How does Algebra and Geometry help us make sense of our world?

Transcription

1 Year 9 senior programme Learning cycle one The KING S Medium Term Plan Mathematics Module Building on prior learning Overarching subject Challenge question Lines of Enquiry Geometry and Algebra (Angles, shapes and lines, Sequences, Algebraic Graphs and functions). In LC1 the pupils did a lot of work on building up their knowledge and understanding of algebra. Within the first 3 weeks of this LC they will work on calculations with angles in polygons and move onto area, perimeter, volume and surface area. They will be able to apply what they developed in algebra from LC1 to solve problems in this shape unit during week 3. After this the algebra work continues with sequences, which in turn develops into higher functions which produce line graphs. How does Algebra and Geometry help us make sense of our world? Week 1: How can we use our knowledge of 2 dimensions to calculate angles? Week 2: How can I use 2D shapes to prove the special properties of other shapes? Week 3: Can ratio and proportion help us to discover similarity between objects? Week 4: How do we apply formulae to predict numbers? Week 5: How can algebraic sequences be applied to straight line graphs? Week 6-7: Revision and assessment followed by gap teaching from assessment analysis. Progress Objectives An overview of the LC s key learning intentions: Recall how to calculate missing angles on a straight line and around a point. Analyse how angles on parallel lines work. Evaluate how to calculate missing angles on parallel lines. Understand how to use triangles to calculate interior and exterior angles of polygons. Identify congruent and similar shapes as well as their intrinsic properties.

2 Recall how to find missing terms of different sequences. Analyse how to calculate the nth term given a sequence. Recall how to plot vertical a horizontal lines as well as their gradient. Evaluate how to plot straight lines given the formula y = mc + n. Interpret gradients and intercepts of linear functions. By the end of LC2 in Mathematics SWBAT: Geometry Angles (AQA G1, 3, 4, 6, 19, 20) Weeks 1-3 In this Geometry unit pupils will master the following: Recognise and use relationships between angles and 2D shapes. Apply the properties of triangles and quadrilaterals in order to calculate missing angles in a variety of problems Calculate angles on sets of parallel lines and pupils will understand the terms alternate and corresponding. Analyse how to find the interior and exterior angles of any polygon and evaluate how they can demonstrate a proof. Understand the meaning of congruence in shapes by applying their knowledge of shape properties and angle facts. Apply Pythagoras Theorem to evaluate congruency of triangles. Algebra Sequences (AQA A23, 24, 25) Week 4 In this Algebra unit pupils will master these skills; Recognise how sequences work and develop. Understand basic rules moving from one term to the next and apply this understanding to sequences made of diagrams and patterns. Apply their knowledge of multiples to find the nth term. Analyse how to find any term in a sequence using the nth term. Generate sequences using the nth term. Apply previous knowledge to quadratic sequences: o Find missing terms in a given sequence. o Apply their knowledge about squared numbers to calculate the nth term of quadratic sequences. o Generate a quadratic sequence given the nth term.

3 Algebra Graphs (AQA A8,9,10,12,14) Week 5 In this Algebra unit pupils will develop their knowledge of algebra further by mastering the following: Understand how to use the equation of a straight line in order to plot them. Recall knowledge on substituting values into algebraic expressions as well as on rearranging formulae. Understand what the gradient and intercept are. Analyse how to draw and identify parallel lines and calculate the gradient of a line. Evaluate how to find a line s gradient and intercept in order to find a line s equation. Study in depth negative gradients, and investigate perpendicular straight-line graphs 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. IMPORTANT INFORMATION AND WEEKLY NEEDS Personalised Learning and Reach work and Mastery Maths in real life Cognitive Acceleration The AQA objectives above cover a wide range of mathematical skills and applications at varying levels of difficulty. 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. 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. CA will be taught in a variety of forms throughout the Learning Cycle, particularly in the Do Now or Plenary phase of the lessons where more open-ended questions/tasks will be provided to provoke deeper thought processes. However, in weeks 2 and 4 full CA lessons will be delivered with resources from Let s Think!

