ocr nationals - the john warner school … · web viewsolve word problems involving fractions...

$: OCR Nationals - The John Warner School … · Web viewSolve word problems involving fractions Recap on adding/subtracting fractions. Introduce addition/subtraction with mixed numbers$
Scheme of Work - Year 10 – J3 & J4

Presumed knowledge:

Long multiplication Long and short division Multiplying and dividing decimals Calculating with money Adding, subtracting, multiplying and dividing negative numbers.

Once a week – numeracy topics should be practiced either as a starter to a lesson or incorporated as part of the lesson so as to ensure these skills are practiced regularly.

Teaching times are a guide – as it is presumed teachers are using a broad and enriched curriculum and not just teaching from text books.

It is important that students are not taught to “jump through hoops”, but are encouraged to think and explore for themselves. Activities involving thinking skills should be used whenever possible.

The curriculum must be enriched, by using rich tasks, investigations, real life activities / scenario’s, functional mathematics and higher level thinking tasks.

Where a topic has taken less teaching time – the remaining time should be used to enrich the curriculum – not jump ahead. This helps pupils to gain a deeper understanding of the material, be able to apply the material to new challenges and broaden their knowledge of mathematics in different contexts.

Functional Maths:

Functional maths must be embedded in all lessons throughout Year 10 and Year 11 – many of the new exam style questions will be functional maths based.

The interactive textbooks have some good functional maths questions that can be used in lessons.

Financial Capability (Compulsory):

All year 10 will have 4 financial capability tasks. These are detailed below and hyperlinked to the appropriate folder. Please familiarise yourself with the content prior to delivery.

First half of Autumn Term – Financial Capability task 1Second half of Autumn Term – Financial Capability task 2Spring Term – Financial Capability task 3Summer term – Financial Capability task 4

Investigations (Compulsory):

There are three investigations which MUST be carried out during Year 10 – one per term. They can be completed at any time during the term; but towards the end of each term is usually preferable. The investigations are “Borders”, “Number Stairs” and “Manhattan Cops”.

Autumn TermOnce a week – numeracy topics should be practiced either as a starter to a lesson or incorporated as part of the lesson so as to ensure these skills are practiced regularly.

Financial capability task 1 must be covered during the first half of the autumn term (Click on task for hyperlink).

Investigation – “Borders” must be completed before the end of the autumn term (Click on task for hyperlink)

GCSE Mathematics J3 & J4

Suggested teaching time 4-6 lessons Topic Transformations

Topic outline Suggested teaching activities Suggested resources Points to noteConstruct enlargements with positive scale factors.

Demonstrate how to draw enlargements with scale factors ½ and 3 using a centre. Alternatively, issue a sheet with the enlargements done and ask for an explanation of the method.

BBC Bitesize:http://www.bbc.co.uk/schools/gcsebitesize/maths/shapes/transformationshirev1.shtml

Construct enlargements with negative scale factors.

Demonstrate how to draw enlargements with scale factors -½ and -3 using a centre. Alternatively, issue a sheet with the enlargements done and ask for an explanation of the method.

Consolidation exercise. Plenary: set an enlargement, scale

factor -1, any centre and then ask for a description of an alternative equivalent transformation.

Draw their own picture and enlarge it using any scale factor, fractional or negative for homework.

Identify the centre and scale factors of enlargements.

Describe fully an enlargement

Ask them to look back at previous work. How can you find the centre and scale factor?

Demonstrate how to find the centre and scale factor of an enlargement.

Issue sheet with enlargements copied

Note – students often lose marks in the exams, because they cannot fully describe a transformation. If they confuse their description – eg: rotation, 90 degrees, clockwise vector (2,1) – they will lose ALL marks because ‘vector’ shows misunderstanding!

http://www.bbc.co.uk/schools/gcsebitesize/maths/shapes/transformationshirev1.shtml

GCSE Mathematics J3 & J4

Suggested teaching time 4-6 lessons Topic Transformations

Topic outline Suggested teaching activities Suggested resources Points to noteon and the students find the centre and work out the scale factor.

Review translations, reflections and rotations.

Describe single transformations given an object and an image.

Combine transformations and describe the effect using a single transformation.

Start with a single object; ask each student to do a rotation, reflection, translation and enlargement on it.

Determine the information required for each transformation. Deal with any problems that arise.

Give out a grid with many objects on it and ask for a description of the single transformation that maps A onto B.

Set the task to combine transformations on a single grid and then describe the single transformation that maps one onto the other.

Past examination papers are very useful as a source of ideas.

