Scheme of Work - Year 10 – J1 & J2
Presumed knowledge:
The following is presumed knowledge for Year 10 J1 & J2:
To be able to:
· Carry out long multiplication & long division.
· Multiply & divide with decimals.
· Calculate with negative numbers
· Add, subtract, multiply & divide with fractions
· Convert between fractions, decimals & percentages
· Rounding to 1 and 2 decimal places and to 1, 2 and 3 significant figures.
However, once a week – these 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 1
Second half of Autumn Term – Financial Capability task 2
Spring Term – Financial Capability task 3
Summer 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 problem
GCSE Mathematics: SOW J1 & J2 /Suggested teaching time / 4-6 lessons / Topic / Percentages /
Topic outline / Suggested teaching and activities / Suggested resources / Points to note /
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 must solve Functional questions on this topic.
Calculate the original amount when given the transformed amount after a percentage change. (Reverse percentage) / · Using whiteboards, give the 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. / Improving Learning in Mathematics Chapter N7:
http://tlp.excellencegateway.org.uk/pdf/mat_imp_02.pdf
Functional mathematics – Students must solve Functional 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 spreadsheet is possible here.
· Jigsaws
Autumn Term
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.
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: J1 & J2 /Suggested teaching time / 4 lessons / Topic / Graphs of quadratics, simple cubics and reciprocals /
Topic outline / Suggested teaching and activities / Suggested resources / Points to note /
Recognise graphs of quadratics, simple cubic functions, and reciprocal functions. / · Group activity: Give each group two quadratic graphs (one y = x2... the other y = -x2...), a cubic graph and a reciprocal graph to draw. Compare graphs with other groups.
· Card sort. Pair activity. On cards put a number of functions and their graphs and ask the pairs to match up the cards.
· Using whiteboards sketch graphs of given functions.
· Short consolidation exercise. / · Autograph could be used here. May have to draw without table of values
Improving Learning in Mathematics Chapter A7 (Pg 176-177):
http://tlp.excellencegateway.org.uk/pdf/mat_imp_02.pdf
Sketch graphs arising from real situations and use and interpret them. / 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. / · Examination papers from previous specifications are useful.
NRich - Fill it up This is a great
enrichment activity.
GCSE Mathematics: J1 & J2 /
Suggested teaching time / 2-3 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 events
Calculate 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.
http://nrich.maths.org/7222 / 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.
· Group activity: card sort, where some cards have events and other cards calculations; the groups match the two. / Functional mathematics – Students could solve Functional questions on probability.
GCSE Mathematics: J1 & J2 /
Suggested teaching time / 4-6 lessons / Topic / 3-D shapes, 3Dcoordinates; midpoints of line segments; Pythagoras’ theorem and coordinates /
Topic outline / Suggested teaching and activities / Suggested resources / Points to note /
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. 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 / This is good revision of Pythagoras
GCSE Mathematics: J1 & J2 /
Suggested teaching time / 4-6 lessons / Topic / Surface area and volume of prisms including cylinders, area and arc length of sectors of a circle. /
Topic outline / Suggested teaching and activities / Suggested resources / Points to note /
Convert between units of area and volume (starter)
Solve a range of problems involving volume and surface area of prisms including working backwards through a problem.
Calculate the area, arc length and perimeter of a sector of a circle.
Solve problems involving arcs and sectors / · Ask students to convert 130m2 into cm2 and show on mini whiteboards. Do similar with volume.
· Design and make packaging for an object. Students could be given an actual object to work to. Students to find the volume and surface area of the packaging. What about wastage? Maximum volume with minimum wastage.
· Revisit briefly area and circumference of a circle. 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. / Nrich have some excellent activities on
volume and surface area of cylinders.
Open box problem activity. (Maximum
volume)
Large paper to make a wizard’s hat. / Volume of prisms should be a review – as it should be prior knowledge.
Relevance to real life manufacturing problems.
Start with an angle of 45, 90° or 120° then move to other angles.
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
GCSE Mathematics: J1 & J2 /Suggested teaching time / 4-5 lessons / Topic / Straight line graphs /
Topic outline / Suggested teaching and activities / Suggested resources / Points to note /
Understand gradient and work out the gradients of straight lines. (A good starter) / · 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 ….
(Good plenary) / · 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)
· 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
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.