as being ‘parts of a whole unit’
Use of a calculator with fractions

By the end of the module the student should be able to:
• Visualise a fraction diagrammatically (5.2, further content
in Unit 2)
• Understand a fraction as part of a whole (5.1)
• Recognise and write fractions in everyday situations (5.1)
• Write a fraction in its simplest form and recognise equivalent
fractions (5.1, 5.2)
• Compare the sizes of fractions using a common denominator (revision of prior
knowledge)
• Write an improper fraction as a mixed fraction (revision of prior
knowledge)
• Recognise common recurring decimals can be written as exact (revision of prior
fractions eg knowledge)

Careful differentiation is essential for this topic and is dependent upon the student’s ability
Relating simple fractions to percentages and vice versa
Use a calculator to change fractions into decimals and look for patterns
Work with improper fractions and mixed numbers
The four rules of number applied to fractions with a calculator
Solve word problems involving fractions and in real-life problems

Understanding of equivalent fractions is key to being able to tackle the content that comes later
Constant revision of this topic is needed
Students should learn how to identify and use each the fraction button on their calculators
Use of fractions for calculations involving compound units (Unit 1 and 2)
Look for Functional Maths questions and examples using fractions,
eg off the list price when comparing prices and discounts

1-9

Percentages

Understand that ‘percentage’ means ‘number of parts per 100’
Use percentage as the operator 'so many hundredths of'
Use percentages (and fractions) in real-life situations
Solve percentage problems, including increase and decrease

Four operations of number
The concepts of a fraction and a decimal
Awareness that percentages are used in everyday life

By the end of the module the student should be able to:
• Understand that a percentage is a fraction in hundredths (5.1)
• Write a percentage as a decimal; or as a fraction in its simplest terms (5.1)
• Write one number as a percentage of another number (5.4)
• Calculate the percentage (or fraction) of a given amount (5.4)
• Find a percentage increase/decrease of an amount (5.4)
• Use a multiplier to increase by a given percent, eg 1.10 ´ 64 increases 64 by 10%

Fractional percentages of amounts, eg 17.5% (VAT)
Percentages which convert to recurring decimals, eg 33 %, and situations which lead to percentages of more than 100%
Problems which lead to the necessity of rounding to the nearest penny, eg Functional Elements contexts

Amounts of money should always be rounded to the nearest penny where necessary

1-10

Ratio and scale

Use ratio notation, including reduction to its simplest form and it various links to fraction notation
Divide a quantity in a given ratio
Solve word problems about ratio, including using informal strategies and the unitary method of solution

Fractions and Decimals

By the end of the module the student should be able to:
• Appreciate that, eg the ratio 1:2 represents and of a quantity (5.9)
• Divide quantities in a given ratio, eg divide £20 in the ratio 2:3 (5.9)
• Solve word problems involving ratios, eg Find the cost of 8 pencils given that 6 pencils cost 78p (5.9)

Currency calculations using currency exchange rates
Use harder problems involving multi-stage calculations
Relate ratios to Functional Elements examples, eg investigate the proportions of the different metals in alloys and the new amounts of ingredients needed for a recipe with different numbers of guests

Students often find three-part ratios difficult
Link ratios given in different units to metric and imperial units (Unit 2)

1-11

Introduction to algebra

Distinguish the different roles played by letter symbols in algebra
Distinguish the meaning between the words ‘equation’, ‘formula’, and ‘expression’

Experience of using a letter to represent a number
Word formulae or rules to describe everyday situations, eg time to cook a nut roast linked to the weight of nut roast

By the end of the module the student should be able to:
• Distinguish the different roles played by letter symbols in algebra (3.3)
• Understand the meaning between the words ‘equation’, ‘formula’, and expression (3.3)

Extend the above ideas to the ‘equation’ of the straight line, y = mx + c
Look at word equations written in symbolic form, eg F = 2C+30 to roughly convert temperature and compare with F = + 32

There are plenty of old exam papers with matching tables testing knowledge of the ‘Vocabulary of Algebra’ (See Emporium website)

1-12

Straight line graphs

Construct linear functions from real-life problems and plotting their corresponding graphs
Discuss and interpret graphs modelling real-life situations
Use the conventions for coordinates in the plane
Plot points in all four quadrants
Recognise (when values are given for m and c) that equations of the form
y = mx + c correspond to straight-line graphs in the coordinate plane

Experience at plotting points in all quadrants
Linear Sequences and basic number patterns

