GCSE Mathematics B1 of 25

Contents

Introduction

Sample Scheme of Work – GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage

Sample Lesson Plan – GCSE Mathematics B J567:Foundation Silver/Higher Initial Stage

Published Resources

GCSE Mathematics B1 of 25

Introduction

In order to help you plan effectively for the implementation of the new specification we have produced sample schemes of work and lesson plans for Mathematics B. These support materials are designed for guidance only and play a secondary role to the specification.

Each sample scheme of work and lesson plan is provided in Word format. You should use it as a foundation to build upon, and amend or add to the content to suit your teaching style and learners’ needs.

This booklet provides examples of how to structure the teaching of this Stage; the teaching hours are suggestions only.

The specification is the document on which assessment is based and specifies what content and skills need to be covered in delivering the course. At all times, therefore, this support materialbooklet should be read in conjunction with the specification. If clarification on a particular point is sought then that clarification should be sought in the specification itself.

GCSE Mathematics B1 of 25

Sample GCSE Scheme of Work

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSN1/HIN1 -Calculating with fractions
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Multiply and divide simple fractions /
  • Multiplication of simple fractions. – Could demonstrate method with diagrams, eg 1/3 of 1/4: show 1/4 being divided into thirds to demonstrate that answer is 1/12, building on knowledge of finding a fraction of a quantity
  • Division of simple fractions, starting from concepts such as “how many halves are there in 4?” into division as multiplicative inverse
/
  • Banks of questions
/
  • This does not include multiplication and division of mixed numbers.

Add and subtract fractions /
  • Addition and subtraction of mixed numbers
  • Recap and build on skills of converting mixed numbers into improper fractions and adding and subtracting fractions

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSA1/HIA1 -Formulae
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Use and generate formulae. Substitute positive and negative numbers into a formula or an expression /
  • Substitute values into expressions and formulae
  • Generate simple formulae and use to calculate unknown values
/ Use real-life formulae and those in other subjects, such as science, where possible. /
  • Eg (1) 4x – 2;
  • (2) 3x2 + 4;
  • (3) V = 2a3

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 2 hours / Topic / FSG1/HIG1 - Lines and angles
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Understand and use the angle properties of parallel and intersecting lines /
  • Deducing the theorems:
  • Use of dynamic geometry software to demo angles or
  • Straws/Sticks: give pairs of students 3 × sets of 3 straws. Ask them to arrange 1st set with one intersection, 2nd set with two intesections, 3rd set with three
  • Draw results and measure all angles - ask students to explain what they notice
  • Link observations to angle theorems: vertically opposite angles and parallel lines
  • Find missing angles, giving reasons for answers
/
  • Appropriate software
  • or straws (or similar) plus angle measurers
  • Worksheet/textbook

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 2 hours / Topic / FSS1/HIS1 - Probability
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1 /
  • Introduce/recap basic ideas about probability
  • Probabilities from mutually exclusive outcomes – find from various given scenarios. Start with simple situations and questions, such as boys and girls.
/
  • An amusing video for introducing probability (requires access to YouTube.com): - can ask students what the given probability means and whether they agree with it

Suggested teaching time / 2 hours / Topic / NFSN2/HIN2 -Fractions and percentages
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Express one quantity as a fraction or percentage of another /
  • The problem - give students an example e.g. 3 different test scores as fractions with different denominators. Ask which is best score. Discuss why it is difficult to compare
  • The solution - change to percentages. Use examples to practice
  • Students could also use examples from newspapers/magazines/surveys, eg x out y people agreed with this statement - what percentage is that? What percentage of home/away games has a football team won etc
  • Percentage profit (or loss/increase/decrease:How to calculate
/
  • Bank of questions and/or newspaper headlines (can generate your own headlines here:

Survey results etc /
  • Will need to include examples where fractions are given explicitly and where students write the amount as a fraction

