The KING’S Medium Term Plan – Mathematics

Year 10 senior programme – Learning cycle 5

Module Developing Number

Overarching

Subject

Challenging

question

‘How can we solve problems using a variety of mathematical skills?’

Lines of

Enquiry

Week 1: How can problem solving and GAP support exam progress?

Week 2: How can trigonometry be applied to real life?

Week 3: How do we represent trigonometry through graphs? (Foundation pupils will continue to develop

trigonometry skills)

Week 4: Foundation pupils will focus on how can we apply our knowledge of volume and density to real life

situations and develop problem solving skills? Higher pupils will also focus on how we apply knowledge of angles

to circle theorems to solve problems?

Week 5: How can the laws of probability effect decisions?

Week 6-7: Revision then assessment followed by gap teaching – from assessment analysis.

Progress

Objectives

By the end of LC5 in Mathematics SWBAT achieve these AQA objectives: Problem solving and exam skill development (AQA objectives S6) Week 1 (total 4 lessons)

The first 2 lessons of this week will be to develop deep mastery of pupil weaknesses from the LC5 exams as extended

GAP. This is due to the fact that the LC5 exam was the first real mock practice and more time is needed to walk through

the exam and then work on the areas for development.

The last 2 lessons will be to master techniques in problem solving and mathematical application. The new spec for

mathematics has a larger proportion of high mark questions based around real life problems, mixed applications and

rewards more marks for mathematical communication. We will use specimen papers from the new spec GCSE in order to

practice and develop problem solving skills. Trigonometry development (AQA objectives G20, G21 and R12) Weeks 2-3 (total 6 lessons) In this unit pupils will develop further mastery in applying knowledge of the 3 ratios of trigonometry. They will;

Know and use the trigonometric ratios

Apply the ratios to find angles and lengths in right-angled triangles in two dimensional figures

Compare lengths using ratio notation

Use the Sin and Cos rule for any triangle

Know the exact values of 0°, 30° 45°, 60° and 90°

Know the exact value of 0°, 30°, 45° and 60°

Plot the graphs of Sin, Cos and Tan

Area, volume and density development (AQA objectives G9, G16, G17, G18 and N8) Week 4 (total 4 lessons) In this unit pupils will develop further mastery in applying knowledge of area, volume and density. They will;

Review and apply formulae to calculate area of:

o triangles

o parallelograms

o trapezia

o compound shapes

o circles – area and circumference, area of sectors and lengths of arcs

Calculate surface area of spheres, cones and composite solids

Calculate the volume of 3D objects and composite shapes, calculate the volume of circular objects

Understand and apply circle theorems to angle problems

Understand and use density, mass in a variety of real life situations

Probability (AQA objectives P2, P3, P5, p6 and P8) Week 5 (total 4 lessons) In this unit pupils will develop a deeper understanding of probability in the real world including relative frequency,

permutations and combinations and probability Venn diagrams.

Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes or multiple future

experiments

Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability scale

Understand that empirical unbiased samples tend towards theoretical probability distributions with increasing sample size

Enumerate sets and combinations of sets systematically using tables, grids, Venn diagrams and tree diagrams

Calculate the probability of independent and dependent combined events, including using tree diagrams and other

representations, and know the underlying assumptions

NOTE: In week 3 there will be a mid LC assessment to check current progress.

Assessment at the end of week 6 will be against the above AQA objectives following on from 2 lessons of REACH

and revision. Gap teaching from analysis of assessments will take place in week 7 and 8 (LC5 has 2 weeks of

GAP).

IMPORTANT INFORMATION AND WEEKLY NEEDS

Personalised

Learning and

The AQA objectives above cover a wide range of mathematical skills and applications at varying levels of difficulty.

Reach work

and Mastery

Each practitioner has access to sets of exam based questions and activities that are aimed at these different levels of application and will ensure that all pupils are provided with work that will both challenge and support them at their targeted Grade Point as well as pushing them towards the next. All pupils will meet the progress objectives outlined above at a pace that suits them and will be delivered in a way that is personalised to how they learn. The use of iPads will be planned for carefully so that they can maximise learning.