By the end of the module the student should be able to:
• Draw linear graphs from tabulated data, including real-world examples (4.1)
• Interpret linear graphs, including conversion graphs and distance-time graphs (4.1)
• Draw and interpret graphs in the form y = mx + c (when values for m and c are given) (4.2)
• Understand that lines are parallel when they have the same value of m (4.2)
• Find the gradient and intercept of a straight line graph (4.2)

Plot graphs of the form y = mx + c where students have to generate their own tables and set out their own axes
Use a spreadsheet to generate straight-line graphs, posing questions about the gradient of lines
Use a graphical calculator or graphical ICT package to draw straight-line graphs
Link to finding the actual equation of the line of best fit (not formally required for Foundation Tier)
Possibly extend to shapes of y = x2 (Unit 3)

Clear presentation with axes labelled correctly is vital
Recognise linear graphs and hence when data may be incorrect
Link to graphs and relationships in other subject areas, ie science, geography etc
Interpret straight line graphs from Functional Elements questions
– Ready reckoner graphs
– Conversion graphs
– Fuel bills
– Fixed charge (standing charge) and cost per unit
Also link conversion graphs to converting metric & imperial units and equivalents (Unit 2)

1-13

Lines and angles

Draw and measure lines and angles
Recall and use properties of angles at a point

An understanding of angle as a measure of turning
The ability to use a ruler and protractor

By the end of this module the student should be able to:
• Distinguish between acute, obtuse, reflex and right angles (2.2)
• Estimate the size of an angle in degrees (revision of
prior knowledge)
• Measure and draw angle to the nearest degree (2.2)
• Measure and draw line to the nearest mm (2.3)
• Use angle properties ‘at a point’ to calculate unknown angles (2.2)

Extend to other angle facts in triangles, parallel lines and/or quadrilaterals (preparation for Unit 2)

Make sure that all pencils are sharp and drawings are neat and accurate
Angles should be within correct to within 2°, lengths correct to the nearest mm
Apply skills to constructing pie charts

1-14

Units and reading scales

Make sensible estimates of a range of measures
Read analogue and digital clocks
Read measurements on different types of scales
Read timetables and calculating time intervals
Convert from one metric unit to another

An awareness of the metric & imperial system of measures
Strategies for multiplying and dividing by 10 (for converting metric units)
Knowledge of the conversion facts for metric lengths, mass and capacity
Knowledge of the conversion facts between seconds, minutes and hours

By the end of this module the student should be able to:
• Make estimates of: length; volume and capacity; weights (1.2)
• Make approximate conversions between metric and imperial units (revision of
prior knowledge)
• Decide on the appropriate units to use in real life problems
• Read measurements from instruments: scales; analogue and digital clocks and thermometers, etc (1.2)
• Recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction
• Convert from one metric unit to another metric unit (1.2)

This could be made a practical activity by collecting assorted everyday items for weighing and measuring and to check estimates of their lengths, weights and volumes
Link with compound units such as speed for travel graphs (m/s or km/h or mph) and Best Buys (g/penny)

Measurement is essentially a practical activity
Use a range of everyday objects to make the lesson more realistic
Use Functional Elements as a rich source of practice questions for this topic area
Students are well advised to regularly bring their calculators to lessons and to become familiar with the various functions of their calculators
They should be confident with entering a range of calculations including those involving time and money
They should realise that 2.5 hrs is 2 hours 30 minutes etc

## Past Papers

## Table of Contents

Unit 1F Practice Paper

## Topic Checklist

A list of Unit 1 topics:## Video Solutions

## Unit 1F Mock Paper:

Question 1 - PictogramsQuestion 2 - Reading Information

Question 3 - Reading Information

Question 4 - Probability

Question 5 - Fractions

Question 6 - Probability

Question 7 - Averages Range

Question 8 - Time

Question 9 - Frequency Diagrams

Question 10 - Two Way Tables

Question 11 - Pie Charts

Question 12 - Conversion

Question 13 - Scatter Graphs

Question 14 - Questionnaires

Question 15 - Probability

Question 16 - Conversion Money

Question 17 - Mean from a Table

## Misc Videos

## Detailed Content Breakdown

A detailed breakdown:Design an experiment or survey

Design data-collection sheets distinguishing between different types of data

Collect data using various methods, including observation, controlled experiments, data logging, questionnaires and surveys

Extract data from printed tables and lists

Design and use two-way tables for discrete and grouped data

Look at data to find patterns and exceptions

Experience of simple tally charts

Experience of inequality notation and signs

• Design a suitable question for a questionnaire (1.3)

• Understand the difference between: primary and secondary data; discrete and continuous data (1.1)

• Design suitable data sheets for surveys and experiments (1.2)

• Understand about bias in sampling (1.4)