NRICHTessellating transformations a very interesting activity on combined transformations

http://nrich.maths.org/4965

GCSE MATHEMATICS SOW J3 & J4

SUGGESTED TEACHING TIME

6-8 LESSONS

TOPIC FRACTIONS, DECIMALS AND PERCENTAGES

TOPIC OUTLINE SUGGESTED TEACHING ACTIVITIES SUGGESTED RESOURCES POINTS TO NOTE

Convert a simple fraction to a decimal using division.

Use and understand terminating and recurring decimals.

Recap on simple fraction to decimal conversions

Introduce other conversions using division

Introduce the idea of recurring decimals

At this stage recurring decimals do not need to be converted to fractions

Use percentages to compare proportion.

Compare situations using percentages, use situations related to real life

Give students scenarios on cards – which is better?

Use and find percentage change. (Link to profit and loss)

Using a multiplier to calculate percentage increase and decrease.

Using whiteboards, repeatedly give a percentage change and ask for the multiplier.

Revisit some of the earlier examples using this more efficient method.

FM - Get local paper job section, income tax and NI tables. Get pupils to workout weekly and monthly take home pay. (A great activity to incorporate real life maths, FM & Pfeg)

Functional mathematics – Students mustsolve Functional questions on this topic.

Calculate the original Using whiteboards, give the Improving Learning in Mathematics Chapter N7:



6-8 LESSONS

TOPIC FRACTIONS, DECIMALS AND PERCENTAGES


amount when given the transformed amount after a percentage change. (Reverse percentage)

percentage change and the final amount. Ask for the original amount. Ask how you would solve .... .

Use “Unjumble” or “Fill in the blanks” to demonstrate the method.

http://tlp.excellencegateway.org.uk/pdf/mat_imp_02.pdf Functional mathematics – Students must solveFunctional questions on this topic.

Solving problems with repeated proportional or percentage change.

Look at different repeated proportional or percentage increase problems. Ask the students to find an efficient way to calculate them.

Finally repeat with decrease.

Additionally, you could use an “Unjumble” or “Fill in the blanks” activity to show the method.

Use of a spread sheet Tarsia

http://tlp.excellencegateway.org.uk/pdf/mat_imp_02.pdf

http://tlp.excellencegateway.org.uk/pdf/mat_imp_02.pdf



3 LESSONS TOPIC PROBABILITY


Use and understand estimated and expected probability.

Use and understand relative frequency of probability from theoretical models or experimental data.

Experiment in pairs then combine all results and discuss the results

Students in groups design an experiment to carry out to test a theory

Consider the effect of the sample size or the number of times the experiment was done

Recording sheet, dice, coins, etc

Student’s need to understand that estimated probability uses theoretical probability to make estimates of what might happen.

GCSE Mathematics: SOW J3 & J4

Suggested teaching time 4 lessons Topic Ratio and proportion

Topic outline Suggested teaching and activities Suggested resources Points to noteReview simplifying ratio, writing ratios as fractions.

Share a quantity in a given ratio, including working backwards to find the total initial amount.

Write ratios in the form 1:n and n:1

Solve problems involving best buys.

Solve problems involving ratio and proportion, including direct and inverse proportion. (NOT using equation of proportionality)

Good starter activity using mini whiteboards

Solve functional mathematics problems from the FM textbook on ratio and proportion.

Get student’s to write their own problems for others to solve. Can be done as groups.

NRICHThe Garrison – problem involving direct proportion

FM: Planning a dinner party

Most of this work is functional mathematics work.

The Garrison is an excellent ratio and proportion problem which enriches the curriculum.

Ensure students understand difference between direct and inverse e.g. 3 builders take 10 days to build a wall, how long for 8 builders?




4 LESSONS TOPIC ANGLES IN POLYGONS


Calculate and use the sums of interior and exterior angles of regular and irregular polygons

Solve problems involving interior and exterior angles of polygons

Appreciate which polygons tessellate

Students draw a polygon with between 4 and 10 sides, they measure and total their interior and their exterior angles, collect results on master sheet or whiteboard

Discuss results - can they see a link? Fill in any gaps

Make a giant football from pentagons & hexagons

Protractors http://www.bbc.co.uk/schools/

gcsebitesize/maths/shapes/polygonsrev1.shtml

Past exam questionsThere are some excellent past exam questionswhich involve a combination of differentpolygons joined together – these require higherlevel thinking, and are becoming popular inexam.

http://www.bbc.co.uk/schools/gcsebitesize/maths/shapes/polygonsrev1.shtml





4 LESSONS TOPIC REAL LIFE GRAPHS


Sketch graphs arising from real situations and use and interpret them.

Draw and interpret distance time graphs.