Maths in real

life

Each week, there will be discussion and slides planned in so that pupils can value the relevance of what they are learning, which areas of life or careers that skill may be useful to and lessons will, as much as possible, contain resources where maths has to be applied to real world problems in order to find solutions. In this LC pupils will plot scatter graphs to find relationships between variables, and calculate rate of change. This will be followed by a large unit of work using Pythagoras’ theorem, trigonometry and area and volume. These skills are highly applicable to real life situations such as architecture, interior design, agriculture, construction, technical drawing, bearings and many more areas.

PSHE and

ASPIRE

development

in maths

The weekly objective slides link maths to careers, life skills and people who have utilised maths to solve world problems. Pupils will get opportunities to research famous mathematicians and how maths has helped to develop countries. Pupils will peer asses work, work with each other, support each other and demonstrate their respect and understanding of others. Independent study will encourage them to become responsible resilient learners. Where relevant maths lessons will provide links to financial safety and making well-judged decisions, ethical investment, understanding of tax, borrowing and lending, the purpose and importance of maths for life and how it has helped others. In week 5 (probability) they will dicuss the ethics of gambling and financial implications.

Planning for

Feedback

Pupils will receive written feedback each week in the form of teacher marking, peer/self-assessment and small quizzes to check key knowledge. Mark schemes will be provided where appropriate for pupil self-assessment and development. REACH lessons each week will allow time for acting on feedback and making improvements to their work in order to develop further and fill in GAPs.

REACH and

Support

Each week there will opportunities for support with in class intervention, group intervention and after school catch-up on a Tuesday. Monday lunch time will provide a time for pupils to REACH by practicing GCSE papers in a club. Friday lunch time will provide pupils in need of homework support, classwork development or just time to practice should they need it.

MEDIUM TERM PLAN

Week 1

4 hours of

lessons plus 1

hour of

homework

each week

Additional

intervention

and reach is

provided

during

lessons and

where

possible

outside of

lessons within

morning

ASPIRE

sessions or

after school.

Line of Enquiry: Shared at the start of each week and reflected upon at the end. Here is how each week is broken down;

Hypotheses for the week’s lessons; These will act as the title for the lessons, in which the work done will be reflected upon to either prove or disprove each hypothesis. It may be that 1 hypothesis can last more than 1 lesson yet others are achieved quickly. This depends upon how far the pupils move on from the knowledge section and get through the different success criteria within the main body of the lesson. All hypotheses should be answered to some degree over the course of the week.

Learning Intentions: These are the key objectives laid out by the exam board (as seen above).

Weekly success criteria for completion across 4 lessons (or across 3 for weeks with REACH lessons or

tests);

This is where after teaching the knowledge necessary the pupils will work at their grade point on exam questions in order to achieve the learning intention. Week 1 Line of Enquiry: How can problem solving and GAP support exam progress? Hypothesis 1 (to last 2 lessons) – We can apply our strengths to develop our weaknesses Learning intention:

Understand the areas for development in order to gain higher marks in the next exam

Knowledge:

All pupils will be provided with REACH and GAP work based on their mock exam analysis from both the non-calculator and

calculator papers. They will utilise the report generated from the exam analysis and be directed to complete exercises

based on their key needs for development and will work at their GP and progress upwards where appropriate.

Success criteria:

All pupils will have specific success criteria based upon their areas of development and will work in groups. Mark schemes

will be provided as well as modelled answers.

Higher pupils will develop algebra and work on quadratics, simultaneous equations and applying this to solve problems.

Hypothesis 2 (this will last for 2 lessons) – There is one clear method and set of steps to follow when solving problems through maths application Learning intentions (not exhaustive):

Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use

appropriate calculation strategies at each stage, including calculator use.

Tabulate systematically the information in a problem or puzzle; identify and record the steps or calculations needed

to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy.

Suggest, plan and develop lines of enquiry; collect, organise and represent information, interpret results and review

methods; identify and answer related questions.