4 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. 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 Line of Enquiry: How can we use our knowledge of 2 dimensions to calculate angles? Here is how each week is broken down; Ø 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. Ø Learning Intentions: These are the key objectives laid out by the exam board (as seen above). Ø 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. Hypothesis 1 The properties of a triangle help when calculating missing angles Learning intention: Ø Derive and apply the sum of angles in a triangle and apply the exterior angle theorem : GP 1/ 2 = Delivery to recall and identify types of angles and the meaning of perpendicular and parallel lines. GP 2 = Pupils will be taught about the properties of different types of triangles and the notation used to show equal sides and angles (e.g. all 3 angles in an equilateral wold be given the same letter).

5 GP 3 = Demonstration of how to position a protractor correctly, then read the numbers in the right direction from zero. Pupils will be given methods for measuring the more difficult reflex angles. Pupils will be taught how to check answers and see that they should add up to 180 degrees. GP 4 = Recall with pupils how to find missing angles in triangles and on straight lines and how to show method. GP 1/2 =Quick quiz questions to match up types of angles to their names, draw sets of parallel and perpendicular lines and use arrow labels to highlight parallel lines on shapes. GP 2 = Students use notation and properties to identify isosceles, scalene, equilateral and scalene triangles. GP 3 = Measure a range of reflex, acute and obtuse angles accurately within 1 degree; analyse and explain why an angle measurement given in a diagram is wrong, GP 4 = Discover for themselves the exterior angle theorem of a triangle by solving missing angle problems with triangles involving an exterior angle. Hypothesis 2 Parallel lines within quadrilaterals determine the size of the angles Learning intention: Ø Deduce and apply the properties and definitions of special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus to find angles : GP 2 = Pupils will be taught about the properties of different types of quadrilaterals such as symmetry, equal sides, equal angles and parallel lines. GP 3 = Recall the angle sum in a triangle. Demonstrate how to calculate missing angles in a quadrilateral, focusing on the properties of parallelograms and kites where some angles are known to be equal. GP 4 = Demonstrate proofs such as why the interior angles of quadrilaterals always add up the angle sums that they have. GP 5 = Recall with pupils how the Pythagoras Theorem works to find right angled triangles. Show pupils how they can split up an isosceles to make 2 right angled triangles. GP 2 = Quick task matching up quadrilaterals and their names. Discussion about how they knew by indicating properties such as 4 equal angles, 2 pairs of parallel lines etc.

6 GP 3 = Pupils will complete questions on calculating missing angles in quadrilaterals, they will have to deduce the correct method by applying knowledge of special properties such as symmetry, angle sums and even how having sets of parallel lines or symmetry can help to locate equal/opposite angles. GP 4 = Pupils will carry out an investigation splitting quadrilaterals into triangles (2 x 180 degrees) and cutting the corners of quadrilaterals off to create a full set of angles around a point (360 degrees). They will use this to describe and prove the fact in a question. GP 5 = Pupils will solve problems where they will need to apply Pythagoras Theorem to deduce if a triangle is isosceles and therefore find any missing angles. Hypothesis 3 The straight line rule helps when calculating angles round a point Learning intention: Ø Recall the properties of angles at a point, angles on a straight line, vertically opposite angles and apply to find missing angles. : GP 2/3 = Test pupils through Q&A quickly on how they would find the missing angle on a straight line and round a point. Show example if necessary (builds on from earlier in the week). GP 3 = Demonstrate how to draw and spot opposite angles and how they differ from angles around a point. Remind pupils to look for straight lines in order to calculate missing angles. Once practice questions have been done, ask pupil to discover the special property about opposite angles. GP 3 / 4 = Show an example on the board where pupils need to work through using the above skills to calculate any missing angles. Provide pupils with the opportunity in groups to at first figure it out and report back. GP 4 = Recall with pupils why the same letter may be used for more than 1 angle in a shape. Discuss methods for finding the size of an angle where only letters are provided and no actual angle sizes. For instance, if a parallelogram has an angle of 55 degrees and 3 unknown angles, but the angles are labelled X, X and Y, how do they calculate them? GP 2/3 = Recall angle facts on straight lines and angles round a point to solve quick questions showing full calculations. GP 3 = Pupils will apply these angle facts in order to calculate vertically opposite angles using different methods such as angles on straight lines. They will discover an important fact about opposite angles which provide a quicker solution to the problems. GP 3 / 4 = Pupils will be provided with a variety of questions where they will need to analyse how to find missing angles in shapes and diagrams by applying the facts developed above. GP 4 = Pupils will solve problems evaluating how to find the value of a missing angle where letters are used in place of numbers.