Individual activity. Give students

(i) Graphs to plot from a description & (ii) a sheet of pre-drawn graphs and ask for interpretation of those graphs. After some time the students are invited to explain their answers to the class.

Draw journey to school

NRich - Fill it up This is a great enrichment activity.

Could be individual or paired work. Use finished results as display

Ensure students can convert between parts ofan hour / minutes e.g. 2.3 hours is 2 hours and3/10 of an hour = 18 minutes. Same forminutes / seconds.

Also – converting from Km/Hr to m/s

Financial Capability Task 1 must have been completed this term.

If Borders was not completed this half term – it must be completed next half term.

Financial capability task 2 must be completed this next half term.

Autumn Half term Assessment test T1




3 LESSONS TOPIC CHECKING SOLUTIONS TO CALCULATIONS, ESTIMATION AND APPROXIMATION


Check solutions to calculations by approximating or by using inverse operations.

Recap on rounding to 1 significant figure and the effect of rounding then multiplying or dividing

Check, using inverse operations and common sense

Questions on whiteboard http://www.bbc.co.uk/schools/

gcsebitesize/maths/number/roundestimaterev1.shtml

Estimate solutions by first rounding to 1 significant figure.

Starter – rounding to 1, 2 and 3 significant figures.

Students invariably round decimals incorrectly e.g. 21 x 39/0.43 = 20 x 40/1

Recognise the effect of multiplying and dividing by numbers less than one and greater than one.

Ask students to multiply/divide by numbers less than and greater than one. What do they find?

Students can work in pairs, using individual whiteboards. One makes up a calculation and the other states if correct or incorrect

Exercise giving calculations, students need to say if incorrect and how they can tell without working out the exact answer

http://www.bbc.co.uk/schools/gcsebitesize/maths/number/roundestimaterev1.shtml





4 LESSONS TOPIC SCATTER DIAGRAMS, STEM & LEAF AND FREQUENCY POLYGONS


Draw and interpret scatter graphs for discrete and continuous variables.Understand the types of correlation.

Video clip is a good starter Discuss the idea of correlation Exercise on interpreting scatter diagrams

http://www.teachers.tv/video/1851 maths 4 real

Get student’s to collect own two sets of data, and plot these for discussion and conclusions.

Use and understand lines of best fit.

Exercise on drawing scatter graphs and lines of best fit

Use the line of best fit to estimate Explain limitations of estimating from a line

of best fit

Students in a group state a hypothesis. Collect data from class or relevant source, students produce their own scatter graph and write a report on their findings

FM task – Reporting the weather

Another useful wall display

Draw and read information from an ordered stem-and-leaf diagram, including finding median and IQR

Draw a Frequency polygon for grouped data

This should just be a recap – Students must be able to fine median and interquartile range from stem and leaf.

Many students forget to put a key on their diagram – this costs them 1 mark in exam

Stress, they plot the midpoint against the frequency, and they must NOT join up the last and first point or they lose a mark.

http://www.teachers.tv/video/1851

GCSE MATHEMATICS J3 & J4


4 LESSONS TOPIC PYTHAGORAS


Understand, recall and use Pythagoras’ theorem in 2-D contexts.

Explain hypotenuse, students name the hypotenuse on triangles in different orientations

Unjumble Card sort Questions in context and not obviously

Pythagoras Pythagorean triples


Pre-made sets of right-angled triangles and squares. Students arrange the triangles with three squares round each one. Complete details on a pre-prepared worksheet.

Include questions which ask the length of a diagonal line, giving only the coordinates of the ends of the line

Pace obviously depends on the ability of individual classes

FM tasks need to be included.




3-4 LESSONS

TOPIC QUADRATIC, CUBIC AND RECIPROCAL GRAPHS


Generate points and plot graphs of simple quadratic functions. Use these to find approximate solutions of simple related equations.

Draw the graphs of cubic and reciprocal functions.

Compare equations and decide if linear or quadratic – use mini whiteboards

Generate tables of values from given equations

Use tables of values to draw quadratic graphs

Use graphs to solve equations

www.emaths.co.uk/powerpoint/numalg /QuadraticGraphs.ppt

If using Casio calculator to square – remind student’s they must do (-2)2 and not -22 or they will get incorrect answer. Discuss how scientific calculator does this.

Curves must be smooth, single line – no hatching or double lines or they lose accuracy mark. Also – no pointed or flat bottoms!

http://www.emaths.co.uk/powerpoint/numalg%20/QuadraticGraphs.ppt

http://www.emaths.co.uk/powerpoint/numalg%20/QuadraticGraphs.ppt


SUGGESTED TIME 8 LESSONS TOPIC ALGEBRA, LINEAR EQUATIONS AND INEQUALITIES


Expand a single bracket, expand linear expressions with brackets and simplify.