Represent and interpret sequences, patterns and relationships involving numbers and shapes; suggest and test

hypotheses; construct and use simple expressions and formulae in words then symbols (e.g. the cost of c pens at

15 pence each is 15c pence at a more basic level). Explain reasoning and conclusions, using words, symbols or

diagrams as appropriate.

Success criteria:

All pupils will have specific success criteria based upon the areas of problem solving they are attempting and will work in

groups in a carousel. Mark schemes will be provided as well as modelled answers.

Home learning: Given Tuesday of each week and due in Tuesday the following week.

This week pupils will complete a specimen GCSE exam to help develop their exam skills and problem solving abilities.

Week 2

4 1hr lessons

plus 1hr

homework

Week 2 Line of Enquiry: How can trigonometry be applied to real life? Lesson 1 - REACH time to be given to respond to feedback. Hypothesis 1 – Angles can be used to calculate missing edges in triangles Learning intention:

Know and use the 3 trigonometric ratios; be able to label the sides of triangles

Apply the ratios to find specific lengths in right-angled triangles in two dimensional figures

Knowledge:

GP 4 – 5 = These pupils will be taught how to label triangles with ‘opposite’, ‘adjacent’ and ‘hypotenuse’ depending upon

the position of the angle given. They will learn how to identify which ratio they would use to find the missing length.

GP 6 = As above plus methods for calculating the missing side of a right angled triangles.

Success criteria:

GP 4 – 5 = Pupils will be able to identify and label the different sides of right angled triangles in a variety of situations. They will label (with reasons) the hypotenuse, adjacent and opposite sides according to where the angle is positioned. These pupils will then use this knowledge in order to note down which trigonometric ratio and lengths would be used to calculate one of the sides given the angle. GP 6 = As above plus pupils will be able to use the ratios to begin calculating the lengths of missing sides of right angled triangles. GP 7 = Pupils will apply the ratios to other 2D shape situations and exam questions.

Hypothesis 2 – Three side lengths are needed when calculating a specific angle in a triangle Learning intention:

Apply the ratios to find angles in right-angled triangles in two dimensional figures

Knowledge:

GP 4 – 5 = These pupils will be taught how to develop skills when calculating the missing side of a right angled triangles.

GP 6 – 7 = Pupils will be taught how to use inverse formulae and methods for calculating the missing angle of a right

angled triangles. They will be taught how labelling the sides will help them to identify which ratio to use.

Success criteria:

GP 4 – 5 = Pupils will be able to master using trigonometry to calculate the length of a side of a right angled triangle by applying the knowledge of the sides and ratios from the first lesson. GP 6 = As above plus pupils will be able to use the inverse ratio method in order to calculate the angle in a right angled triangle. They will need to practise using a calculator effectively and how the buttons are needed when working with Sin, Cos and Tan. These pupils will need to decide which lengths of the triangle are needed and which ones are unnecessary. GP 7 = Pupils will apply the ratios to other more complex 2D shape situations and GCSE questions from the new spec and

past papers.

Hypothesis 3 – Trigonometry can be used for any triangle Learning intention:

Use the Sin and Cos rule for any triangle

Knowledge:

GP 4 – 5 = These pupils will be taught how to calculate the missing angle of a right angled triangles if they have mastered

the previous learning intentions.

GP 6 – 7 = Pupils will be taught how to apply the Sine and Cosine rules for calculating sides and angles of any type of

triangle.

Success criteria:

GP 4 – 5 = Pupils will be able to calculate the angle in a right angled triangle using Sin, then move on to Cos and Tan questions. They will practise using a calculator and the ‘shift’ button to apply the inverse method. REACH: Pupils will figure out which ratio to use in mixed questions. GP 6 = As above plus pupils will be able to continue mastery in finding a mixture of angles and sides using trigonometry by selecting the correct ratio and method on the calculator. GP 7 = Pupils will apply knowledge to problem solving type questions and mixed problems.

Hypothesis 4 – Trigonometry can be applied to 3D shapes (2 lessons will be spent on this hypothesis as it needs a

lot of time to develop mastery)

Learning intention:

Apply the ratios to problems with 3 dimensional figures

Knowledge:

GP 4 – 5 = Pupils will be given exam questions on Pythagoras’ Theorem and basic Trigonometry.