• Choose and justify an appropriate sampling scheme, including random and systematic sampling (1.4)

• Deal with practical problems in data collection, such as non-response, missing or anomalous data (in context 2.2, 4.4)

• Gather information from two-way tables

Investigate into other sampling processes, such as cluster and quota sampling

Emphasise the differences between primary and secondary data

Use Mayfield data as an example of secondary data

Discuss sample size and mention that a census is the whole population. In the UK, the census is every year that ends in ‘1’, so the next census is in 2011

If students are collecting data as a group, they should all use the same procedure

Emphasise that continuous data is data that is measured, eg temperature

Mayfield High data can be used to collect samples and can be used to make comparisons

Interpret a wide range of graphs and diagrams and drawing conclusions

Experience of inequality notation and symbol

Some basic fraction work for pie charts (link with Unit 2)

Use a protractor to measure and draw angles (link with Unit 2)

• Represent data as:

- Pictograms (2.1)

- Pie charts (for categorical data) (2.2)

- Bar charts and histograms (equal class intervals) (2.3, 2.4)

- Frequency polygons (2.6)

- Stem and leaf diagrams (3.6)

• Choose an appropriate way to display discrete, continuous and categorical data (2.1 - 2.6)

• Understand the difference between a bar chart and a histogram (2.3, 2.5)

• Compare distributions shown in charts and graphs (2.3 - 2.6)

Use a spreadsheet to draw different types of graphs

Collect examples of charts and graphs in the media which have been misused, and discuss the implications

Stem and leaf diagrams must have a key

Show how to find the median and mode from a stem & leaf diagram

Angles for pie charts should be correct to within 2°

Make comparisons between previously collected data, eg Mayfield boys vs girls or Yr 7 vs Yr 8

Encourage students to work in groups and present their charts, eg display work in classroom/corridors

Use Excel graph wizard

Use Functional Elements questions, eg comparing rainfall charts, distribution of ages in cinemas etc

Estimate the mean for large data sets from a table (with grouped data)

Find the (mode) median, mean and range of small data sets with discrete data

Compare distributions and make inferences

Compare distributions and make inferences, using the shapes of distributions and measures of average and spread

Stem and leaf diagram to find mode and median

Ability to order and find the mid-point of two numbers

• Find the mean of data given in an ungrouped frequency distribution (3.2)

• Find the mode, median and range for a small set of data (3.2, 3.5)

• Find the modal class for grouped data (3.8)

• Find the median by using , where n is the number of data (3.2)

• Find the mean from a frequency table by using ‘fx’ (extend table to extra columns) (3.7)

• Use the midpoint of equal class intervals to find an estimate for the mean of grouped data (3.9)

• Know the advantages/disadvantages of using the different measure of average (3.4)

• Compare data sets by using statistics like averages, range, and frequency polygons (3.5, 3.6)

Use statistical software to calculate the mean for grouped data sets

Discuss occasions when one average is more appropriate, and the limitations of each average

Show how the mean can be affected by extreme values

from the internet, eg ‘boys are taller on average but there is a much greater spread in heights’ (use data collected from earlier work done or use Mayfield High data)

Previous coursework tasks provide a rich source of data to work with, eg Second-Hand Car Sales

Students tend to select modal class, but identify it by the frequency rather than the class itself

Explain that the median of grouped data is not necessarily from the middle class interval and will almost certainly not be the one in the centre for an examination

Show a quick method for finding the middle value (for either the median of an even number of values or the midpoint for grouped data) by adding the two values and dividing the total by two

Interpret a scatter graph

Recognise correlation is a measure of the strength of association between two variables

Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’

Distinguish between positive, negative and zero correlation and using a line of best fit

Draw a line of best fit by eye, and understand what this represents

An understanding of the concept of a variable

Recognition that a change in one variable can affect another

• Draw and produce a scatter graph (4.4)

• Appreciate that correlation is a measure of the strength of association between two variables (4.5)

• Distinguish between positive, negative and zero correlation using a line of best fit (4.5)

• Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’ (4.5)

• Draw a line of best fit by eye and understand what it represents (4.6)

• Use a line of best fit to interpolate/ extrapolate (4.7)

Carry out a statistical investigation of their own including; designing an appropriate means of gathering the data, and an appropriate means of displaying the results

Use a spreadsheet, or other software, to produce scatter diagrams/lines of best fit

Investigate how the line of best fit is affected (visually) by the choice of scales on the axes

Clearly label all axes on graphs and use a ruler to draw straight lines

Warn students that the line of best fit does not necessarily go through the origin or ‘corner’ point of the graph

Listing all outcomes for single events, and for two successive events, in a systematic way

Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1

Compare experimental data and theoretical probabilities

Understand that if they repeat an experiment they may, and usually will, get different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics

Know how to add simple fractions and decimals (link with Unit 2 topics)

Recognise the language of statistics, eg words such as likely, certainty, impossible, etc

• Mark events and/or probabilities on a probability scale of 0 to 1 and/or express probability in words (5.1)

• List all the outcomes from mutually exclusive events, eg from two coins, and sample space diagrams (5.5)

• Write down the probability associated with equally likely events, eg the probability of drawing an ace from a pack of cards (5.2)

• Know that if the probability of an event occurring is p than the probability of it not occurring is (1 – p) (5.3)

• Find the missing probability from a list or table (decimal or fractional values) (5.3)

• Find estimates of probabilities by considering relative frequency in experimental results (including two-way tables) (5.6)

• Know that the more an experiment is repeated the better the estimate of probability (5.6)

• Add simple probabilities (5.3)

• Estimate the number of times an event will occur, given the probability and the number of trials (5.8)

Show sample space for outcomes of throwing 2 dice. Stress that there are 36 outcomes (students will initially guess it’s 12 outcomes for 2 dice)

Show that P(Double 6) can be found by seeing that there is only 1 outcome from 36 in the

sample space or by P(6) P(6) = =

Probabilities written as fractions do not have to be cancelled to the simplest form

Approximate to specified or appropriate degrees of accuracy

Add, subtract, multiply and divide any integer

Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations

Use calculators effectively and efficiently

Use standard column procedures for multiplication of integers

Multiply or divide any number by powers of 10

Appreciation of place value

Experience of the four operations using whole numbers

Knowledge of integer complements to 10

Knowledge of multiplication facts to 10 ´ 10

Knowledge of strategies for multiplying and dividing whole numbers by 10

• Understand and order integers (1.1)

• Add, subtract, multiply and divide integers (3.1)

• Understand simple instances of BIDMAS, eg work out 12 ´ 5 – 24 ¸ 8 (3.1)

• Round whole numbers to the nearest, 10, 100, 1000, … (1.5)

• Multiply and divide whole numbers by a given multiple of 10 (1.1)

• Check their calculations by rounding, eg 29 ´ 31 » 30 ´ 30 (3.10)

Estimating answers to calculations involving the four rules

Directed number work with two or more operations, or with decimals

Encourage effective use of a calculator

Show what is entered into your calculator, not just the answer

Order rational numbers

Approximate to a given number of significant figures (and decimal places)

Estimate answers to calculations

The concepts of a fraction and a decimal

• Put digits in the correct place in a decimal number (1.1)

• Write decimals in ascending order of size (5.5)

• Approximate decimals to a given number of decimal places or significant figures (3.10, further

content in Unit

Use Functional Elements examples such as entry into theme parks, costs of holidays and cost of sharing a meal

Money calculations that require rounding answers to the nearest penny

Multiply and divide decimals by decimals (more than 2 decimal place)

Round answers to appropriate degrees of accuracy to suit the context of the question

Link decimals to statistics and probability, eg the mean should not be rounded, all events’ probabilities add up to 1

Also link decimals to converting units and compound measures (Unit 1 and 2)

Order fractions by rewriting them with a common denominator

Ability to find common factors

A basic understanding of fractions as being ‘parts of a whole unit’

Use of a calculator with fractions

• Visualise a fraction diagrammatically (5.2, further content

in Unit 2)

• Understand a fraction as part of a whole (5.1)

• Recognise and write fractions in everyday situations (5.1)

• Write a fraction in its simplest form and recognise equivalent

fractions (5.1, 5.2)

• Compare the sizes of fractions using a common denominator (revision of prior

knowledge)

• Write an improper fraction as a mixed fraction (revision of prior

knowledge)

• Recognise common recurring decimals can be written as exact (revision of prior

fractions eg knowledge)

Relating simple fractions to percentages and vice versa

Use a calculator to change fractions into decimals and look for patterns

Work with improper fractions and mixed numbers

The four rules of number applied to fractions with a calculator

Solve word problems involving fractions and in real-life problems

Constant revision of this topic is needed

Students should learn how to identify and use each the fraction button on their calculators

Use of fractions for calculations involving compound units (Unit 1 and 2)

Look for Functional Maths questions and examples using fractions,

eg off the list price when comparing prices and discounts

Use percentage as the operator 'so many hundredths of'

Use percentages (and fractions) in real-life situations

Solve percentage problems, including increase and decrease

The concepts of a fraction and a decimal

Awareness that percentages are used in everyday life

• Understand that a percentage is a fraction in hundredths (5.1)