Factorise a linear expression and a quadratic expression into ONE bracket only. (eg: 12x2 – 32x)

Solve linear equations unknowns on one side, both sides and with brackets and fractions.

Solve simple linear inequalities in one variable

Represent the solution set on a number line, using the convention for distinguishing ≤ and ≥ from < and >.

List all possible integers for a given inequality

Mini whiteboards to show understanding. Card sort Unjumble

Unjumble Card sort Find the error – have worked solutions and

students to find the mistakes.

Play higher / lower with pack of cards – using inequality signs. Eg: Teacher turns over 4, class guess next card – say it is 8; teacher writes 8 > 4 on board.

Revise symbols

Tarsia

Cards with sets of numbers on, students fill in the gaps with the correct sign

Stress, when solving inequality – student must write x > 4, x < 6 etc on answer line and not just 4 or 6.



3 LESSONS TOPIC CALCULATE THE MEAN FROM GROUPED CONTINUOUS DATA


Revisit calculating the mean, finding the median and mode from a frequency table.

Calculate the mean form grouped continuous data.

Put frequency table on board and get students to find the mean, mode and median. Discuss findings.

Introduce the idea of midpoint explain why it is used

Students collect data and work out an estimate for the mean of eg heights of students in their maths class

http://www.emaths.co.uk/tutorials/ meangrouped/ Grouped 20Mean/Presentation_Files/index.html

Data collection sheets Metre rulers, tape measures, scales etc

Financial capability task 2 must have been completed this half term

Borders investigation must have been completed this half term if it was not completed in the last half term

End of autumn term Assessment test T2

XMAS BREAK

http://www.emaths.co.uk/tutorials/meangrouped/Grouped%20Mean/Presentation_Files/index.html



SPRING TERM

Financial capability task 3 must be completed during the Spring term (Click on task for hyperlink)

Investigation – “Number Stairs” must be completed this Spring term



3-4 LESSONS

TOPIC COMPOUND MEASURES


Understand and use rates and compound measures, for example speed, distance, time; mass, density, volume; rate of flow.

Solve problems involving compound measures

Explain how compound measures are calculated

Speed in km/h or m/s Introduce density, population density and

rate of flow

Students must be able to convert from m/s to Km/hr

Students must know 2.4 hours on calculator is NOT 2 hours 40 minutes.

These may well be functional mathematics style questions in exam.



2-3 LESSONS TOPIC RECIPROCALS, FACTORS AND MULTIPLES


Use and understand the terms reciprocal, highest common factor, lowest common multiple, prime number.

Find the prime factor decomposition of positive integers.

Find the reciprocal of a number.

Recap prime numbers Practise decomposing numbers into prime

factors Higher common factors and lowest common

multiples Introduce Venn diagram for HCF Pairs and spares method.

Number fans List of numbers, students work out the

reciprocals

http://www.bbc.co.uk/schools/ gcsebitesize/maths/number/primefactorshirev1.shtml

http://www.bbc.co.uk/schools/gcsebitesize/maths/number/primefactorshirev1.shtml





2 LESSONS TOPIC CHANGING THE SUBJECT OF A FORMULA


Change the subject of a formula in cases where the subject only appears once.

Change the subject of a formula using addition, subtraction, multiplication and division

Introduce formulae containing brackets Introduce equations to be solved in cases

where the formula has to be re-arranged first

Tarsia



3-4 LESSONS

TOPIC LOCI & CONSTRUCTION


Use straight edge and a pair of compasses to produce standard constructions, including the midpoint and perpendicular bisector of a line segment and the bisector of an angle.

Find the midpoint of a line segment Construct the bisector of a line segment

Construct an angle bisector

Rulers, pencils, compasses www.emaths.co.uk/shape.htm PowerPoint

on perpendicular bisector

Past GCSE exam questions Rulers, pencils, compasses www.emaths.co.uk/shape.htm PowerPoint

on angle bisector

Construct loci to show paths and shapes.

http://www.bbc.co.uk/schools/ gcsebitesize/maths/shapes/locirev1.shtml(This covers all topics and could be split

so the relevant part is shown in each lesson.) Rulers, pencils, compasses Past GCSE exam questions Gilbert the goat

http://www.bbc.co.uk/schools/gcsebitesize/maths/shapes/locirev1.shtml

http://www.bbc.co.uk/schools/gcsebitesize/maths/shapes/locirev1.shtml

http://www.emaths.co.uk/shape.htm

http://www.emaths.co.uk/shape.htm

GCSE MATHEMATICS J3 & J4


2 LESSONS TOPIC ACCURACY


Recognise that a measurement given to the nearest whole unit may be inaccurate by up to half a unit in either direction.