GP 6 – 7 = Pupils will be taught how to solve problems applying trigonometry to 3D problems and scenarios.

Success criteria:

GP 4 – 5 = Pupils will be able to solve problems on both Pythagoras and trigonometry in a REACH situation. This is an opportunity for them to practise and improve on areas they are still unsure of in this unit. GP 6 – 7 = Pupils will be able to find angles and lengths of dimensions within 3D objects such as pyramids, cuboids, prisms etc. They will solve real life problems and need to figure out how to apply different sections of trigonometry and Pythagoras to find the solution. Home learning: Given Tuesday of each week and due in Tuesday the following week.

This week pupils will complete a GCSE exam based booklet with a variety of questions involving Pythagoras and trigonometry.

Week 3

4 1hr lessons

plus 1hr

homework

Week 3 Line of Enquiry: (Higher) How do we represent trigonometry through graphs? (Foundation pupils will continue to develop trigonometry skills and recall knowledge on Pythagoras’ Theorem and using this with 3D objects) There will not be a full REACH lesson due to the midterm test being completed in lesson 3, but students will be given the opportunity to respond to feedback and make quick improvements within that time. Exam technique will be developed and studied in lesson 4. During this week LGP pupils will continue to practice and master Pythagoras and trigonometry.

Hypothesis 1 – y=cosx and y=sinx go through the origin Learning intention:

Understand how to plot the graphs of Sin and Cos:

Know the exact values of 0°, 30° 45°, 60° and 90°

Understand the effect of a coefficient higher than 1 in y=sinx and y=cosx

Knowledge:

Pupils will be taught how to create tables of values for plotting sin and cos graphs in order to find trigonometrical solutions.

Success criteria:

GP 6 = Pupils will plot graphs of sin and cos onto a 4 quadrant axis. They will comment on the differences between the sin

and cos graphs.

GP 7 = Pupils will plot graphs and will use these to find solutions such as cosx = 0.5 etc. Pupils will use the graphs to

understand and explain why the values of sin and cos (as seen in the second learning intention above) are what they are.

GP 8 = Pupils will determine and demonstrate how adding a coefficient effects the graphs of sin and cos.

Hypothesis 2 – y=tanx is an infinite wave Learning intention:

Understand how to plot the graph of Tan and it’s differences to sin and cos:

Know the exact values of 0°, 30° 45°, 60° and 90°

Understand the effect of a coefficient higher than 1 in y=tanx

Knowledge:

Pupils will be taught how to create tables of values for plotting graphs of tan in order to find trigonometrical solutions.

Success criteria:

GP 6 = Pupils will plot graphs of tan onto a 4 quadrant axis. They will comment on the differences between the sin and cos

graphs to the graph of tan.

GP 7 = Pupils will plot graphs and will use these to find solutions. Pupils will use the graphs to understand and explain why

the values of tan (as seen in the second learning intention above) are what they are.

GP 8 = Pupils will determine and demonstrate how adding a coefficient effects the graph of tan.

Lesson 3 – Midterm test and mini gap The midterm will contain quick knowledge check questions on weeks 1 to 3 content as well as a problem solving application task. Lesson 4 – Exam practice lesson Pupils will do an exam walk through and develop exam techniques. A past GCSE paper will be used and focus will be on the larger problem solving questions.

Home learning: Given Tuesday of each week and due in by Tuesday of the following week.

This week pupils will complete a new spec specimen GCSE paper in order to develop exam technique and gain further exposure to develop their question comprehension. They will be directed to certain questions to make it personalised.

Week 4

4 1hr lessons

plus 1hr

homework

Week 4 Line of Enquiry: Foundation pupils will focus on how can we apply our knowledge of volume and density to real life situations and develop problem solving skills? Higher pupils will also focus on how we apply knowledge of angles to circle theorems to solve problems? Lesson 1 - REACH time to be given. Pupils can work through key areas from the midterm or the past paper done in lesson 4 week 3 as well as respond to feedback in marking last week.