7 They will need to show applications of shape and angle properties learned throughout the week so far. Hypothesis 4 Parallel lines cannot create angles Learning intention: Ø Understand and use alternate and corresponding angles on parallel lines. : Note: The 3 lessons prior contain all the knowledge that must be recalled and applied in order to achieve this learning intention and answer the hypothesis to its fullest. GP 3 = The class will recall and discuss both straight line and opposite angle facts. Demonstration of a line crossing over a set of parallel lines creating a number of angles. GP 4 = Skill recall of how to position protractors correctly by asking pupils to draw a quick angle and measure it. Provide pupils with diagrams of parallel line angles and help them to measure and record their findings. GP 4-5 = Demonstrate an example of a more complex diagram of a parallel lines problem, which also incorporates a triangle and opposite angle aspect. Work through the order of calculations with the pupils and the steps needed to score maximum marks. GP 3 = Understand how to calculate angles on parallel lines simply by using the straight line angle rule and knowledge of opposite angles or those around a point. GP 4 = Pupils will measure angles accurately on a diagram in order to investigate how angles work along sets of parallel lines. Through their own discovery they will understand how we calculate alternate, interior and corresponding angles (also known as Z, C and X angles respectively) without the need for measuring, but by uncovering the rules and facts (e.g. alternate angles look like a Z and are always equal). GP 4-5 = Pupils will work through a set of problems where they will need to evaluate how to calculate angles in diagrams involving sets of parallel lines that also incorporate other situations, such as triangles and opposite angles. They will need to apply and use their knowledge of types of triangles, notation marks and angle sums. Home learning: Given every Tuesday, due in by Tuesday each week.

8 Week 2 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 For the first home learning tasks, pupils will do an online assignment using the Stuck for schools website. Questions will be based around all work done this week and will last for 1 hour. Videos and hints are available to support development. Pupils will get instant feedback on their progress and have the opportunity to improve scores. Line of enquiry; How can I use 2D shapes to prove the special properties of other shapes? Lesson 1 (first half) of the week: Cognitive Acceleration Task Illusion or Reality? Look at the following pictures. Do the lines really touch? Why/Why not? What do you think is happening there? How far can you see in the distance? Now look at the following picture. What do you see there? What could you calculate there?

