Unit+1+Foundation

=Past Papers= toc - FULL Video Solutions - - FULL Video Solutions - Unit 1F Practice Paper - FULL Video Solutions - - FULL Video Solutions - - FULL Video Solutions - - FULL Video Solutions -

=Topic Checklist= A list of Unit 1 topics:
 * ~ Unit ||~ Module number ||~ Title ||
 * 1 || 1-1 || Collecting data ||
 * 1 || 1-2 || Displaying data, charts and graphs ||
 * 1 || 1-3 || Averages ||
 * 1 || 1-4 || Scatter graphs and correlation ||
 * 1 || 1-5 || Probability ||
 * 1 || 1-6 || Integers ||
 * 1 || 1-7 || Decimals ||
 * 1 || 1-8 || Fractions ||
 * 1 || 1-9 || Percentages ||
 * 1 || 1-10 || Ratio and scale ||
 * 1 || 1-11 || Introduction to algebra ||
 * 1 || 1-12 || Straight line graphs ||
 * 1 || 1-13 || Lines and angles ||
 * 1 || 1-14 || Units and reading scales ||

=Video Solutions=

Unit 1F Mock Paper:
Question 1 - Pictograms media type="youtube" key="YS4i35hIP04" height="315" width="420" Question 2 - Reading Information media type="youtube" key="Erw7hx89yB0" height="315" width="420" Question 3 - Reading Information media type="youtube" key="9Jjd39xqAcY" height="315" width="420" Question 4 - Probability media type="youtube" key="vRA4YDDRM48" height="315" width="420" Question 5 - Fractions media type="youtube" key="jCj7jFy85r4" height="315" width="420" Question 6 - Probability media type="youtube" key="EK7xBt0VwG4" height="315" width="420" Question 7 - Averages Range media type="youtube" key="HbUj7fxhmxU" height="315" width="420" Question 8 - Time media type="youtube" key="fG2sQx_UCDI" height="315" width="420" Question 9 - Frequency Diagrams media type="youtube" key="lrx2hTiqQh8" height="315" width="420" Question 10 - Two Way Tables media type="youtube" key="ZJaHOIn6Mp8" height="315" width="420" Question 11 - Pie Charts media type="youtube" key="yJ8rmoA4WCo" height="315" width="420" Question 12 - Conversion media type="youtube" key="KSonniu2Oz0" height="315" width="420" Question 13 - Scatter Graphs media type="youtube" key="q9HfL8Qtqto" height="315" width="420" Question 14 - Questionnaires media type="youtube" key="0NEOQKzlev8" height="315" width="420" Question 15 - Probability media type="youtube" key="3pZL1LQa-ls" height="315" width="420" Question 16 - Conversion Money media type="youtube" key="rwDXNc88PFI" height="315" width="420" Question 17 - Mean from a Table media type="youtube" key="uXIxE9-nrRg" height="315" width="420"

Misc Videos
media type="youtube" key="s70vU9gm-s8" height="344" width="425" media type="youtube" key="EYUmx2gPc_A" height="315" width="420"

=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 || 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 || 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 || 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 || 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 || 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 || 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 || 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) || 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 || 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 || 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) || 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) || 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) || 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 || 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 ||
 * ~ MODULE ||~ CONTENTS ||~ PRIOR KNOWLEDGE ||~ OBJECTIVES ||~ DIFFERENTIATION & EXTENSION ||~ NOTES ||
 * 1-1 || Collecting data || Understand and use statistical problem solving process/handling data cycle
 * 1-2 || Displaying data, charts and graphs || Draw and produce a wide range of graphs and diagrams
 * 1-3 || Averages || Calculate the mean for large data sets
 * 1-4 || Scatter graphs and correlation || Draw a scatter graph
 * 1-5 || Probability || Use and understand the vocabulary of probability and probability scale
 * 1-6 || Integers || Order integers
 * 1-7 || Decimals || Use decimal notation and recognise that each terminating decimal is a fraction
 * 1-8 || Fractions || Understand equivalent fractions; simplifying a fraction by cancelling all common factors
 * 1-9 || Percentages || Understand that ‘percentage’ means ‘number of parts per 100’
 * 1-10 || Ratio and scale || Use ratio notation, including reduction to its simplest form and it various links to fraction notation
 * 1-11 || Introduction to algebra || Distinguish the different roles played by letter symbols in algebra
 * 1-12 || Straight line graphs || Construct linear functions from real-life problems and plotting their corresponding graphs
 * 1-13 || Lines and angles || Draw and measure lines and angles
 * 1-14 || Units and reading scales || Make sensible estimates of a range of measures