Hypothesis 1 – Volume and surface area require the same method Learning intention:

Calculate the surface area of 3D shapes

Calculate the volume of 3D shapes and prisms, including cones and spheres

Knowledge:

GP 4 – 5 = Pupils will be taught why the formulae for volume of cubes, cuboids and prisms work and where they come

from to develop a deeper understanding. Problems will be modelled so that pupils demonstrate the appropriate steps in

their work when solving questions. Pupils will be taught how to calculate surface area and set out the problem clearly.

GP 6 – 7 = Pupils will be taught how to calculate the surface area and volume of cones and spheres.

Success criteria:

GP 4 – 5 = Pupils will solve problems calculating the volume of cubes and cuboids, triangular prisms and composite shapes. They will apply this to real life problems, practice past GCSE questions and self-assess against a mark scheme. Pupils will look at NETS and viewpoints in order to understand the meaning of surface area. They will recall area from an earlier LC this year and apply it to calculate the surface area of cuboids, triangular prisms (may need to apply Pythagoras) and composite shapes. Pupils will create a VIF about the differences between volume and surface area. GP 6 – 7 = Pupils will recall the above. They will calculate volume and surface area of triangular prisms (applying Pythagoras and trigonometry) before moving on to cones and spheres. They will learn the formulae off by heart via a memory task. Hypothesis 2 – Volume and capacity represent the same thing Learning intention:

Solve problems with real life volume and capacity

Knowledge:

Pupils will be reminded of the units of volume and of capacity and the purposes of these in life.

Success criteria:

GP 4 – 5 = Pupils will be able to sort units into categories of metric, imperial, capacity and volume. They will provide examples of each and where they are used. Pupils will solve problems calculating the volume and capacity of real life objects. Pupils will use conversion graphs. GP 6 – 7 = As above as pupils need to revise this unit. Pupils will carry out more complex conversions and draw/use conversion graphs. Hypothesis 3 – Density, volume and mass have a direct proportion to each other

Solve problems in a real life context with density, volume and mass

Knowledge:

GP 4 – 5 = These pupils will continue with volume, surface area and basic density problems.

GP 6 – 7 = Pupils will be taught about density and mass and how to calculate them. Problems will be modelled as full

written examples using real life worded questions and GCSE tasks.

Success criteria:

GP 4 – 5 = Pupils will practice a variety of application, real life and exam style questions to master the content from this week. GP 6 + = Pupils should be able to recall the formula for calculating mass, density and volume. They will apply the formulae to solve a variety of problems with density in a range of real life situations. This is an opportunity for them to make links to physical science and they will also answer questions on types of matter, define density and volume, mass and capacity and understand the differences between them and what they are used for as units.

Home learning: Given Tuesday of each week and due in Tuesday the following week.

This week pupils will complete a GCSE exam based booklet with a variety of questions involving volume, density and problem solving applications.

Week 5 Line of Enquiry: How can the laws of probability effect decisions? Lesson 1 of the week: REACH time followed by start of probability unit Pupils will have time to make improvements from their feedback before starting the next unit of work.

4 1hr lessons

plus 1hr

homework

Hypothesis 1 – Experimental probability backs up theoretical probability Learning intention:

Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes or multiple future

experiments

Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability

scale

Knowledge:

ALL GP = Pupils will need to recall the key terms and definitions, how to label the probability scale and write probabilities

as fractions.

Success criteria:

ALL GP = Pupils will define with examples the terms; probability, impossible, certain, even chance, equally likely, likely, unlikely, outcomes, event and mutually exclusive. They will calculate probabilities of events happening and NOT happening using both words and fractions (FDP). Pupils will discuss a variety of theoretical situations and compare them to real life. Pupils will carry out an experiment to test probabilities. GP 4 – 5 = Pupils will carry out the experiment with coins. They will make a prediction and back it up with theoretical probability. They will come up with their own conclusion. Data collection tables will be provided. GP 6 + = Pupils will create and design their own experiment with hypotheses and a small plan. They will analyse their findings and apply calculations such as percentages to compare results. All pupils will then calculate the relative frequency from their results and describe the meaning of this in their books. Hypothesis 2 – Bias is a matter of opinion Learning intention:

Understand that empirical unbiased samples tend towards theoretical probability distributions with increasing

sample size

Enumerate sets and combinations of sets systematically using tables, grids, Venn diagrams and tree diagrams

Knowledge:

GP 4 – 5 = Pupils will be taught how to complete tree diagrams for problems involving replacement. They will be shown

how to calculate probabilities of single and dual events from probability trees.