Give reminder of rounding Examples of discrete/continuous data Discuss the idea that counting is exact Write upper and lower bounds for given

numbers eg: 2 < w < 7, explain reason for strict inequality.

Explain notation for whether a boundary is included or not

Students measure items and record lowest and highest boundaries of their measurements

Discuss practical implications ie fitted kitchen – will all units fit in a certain space if using rounded measurements?

Items for students to measure - boxes, cans etc

Rulers, string etc

NOT calculating with upper and lower bounds.



4 LESSONS TOPIC INDICES


Use the index laws with numerical and algebraic expressions involving multiplication and division of positive integer powers.

Use the terms cube root and negative square root.

Introduce the idea of multiplying numbers in index form eg 23 x 27

Introduce dividing

Remind about square roots and introduce negative square roots

Introduce cube roots

Remind students of the cube roots they need to be able to recall in an examination

http://www.bbc.co.uk/schools/ gcsebitesize/maths/algebra/indicesrev1.shtml

Ensure students know how their own calculators operate

http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/indicesrev1.shtml





3-4 LESSONS

TOPIC SEQUENCES


Generate integer sequences using a rule for the nth term. Use linear expressions to describe the nth term of an arithmetic sequence.

Generate sequences from practical contexts.

Explain linear sequences Ask each student to write a sequence on a

mini whiteboard. Hold up in turn, others decide if it is linear or not

Continue a sequence Give a formula, write down the first 4 terms Find the formula for the nth term Card sort. Sets of 30 cards. 15 are

sequences, 15 are rules. In pairs students find the matches

Could have another set of cards for students to match

Tarsia

Spring term Assessment T3

If the Financial capability task 3 was not completed by now, it must be completed before the end of the Spring term (Click on task for hyperlink)

If Investigation – “Number Stairs” has not been completed by now, it must be completed before the end of the Spring term



4-6 LESSONS

TOPIC VOLUME AND SURFACE AREA OF PRISMS AND CHANGING UNITS


Calculate the surface area and volume of prisms, including cylinders.

Convert between measures for area or for volume, for example between mm2 and cm2 or between cm3 and litres.

Recap on volume of a cuboid, define prism and introduce idea of cross section. Move on to volume of a prism

Introduce idea of surface area

Recap changing linear units Introduce relationship between metric units

of area and volume

Students often find SA difficult. Let them draw the net on squared paper, cut it out and work out the total surface area



4 LESSONS TOPIC FRACTIONS


Use the four operations on fractions, including mixed numbers.

Solve word problems involving fractions

Recap on adding/subtracting fractions Introduce addition/subtraction with mixed

numbers Multiplying/dividing with mixed numbers Calculating with fractions using a calculator Card sort

Could convert to improper fractions rather than dealing with the whole numbers first

Students are often unsure of how to use a calculator to deal with fractions

GCSE MATHEMATICS: J3 & J4


4-6 LESSONS TOPIC PROBABILITY SAMPLE SPACE AND TREE DIAGRAMS

TOPIC OUTLINE SUGGESTED TEACHING AND ACTIVITIES SUGGESTED RESOURCES POINTS TO NOTE

Complete a sample space diagram to list all possible outcomes for two mutually exclusive eventsCalculate probabilities from a sample space diagram.

Inform class you are going to roll a 6 sided fair dice, and spin a fair spinner numbered 1,3,5,7,9 together and ADD the sum of their scores. Ask class to write down all possible outcomes for this. Discuss different methods used.

NRICH – Do you feel lucky; A good FIRST lesson for discussing probability – it encourages students to discuss statements and decide if they think they are true or not.


In exam – students may not be asked to draw a probability space diagram – they do however, need to realise this is one way of recording all possibilities in order to find a particular probability.

Draw a tree diagram to show possible outcomes, and find the probability of independent events.

Demonstrate how to draw a tree diagram horizontally to show outcomes, or issue sheet of tree diagrams and ask what they show.

Draw a tree diagram for two dice showing all outcomes. Appreciate the limitations of tree diagrams.

Mixed problems using tree diagrams to find the outcomes.

A card sort is possible here with pre-drawn tree diagrams matching to specific events.

Mixed problems to solve.

Nrich – In the box. Ideal starter for the first lesson on tree diagrams.http://nrich.maths.org/919

In exam – students may not be asked to draw a tree diagram – they do however, need to realise this is one way of recording all possibilities in order to find a particular probability.