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 2 hours / Topic / FSA3/HIA3- Brackets
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Manipulate algebraic expressions by multiplying a single term over a bracket and by taking out common factors /
  • Multiply out single brackets
  • Link to numeric examples: discuss how to calculate eg 2(3+4), 5(7-3), 8(10-3) and area of compound shapes, eg
7 4

  • Two ways of approaching these.
  • Then consider algebraic examples e.g. 2(x+4), 5(7-y), 8(10a − 3)
  • Introduce technique of multiplying out/expanding brackets
  • Multiply out brackets - more complex examples: eg 3 terms inside bracket, more challenging algebra
  • Factorising: Single brackets. Could use a ‘gap fill’ exercise with partially completed examples to introduce factorisation skills
/
  • Support worksheet: multiply out single brackets (Word)/ (RTF)
nb Final section is a ‘gap fill’ starting to think about factorisation skills, but factorisation not mentioned at this point
  • Get some more practice with brackets section of PacAlgebra game from :
  • Support worksheet: factorising: (Word)/ (RTF)

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSG2/HIG2 -Constructions
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Construct triangles and other 2-D shapes using a ruler and a protractor, given information about their sides and angles. Use a straight edge and a pair of compasses to do constructions.
Construct inscribed regular polygons.
Construct nets of cubes, regular tetrahedra, square-based pyramids and other 3-D shapes /
  • Construct triangles etc – could demo methods either on paper, or ask groups of students to follow different examples from textbook and then show rest of class how to do each type, or use the Flash program on the right.
  • Construct inscribed regular polygons by equal division of a circle
  • Construct nets - could use these to make gift boxes or packaging. Could link to surface area (FSG4/HIG4)
/
  • Rulers, angle measurers etc
  • Card, rulers, angle measurers etc
/
  • If students all use same size of circle to start with, provides opportunity for displays of tessellating/non-tessellating polygons

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSS2/HIS2 -Averages from grouped data
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Identify the modal class of grouped data. Calculate the mean of grouped discrete data /
  • Calculate the mean from a table - start with small data set (10 - 15 items) and demo mean both ways - from list and from table, move onto larger data sets - need for tables should become obvious
  • Calculate the mean from grouped data - use of mid-points
  • Identify the modal class
/
  • Sets of data, organised into tables
  • Worksheet/textbook

Suggested teaching time / 3 hours / Topic / FSN3/HIN3 - Percentage increases and decreases
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Increase and decrease quantities by a percentage /
  • Percentage increases - eg inflation, pay rises, VAT etc. Work out increases using step methods or single multipliers
  • Percentage decreases - e.g. reduced prices in sales, discounts, falling populations etc. Work out decreases using step methods or single multipliers
/
  • Banks of questions, or collection of newspaper headlines to use as starting points. (Can generate your own headlines here:

NRICH “Are you a smart shopper?”

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSS2/HIA2 -Linear equations
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Set-up and solve linear equations with integer coefficients. This will include equations in which the unknown appears on both sides of the equation, or with brackets /
  • Some students may need to review basic equations
  • Solve equations with unknowns on both sides
  • Solve equations with brackets (single term outside a single bracket)
/
  • Online gamesfor equations include:


Lesson A2 from Improving Learning in Mathematics:

with Balance 1, Balance 2 and Cover Up programs from the CD-ROM included in the box

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GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSG3/HIG3 -Circles
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Recall the meaning of circle, chord, tangent, arc, sector and segment. Recall and use the formulae for the circumference and the area of a circle.
NB Candidates may be required to give answers in terms of pi. /
  • Discover pi: students measure circumferences and diameters of cylinders, then calculate ratio
  • Calculate circumferences and diameters
  • Find areas - demo derivation of formula by cutting paper circles (or a pizza?) into sectors and rearranging to form an approximate rectangle/parallelogram
/
  • Cylinders, tape measures (or string - but tape measures will probably result in more accurate results)
  • Problems to solve, eg from published texts
  • Circle (cut up) as a visual aid; problems
  • Pi rap:
/
  • Probably worth discussing if measurements will be 'perfect' or accurate - can use this to justify less than brilliant results that will inevitably be encountered.
  • Results could be collected via a Google form and displayed using a data projector (Tom Barrett has a useful guide to using Google forms here:
  • Opportunites for functional maths - design a trundle wheel, calculate how far a bicycle or wheelcahir will travel if wheels turn through × revolutions, extension - design a 400m running track to fit in a given space
  • Could work out answers to practical problems, e.g. amounts of fertilser needed to cover circular grassed areas - (see for some good suggestions about framing this type of question) Video introducing idea of scaling up/down:

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 2 hours / Topic / FSS5/HIs5 -Surveys
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Design and criticise questions for use in a survey, taking possible bias into account /
  • Consider example questionnaire and criticise: teacher could create a survey to be done by a group of teachers/students. An example of where this done with input from a global network is here:
  • Students create own quesionnaires and discuss
/
  • Use of Google forms: Tom Barrett has a useful guide here;
/
  • Students could work in small groups to critique each others' questions. If data is actually collected, it could be used for organising/interpreting data (FSS3/HIS3) at a later stage
  • This could be set in a school context if appropriate, e.g. students design a questionnaire to survey students’ opinions about school meals (or similar) and present findings to the school council

Suggested teaching time / 3 hours / Topic / FSS3/HIS3 -Organising data
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Draw and interpret a wide range of graphs and diagrams for discrete and continuous data, including frequency polygons and stem and leaf diagrams.
Compare distributions and make inferences, using the shapes of the distributions and measures of average and range /
  • Group data, working with frequency diagrams and frequency polygons
  • Stem and leaf diagrams - constructing and using (to find median, mode, range)
  • Compare data sets - either draw graphs and charts to compare data, or use pre-prepared diagrams and reach conclusions. Could link to data collected from questionnaires (FSS5/HIS5)

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSN4/HIN4 -Calculating with decimals
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Use the four operations on decimals without the use of a calculator /
  • Add and subtract decimals - a teacher demo with lots of deliberate errors (eg mis-aligned numbers, arithmetical errors) can provide a good stimulus for discussion. Students could be encourgaed to generate 'checklist' of points to remember
  • Multiply - students can investigate by working out arious sets of multiplications (eg 6 × 4, 0.6 × 4, 0.06 × 0.4)with a calculator and trying to generalise
  • Division - could demo how to reduce all problems to a division by a whole number by treating division as a fraction, then place values in the answer will be straightforward
/
  • Bank of questions - both in figures and word problems
/ Students should be encouraged to try different algorithms for multiplication in order to find the one they are most comfortable with.
GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSA4/HIA4 -Linear graphs
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Use tables to plot graphs of linear functions given explicitly /
  • Generate tables of values from given equations.
  • Use tables of values to draw graphs.
  • Test own learning with Save Our Dumb Planet game from - N.B. non-linear graphs occur once players progress beyong level 6 in the game:
Students will need to be fast at finding points on the graphs, and some have negative x coefficients. / Spreadsheets: good chance to use ICT to create tables of values
Graph plotting software
GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSG4/HIG4 -Perimeter and area
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Recall and use the formula for the area of a parallelogram and a triangle.
Use the formula for the area of a trapezium.
Calculate perimeters and areas of shapes made from triangles and rectangles.
Find the surface area of simple solid shapes using the area formulae for triangles and rectangles /
  • Review basic concepts of perimater and area of a rectangle. Formulae for triangle, parallelogram, rhombus can then be derived from this
  • Calculate areas and perimeters of a variety of shapes
  • Find surface area. Can be set in context by looking at various net designs (FSG2/HIG2) and working out which will use the least/most card
  • Test own learning with Pyramid Panic game from - N.B. game includes some higher level skills (Pythagoras, trigonometry), but players can record achievemnetsin other areas even if they cannot do some sections:
/
  • Review basic perimeter and area:
  • Demonstrate for various 2D shapes:
/
  • The formula for the area of a trapezium is given on the formulae sheet