GP 6 – 7 = Pupils will recall tree diagrams then be shown what happens when dealing with non-replacement events.

Success criteria:

GP 4 – 5 = Pupils will complete tree diagrams with both 2 and 3 sets of outcomes (with replacement). GP 6 – 7 = As above but will also complete tree diagrams without replacement. These pupils will then move on to worded problems where they will be required to understand the events and draw the probability tree themselves before answering a variety of questions to calculate probabilities. All pupils will need to learn and apply the AND/OR rules. They will write VIFs to help them understand when to use them. REACH: HGP pupils will use Venn diagrams and apply the AND/OR rules to calculate probabilities. Further discussion and development may be done here for HGP to deepen understanding of theoretical probabilities and bias. This will be supported through a worksheet. Hypothesis 3 – Theory does not allow room for assumption

Learning intention:

Calculate the probability of independent and dependent combined events, including using tree diagrams and other

representations, and know the underlying assumptions

Further knowledge:

GP 4 – 5 = Pupils will continue to calculate probabilities in different scenarios to master understanding and develop

knowledge.

GP 6+ = Pupils will develop through discussion a deeper understanding of theory vs real life and why we cannot make

assumptions within theoretical situations.

HGP pupils will continue in this lesson to work on Venn diagrams, tree diagrams and more complex probability questions.

Hypothesis 4 – OR & AND are important in probability calculations

Learning intention:

Understand how to apply the AND/OR rules in a variety of circumstances

Further development:

ALL GP = Pupils will all further develop the application of the AND/OR rules in a number of situations form a variety of

problems (mainly from GCSE papers and functional maths). They will need to apply all of the different methods learned

within this unit and will be provided with problems at different GP to allow them to master and develop.

Home learning: Given Tuesday each week and due in by Tuesday the following week.

This week pupils will have a graded revision booklet on LC5 content which will be worked through and marked with peers at the start of week 6 to help with exams.

Week 6

2 1hr lessons

including end

of term exam (2

hours).

Line of enquiry: Continued from week 5 Lesson 1 will be REACH work to develop further mastery of week 5 content. Lesson 2 will be for Revision and home learning resources will be used to support. Lessons 3 and 4 will be rationalised for the end of LC5 exams to be taken in the main hall – one calculator and one non-calculator paper spanning 2 hours 45 minutes.

Gap Analysis Reinforcement

Gap

Reinforcement

in week 7

As seen in the lesson activities each week, gap teaching will not just be at the end of the semester after exam analysis has

taken place. Gap teaching is an integral part to each unit of work and will consist of summary sheets, mini-tests and tasks

where gaps can be filled and REACH activities can be delivered.

Extended Learning and links across the curriculum for numeracy.

(This is not part

of the ‘timed’

schedule but is

seen as

additional

support)

Extended learning will in a variety of forms. During home learning pupils may be asked to use the following sites where

they complete quick quizzes, CIMT tasks, GCSE style questions and more open ended tasks.

1) Levelled quizzes

http://www.educationquizzes.com/ks3/maths/ 2) Lots of maths online help and activities – as well as mini tests

http://www.bbc.co.uk/schools/websites/11_16/site/maths.shtml

3) http://uk.ixl.com/math/year-7

This link is useful for additional revision and practice on all areas of maths. For semester 4 pupils should click on

the Geometry areas for practice questions.

4) Maths Made Easy provides a large bank of graded GCSE revision tasks, tests, lessons and topic papers.

http://www.mathsmadeeasy.co.uk/

http://keshmaths.com/gcse-maths-takeaway-3/

5) Maths-drills is another website with a rich variety of resources for revision and practice.