Drawing tree diagrams for independent events when there is more than one outcome required.(AND / OR rules)

Use previous tree diagrams and discuss how to find the probability of events with more than one possibility.

Discuss in groups when to multiply and when to add.

Functional mathematics – Students could solve Functional questions on probability.





6 LESSONS TOPIC STRAIGHT LINE GRAPHS


Understand gradient and work out the gradients of straight lines.

Use students’ experience to identify the meaning of gradient and define the term; include positive, negative and zero gradients.

Draw some straight lines on 4 quadrant grid and work out the gradient using “counting the squares up”

Use these same lines to find gradient using difference in y difference in x

A pre-printed table and a sheet with lines drawn will speed up the lesson and leave time for conjectures about the relationships.

Students should realise lines parallel to x axis have gradient = 0, and lines parallel to y axis the gradient is undefined.

Must understand difference between positive and negative gradient.

Students need to be able to find gradient of a line from two coordinates.

Understand that the form y = mx + c represents a straight line and that m is the gradient of the line and c is the value of the y-intercept. Know lines with same gradient are parallel.

Write the equation of a straight line in the form y = mx + c.Recognise lines of the form y = a, x = k, y = x, y = -x

Given a point, deduce if it lies on the line with equation

Using mini whiteboards, give the students some equations of straight lines and ask for the gradient and y-intercept, AND give the gradient and y-intercept and ask for the equation of the lines. Y given explicitly in terms of x. (Good starter to assess prior knowledge)

Find line parallel to another line.

On whiteboards they can be asked to sketch the graph of ….

Students to be able to generate coordinate pairs and sketch the equation of a line in the form y=mx+c

Use of autograph in ICT room or on netbooks. Knowing y = mx + C is equation of line, with m = gradient and c = y intercept should be prior knowledge, and can be done as a starter.

Much of this will be revision, and could be done in 1 lesson before moving on to lines of the form ax + by = c



6 LESSONS TOPIC STRAIGHT LINE GRAPHS


…. Good plenary

Draw lines with equation ax + by = c using the cover up method.

Rearrange equation in form ax + by = c into y=mx+c and identify gradient and y intercept.

Write 2x + 3y = 12 on board. Ask student’s to write gradient and y intercept on mini whiteboards. Discuss their answers.

Students need to realise when the equation is of the form ax+by=c, that a is not the gradient and c is not the intercept; and that it needs to be re-arranged to find these two values.

EASTER BREAK

YEAR 10 Exams are usually the 2nd week back after Easter

SUMMER TERM – Year 10 annual exams are 2nd week of Summer TermFinancial Capability task 4 must be completed during the summer term (Click on task for hyperlink)

Investigation – “Manhattan Cops” must be completed this Summer term



4 LESSONS TOPIC SOLVE LINEAR EQUATIONS; SET UP EQUATIONS FROM PROBLEMS AND SOLVE THEM.


Solve cubic and quadratic equations using trial and improvement to 1 d.p.

Give students solutions with a mistake in it, and see if they can find it.

This is a 4 mark question in the exam, but students often lose marks because they do not show a full method.

Forming linear equations, including equations with brackets and fractions.

Writing expressions and solving equations involving geometrical shapes. (e.g. Write an expression for the perimeter of a rectangle; given the perimeter – use the expression to write and equation and solve it).

Start with two problems to solve and give them time to attempt a solution. Allow a student to give the class their solution. Discuss.

Give a past exam question, and ask students to try and solve it in pairs – discuss methods used.

Unjumble

You can get ideas from past examination papers for forming equations.



4-5 LESSONS TOPIC USE & CALCULATE WITH STANDARD INDEX FORM EXPRESSED IN CONVENTIONAL NOTATION

AND ON A CALCULATOR DISPLAY.

TOPIC OUTLINE SUGGESTED TEACHING AND HOMEWORK ACTIVITIES SUGGESTED RESOURCES POINTS TO NOTE

Convert between ordinary numbers and standard index form without a calculator

This is ideal for a card matching activity; in pairs match up two sets of cards, one has ordinary numbers and the other has standard index form numbers - include some blank cards to complete.

Jigsaws

Calculate with standard index form and write the answer in standard index form.

Students work in pairs to calculate answers to problems presented on a sheet.

You can have some cards with the answers on and students pick a card as they get an answer. It is a self-checking procedure.

You can use a card matching activity; put the problems and the solutions on cards.

Space provides useful data: http://en.wikipedia.org/wiki/Planet Earth timeline http://en.wikipedia.org/wiki/

Timeline_of_early_prehistoryAtoms: http://en.wikipedia.org/wiki/Atom

FM: Oil crisis

It is a good idea to estimate the answers as well.