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 2 hours / Topic / FSS4/HIS3 -Two-way tables
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Design and use two-way tables for discrete and grouped data /
  • Use two way tables - read information, find missing values
  • Organisegiven data using two-way tables
/
  • Variety of examples of two way tables
  • Extension activity – can link to Venn diagrams (not in the specification) and/or Task A below:

Suggested teaching time / 3 hours / Topic / FSN5/HIN5 -Ratio
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Use ratio notation including reduction to its simplest form. Understand and use ratio and proportion, including dividing a quantity in a given ratio /
  • Work with ratio notation: writing ratios, simplifying ratios
  • Use ratios to solve problems, e.g. working with recipes
  • Divide quantities in a given ratio
/
  • Video introducing idea of scaling up/down: [nb videos on Teachers TV are only available within the UK and don't remain available indefinitely - you are advised to register with the site and download a copy - there is no charge for this]
  • Real recipes may be used
  • NRICH “Mixing Lemonade”

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 2 hours / Topic / FSA5/HIA5 - Trial and improvement
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Use trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them.
Eg (1) x3 - 2x = 2; (2) The positive solution of x2 − 4 = 1/x ; (3) I think of two numbers. They add together to equal 6. They multiply together to equal 8·64. Find the two numbers /
  • Solve equations given algebraically using trial and improvement
  • Form equations (e.g. from 'I think of a number…' type questions) and solve using trial and improvement
/
  • Support sheet may help students to structure their working during initial questions: (Word)
/
  • Graphing software

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 2 hours / Topic / FSG5/HIg5 -Plans and elevations
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Use 2-D representations of 3-D shapes, including plans and elevations /
  • Introduce plans and elevations - students can work with multi-link, solids or could use Google maps - satellite and streetview ( see )
  • Draw plans and elevations from diagrams of 3-D objects
  • Create objects from multi-link from given plans and elevations
  • Isometric drawings of cubes, cuboids etc
/
  • Multi-link / solids
  • Multi-link cubes

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSN6/HIN6 -Using a calculator
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Use a calculator effectively and efficiently, entering a range of measures including 'time', interpreting the display and rounding off a final answer to a reasonable degree of accuracy. Perform calculations using the order of operations /
  • Introduce order of operations using calculations or the 24 game
  • Move onto actual calculations, based on 24 cards/written examples/online game
  • Examples toinclude roots and/or division
  • Investigate calculator functions - can be teacher led, or students can work in small groups and feed back what they have learned
  • Investigate time on the calculator and accuracy/rounding
/
  • Basic & scientific calculators, 24 Game (optional), online activity at
  • Workcards: (Word)
  • Calculations involving times - eg working out recording times for TV programmes/series, cooking times
/
  • This includes using the memory and bracket keys, and function keys for squares and powers where appropriate
  • Opportunity for paired or group work

GCSE Mathematics B J567: Foundation Silver/Higher Initial Stage
Suggested teaching time / 3 hours / Topic / FSG6/HIG6 -Transformations
Topic outline / Suggested teaching and homework activities / Suggested resources / Points to note
Transform triangles and other 2-D shapes by rotation, reflection, or translation using column vectors. Recognise and visualise rotations, reflections and translations. Understand the properties preserved by these transformations; understand the congruence of these transformations. /
  • Human transformations: Set up a grid in a large area, eg a playground or hall. Some students can stand at regular intervals, holding numbered mini-whiteboards to form axes. Others make shapes by holding string or linking hands. Ask them to move, rotate etc. This is even better if it can be videoed and reviewed
  • Draw the different types of transformation
  • Recognise transformations
  • Test own learning or practise skills with Transtar game from MangaHigh.com:
/
  • Mini-whiteboards, string/cloth (optional), large space
  • Dynamic geometry software

GCSE Mathematics B1 of 25