• Write a percentage as a decimal; or as a fraction in its simplest terms (5.1)

• Write one number as a percentage of another number (5.4)

• Calculate the percentage (or fraction) of a given amount (5.4)

• Find a percentage increase/decrease of an amount (5.4)

• Use a multiplier to increase by a given percent, eg 1.10 ´ 64 increases 64 by 10%

Percentages which convert to recurring decimals, eg 33 %, and situations which lead to percentages of more than 100%

Problems which lead to the necessity of rounding to the nearest penny, eg Functional Elements contexts

Divide a quantity in a given ratio

Solve word problems about ratio, including using informal strategies and the unitary method of solution

• Appreciate that, eg the ratio 1:2 represents and of a quantity (5.9)

• Divide quantities in a given ratio, eg divide £20 in the ratio 2:3 (5.9)

• Solve word problems involving ratios, eg Find the cost of 8 pencils given that 6 pencils cost 78p (5.9)

Use harder problems involving multi-stage calculations

Relate ratios to Functional Elements examples, eg investigate the proportions of the different metals in alloys and the new amounts of ingredients needed for a recipe with different numbers of guests

Link ratios given in different units to metric and imperial units (Unit 2)

Distinguish the meaning between the words ‘equation’, ‘formula’, and ‘expression’

Word formulae or rules to describe everyday situations, eg time to cook a nut roast linked to the weight of nut roast

• Distinguish the different roles played by letter symbols in algebra (3.3)

• Understand the meaning between the words ‘equation’, ‘formula’, and expression (3.3)

Look at word equations written in symbolic form, eg F = 2C+30 to roughly convert temperature and compare with F = + 32

Discuss and interpret graphs modelling real-life situations

Use the conventions for coordinates in the plane

Plot points in all four quadrants

Recognise (when values are given for m and c) that equations of the form

y = mx + c correspond to straight-line graphs in the coordinate plane

Linear Sequences and basic number patterns

• Draw linear graphs from tabulated data, including real-world examples (4.1)

• Interpret linear graphs, including conversion graphs and distance-time graphs (4.1)

• Draw and interpret graphs in the form y = mx + c (when values for m and c are given) (4.2)

• Understand that lines are parallel when they have the same value of m (4.2)

• Find the gradient and intercept of a straight line graph (4.2)

Use a spreadsheet to generate straight-line graphs, posing questions about the gradient of lines

Use a graphical calculator or graphical ICT package to draw straight-line graphs

Link to finding the actual equation of the line of best fit (not formally required for Foundation Tier)

Possibly extend to shapes of y = x2 (Unit 3)

Recognise linear graphs and hence when data may be incorrect

Link to graphs and relationships in other subject areas, ie science, geography etc

Interpret straight line graphs from Functional Elements questions

– Ready reckoner graphs

– Conversion graphs

– Fuel bills

– Fixed charge (standing charge) and cost per unit

Also link conversion graphs to converting metric & imperial units and equivalents (Unit 2)

Recall and use properties of angles at a point

The ability to use a ruler and protractor

• Distinguish between acute, obtuse, reflex and right angles (2.2)

• Estimate the size of an angle in degrees (revision of

prior knowledge)

• Measure and draw angle to the nearest degree (2.2)

• Measure and draw line to the nearest mm (2.3)

• Use angle properties ‘at a point’ to calculate unknown angles (2.2)

Angles should be within correct to within 2°, lengths correct to the nearest mm

Apply skills to constructing pie charts

Read analogue and digital clocks

Read measurements on different types of scales

Read timetables and calculating time intervals

Convert from one metric unit to another

Strategies for multiplying and dividing by 10 (for converting metric units)

Knowledge of the conversion facts for metric lengths, mass and capacity

Knowledge of the conversion facts between seconds, minutes and hours

• Make estimates of: length; volume and capacity; weights (1.2)

• Make approximate conversions between metric and imperial units (revision of

prior knowledge)

• Decide on the appropriate units to use in real life problems

• Read measurements from instruments: scales; analogue and digital clocks and thermometers, etc (1.2)

• Recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction

• Convert from one metric unit to another metric unit (1.2)

Link with compound units such as speed for travel graphs (m/s or km/h or mph) and Best Buys (g/penny)

Use a range of everyday objects to make the lesson more realistic

Use Functional Elements as a rich source of practice questions for this topic area

Students are well advised to regularly bring their calculators to lessons and to become familiar with the various functions of their calculators

They should be confident with entering a range of calculations including those involving time and money

They should realise that 2.5 hrs is 2 hours 30 minutes etc