Ensure pupils know how to read standard form from their calculators – some display it as 26; students need to know what this means for their calculator.

Functional mathematics – Studentsmust solve Functional questions onthis topic.

http://en.wikipedia.org/wiki/Atom

http://en.wikipedia.org/wiki/Timeline_of_early_prehistory

http://en.wikipedia.org/wiki/Timeline_of_early_prehistory

http://en.wikipedia.org/wiki/Planet



5-6 LESSONS TOPIC 3-D SHAPES, 3DCOORDINATES; MIDPOINTS OF LINE SEGMENTS; PYTHAGORAS’ THEOREM AND

COORDINATES


Draw planes of symmetry in 3D solids

Draw and interpret plans and elevations

Give a sheet with 9 cubes – ask class to draw all 9 planes of symmetry.

Using 3-D coordinates.

Finding the coordinates of the midpoint of a line segment AB given points A and B in 2-D.

Introduce 3-D coordinates and give them some shapes plotted in 3-D to write down the coordinates of some of the points on those shapes and the midpoints of some of the line segments.

Issue a sheet with pairs of plotted points and ask them to find the midpoints. Can they find a pattern?

Give answers to midpoints jumbled up and they have to select the correct answer for each pair of points.

Pupils need to be able to find midpoint from just Two coordinates using (X1 + x2, y1 + y2) 2 2

Use Pythagoras’ theorem to find the length of a line segment AB given the points A and B in 2-D.

Draw line segments on grids and measure the lengths. Appreciate that these are approximate lengths. Look at one pair. Draw more lines to form right-angled triangles. Ask how to work out the two sides. Calculate the accurate length using Pythagoras’ theorem.

This is good revision of Pythagoras



5-6 LESSONS TOPIC 3-D SHAPES, 3DCOORDINATES; MIDPOINTS OF LINE SEGMENTS; PYTHAGORAS’ THEOREM AND

COORDINATES


Students complete the other pairs.

Give students a sheet with pairs of points to find the length and the answers separately, with some extra distractors. Match the points with the correct answers.

Progress to giving students just the coordinates, and finding the length using (x1 – x2)

2 + (y1 – y2)2



4-6 LESSONS TOPIC CIRCLES, AREA AND ARC LENGTH OF SECTORS OF A CIRCLE.


Review calculating the area and circumference of a circle, semi-circle and quarter circle; answers in terms of pi and decimal format.

Solve complex problems involving area and circumference of circles.

Calculate the area, arc length and perimeter of a sector of a circle.

Solve problems involving arcs and sectors

Set a challenge to find the perimeter and area of a sector of that circle.

Show that a sector of a circle folds to give a cone. Discuss how to calculate the angle at the centre to make a wizard’s hat to fit your head. Alternatively you could make a popcorn cone.

There are some good past exam questions on this. Circles inside squares, functional maths questions.

Large paper to make a wizard’s hat.Start with an angle of 45, 90° or 120° then move to other angles.



4 LESSONS TOPIC SOLVING LINEAR INEQUALITIES IN TWO VARIABLES


Recap - Solve linear and quadratic inequalities.

Recap - Represent and read inequalities on a number line; identify all integers that satisfy a given inequality.

Unjumble or tarsia NRICHMarbles – how many of each in the bag? Uses inequalities to set up the problem.

Student’s often lose mark in the exam for not writing whole answer e.g. x<4 , they write just 4!

Plot lines on a grid and shade the correct region. Use the convention for distinguishing ≤ and ≥ from < and >.

It is essential to be able to draw correct lines, use mini whiteboards and give students equations of lines to draw, eg x = 3, y = -2, y = x + 3 etc.

Issue grids with lines and allow the students to calculate values of the function at various points, they will then see which region satisfies the inequality.

As plenary give them three inequalities to draw on three grids.

Where a line is included in the region, it will be solid; where it is not included, it will be dashed.

Draw two or more regions on a single grid. Indicate the intersection of all the regions.

Demonstrate the difficulty of shading the required regions, so we shade the unwanted regions instead.

Consolidation exercise to shade the intersection of inequalities. (Could include applications where the inequalities have to be written.)

Pre-drawn grids would be an advantage.

BBC Bitesize:http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/inequalitiesrev4.shtml

http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/inequalitiesrev4.shtml




4 LESSONS TOPIC ESTIMATED MEAN, CUMULATIVE FREQUENCY TABLES AND DIAGRAMS AND BOX PLOTS


Draw cumulative frequency tables and diagrams.

Have data in grouped frequency table – get class to explore how they might present this on their mini whiteboards.

Card matching exercise – cumulative frequency tables and graphs and data.

Pre-drawn grids will make it easier to check the work.

BBC Bitesize:http://www.bbc.co.uk/schools/gcsebitesize/maths/data/representingdata3hirev1.shtml

Interpret a cumulative frequency diagram.

Discuss how to find the median and quartiles of the original data.

Demonstrate how to use the diagram to find the median and quartiles.

Draw and interpret box plots. Give examples to draw box plots and to interpret them, or put a number of cumulative frequency diagrams and their associated box plots on a sheet in the wrong order and ask the students to match them up. These could be done on cards.

Compare distributions and make inferences, using themeasures of average and spread, including median and quartiles.

Group activity: give each group a set of tables and diagrams and ask them to summarise their inferences about the data. Have a feedback session towards the end of the lesson.

You will find past examination questions a good source of inspiration for these sheets of data. You can make the questions open-ended and add more information of your own.

.When interpreting, pupils must use median and IQR – and must include values of these in their comparisons of dual box plots

http://www.bbc.co.uk/schools/gcsebitesize/maths/data/representingdata3hirev1.shtml

GCSE Mathematics: J3 & J4

Suggested teaching time 4-5 lessons Topic Manipulate algebraic expressions by expanding BRACKETS AND factorising quadratic expressions.

Solve quadratic equations of the form ax2 + bx + c = 0 A = 1.

Topic outline Suggested teaching and activities Suggested resources Points to noteExpand the product of two linear expressions, simplifying the result. Include the difference of two squares.

Review expanding single brackets Write (x – 7)(x + 4) on board – pupils to

answer on whiteboards. Look for different methods.

Express the product of two linear expressions as the area of a rectangle. Divide the rectangle into four and invite the students to work out a simplified expression for the entire area of the rectangle.

Repeat with other brackets and include the difference of two squares.

A sheet with rectangles divided into four parts will speed the work up.

BBC Bitesize:http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/symbolsrev5.shtml

You should demonstrate FOIL, Grid and ‘happy man’ methods too – as pupils can use any method in the examination.

Factorise quadratic expressions a = 1, including the difference of two squares.

Card matching exercise (in pairs): some cards have two brackets and others have expanded expressions. Match the cards up. Ensure that there are some extra distractors.

A sheet with rectangles divided into four parts will speed the work up.

Tarsia jigsaws

Encourage the students to try out their ideas.

Solve quadratic equations of the form ax2 + bx + c = 0 by factorisation a = 1 and a negative.

Understand the link between the equation, the solutions and the graph.

Look at xy = 0. What are the solutions? Establish that either x or y or both can be 0 but one of them must be.

“Fill in the blanks” or “Unjumble” activity. Card matching activity; include some

blanks so that by checking the blank cards you have a good idea if they have understood the activity.

Card sort – equation on one card, factorised form on another card, graph on another card. Have some blanks for students to fill in themselves. Have

Jigsaws

BBC Bitesize:http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/quadequationshirev1.shtml

http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/quadequationshirev1.shtml



http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/symbolsrev5.shtml




Suggested teaching time 4-5 lessons Topic Manipulate algebraic expressions by expanding BRACKETS AND factorising quadratic expressions.

Solve quadratic equations of the form ax2 + bx + c = 0 A = 1.

Topic outline Suggested teaching and activities Suggested resources Points to notesome with same factor form but different y intercept.


Suggested teaching time 4 lessons Topic Understand similarity of triangles and other plane figures and use this to make geometrical inferences.

Topic outline Suggested teaching and activities Suggested resources Points to noteUnderstand the term “similar” and apply it to triangles.

Give students a sheet of triangles and they have to find out which ones are similar. Check with each other. Feedback to the class.

Look at cases of similarity where the scale factor is an integer.

Make geometrical inferences from similar figures including similar triangles.

Look at cases of similar triangles where the scale factor is not an integer. Calculate the scale factor. Calculate the lengths of missing sides in similar triangles.

Look at similarity in other plane shapes. Issue a sheet with similar plane shapes

and the answers at the bottom of the sheet. Students work out the answers and select the correct answer for each question from the bottom of the page.

Images for questions:http://images.google.co.uk/images?hl=en&q=similar+triangles&um=1&ie=UTF-8&ei=q2QeS8z-FInUjAfcucGmCw&sa=X&oi=image_result_group&ct=title&resnum=4&ved=0CBkQsAQwAw

http://images.google.co.uk/images?hl=en&q=similar+triangles&um=1&ie=UTF-8&ei=q2QeS8z-FInUjAfcucGmCw&sa=X&oi=image_result_group&ct=title&resnum=4&ved=0CBkQsAQwAw



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