9 Lesson 1 (second half): REACH improving my knowledge of angles on parallel lines Pupils will use this lesson to engage with and respond to work marked and done the previous week. They will read through teacher comments and respond by following a given set of criteria. This will allow them to make improvements on their work, carry out corrections, seek help and make further progress before moving to the next unit of work. To extend their knowledge of the content from week 1, pupils will be given examination type problems from the new GCSE specification at and above their targeted grade point to stretch their comprehension. Stuck for schools will also be used as REACH activities and can be personalised in the level of difficulty. Hypothesis 1: Triangles are useful when calculating the interior angles of polygons with many sides Learning Intention: Ø Understand how to calculate interior angles of regular polygons. GP 2+ = A quick recall question task to be provided in order to check retention of triangle angle facts. Demonstrate that all quadrilaterals can be split into 2 triangles and explain to pupils that they will apply this principle to other polygons. GP 3+ = Show an example of a regular pentagon and discuss with pupils how to find the size of one angle. GP 2+ = Pupils will solve problems which will require them to apply their knowledge of the angles in triangles in order to investigate and deduce the sum of interior angles of polygons by breaking a polygon down into triangles, GP 3+ = Pupils will understand how to calculate the interior sum of angles of polygons up to a decagon and analyse how to calculate the missing interior angles of regular polygons. A variety of polygon questions will be provided. Hypothesis 2: Interior angles can only be calculated in regular polygons Learning intention: Ø Apply knowledge of interior angles to understand how to calculate interior angles of irregular polygons. GP 4 = Demonstrate with an example how to calculate the missing angle in an irregular pentagon. Show pupils how to record their findings of angle sums into a table. GP 5 = Discuss with pupils what they notice about what happens to the interior angles sum when a polygon gains an extra side.

10 GP 4 = Pupils will have a range of different polygons up to a decagon and will analyse how to calculate the missing interior angles of irregular polygons by using the angle sums discovered in answering previous hypothesis. GP 5 = Pupils will discover for themselves a pattern in the angle sums of interior polygons linked to the number of sides they have. They will therefore evaluate, deduce and create the formula for calculating interior angles. The table created in GP 4 will be used to support. Hypothesis 3: Exterior angles have to be calculated in the same way as interior angles Learning intentions: Ø Analyse how to calculate the exterior angles of regular and irregular polygons. Ø REACH: Evaluate how to demonstrate proofs. GP 3 = Task delivered to recall angle properties of straight lines, identify what an exterior angle is and how to label them. GP 4 = Demonstrate how exterior angles add up to 360 degrees on polygons. Discuss how on a regular polygon they will all be the same size hence a simpler type of problem. GP 5 = Demonstrate an exam question where the pupils are given the sum of interior angles of a regular polygon and are to work out how many sides it has (no diagram is provided). Discuss how this can be applied if the exterior angle is the one that is given (they may need to recall knowledge of straight line angles again). GP 6 = Show exam questions which ask for an explanation as to what the interior or exterior angles add up to in polygons and how they can prove it. Discuss ideas with the pupils and facilitate them with opportunities to investigate. GP 4 = Pupils will complete questions to develop their understanding of how to calculate the exterior angles of regular polygons by applying the rule that they always add up to 360 degrees. GP 5 = Pupils will need to apply this knowledge in order to calculate the exterior angles of irregular polygons where each angle is a different size. GP 5+ = Pupils will evaluate how many sides a shape has, given the exterior angle of a regular polygon, or the interior angle sum of regular polygons. They will need to use their angle sum table and the facts found previously to solve problems. GP 6 = Pupils able to move onto high REACH tasks will evaluate how to prove the interior angle sums and the exterior angle sum of polygons (use of simple formulae and triangles). They can use previous knowledge of triangles and how they fit into other polygons.

11 Key to success: GCSE questions GP2 to GP 6 apply all geometry work done so far to solve problems involving a variety of these skills in one. Home learning: Given every Tuesday, due in by Tuesday each week. Home learning this week will be a targeted booklet on all work done over the last 2 weeks in preparation for their mid LC mini test in week 3. Week 3 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 Line of enquiry; Can ratio and proportion help us to discover similarity between objects? Lesson 1 of the week: REACH lesson improving my calculations with exterior and interior angles Pupils will use this lesson to engage with and respond to work marked and done in week one. They will read through teacher comments and respond by following a given set of criteria. This will allow them to make improvements on their work, carry out corrections, seek help and make further progress before moving to the next unit of work. To extend their knowledge of the content from week 1 pupils will be given examination type problems from the new GCSE specification at and above their targeted grade point to stretch their comprehension. Stuck for schools will also be used as REACH activities and can be personalised in the level of difficulty. Prior learning will be ascertained in this lesson about simple properties of shapes and the meaning of the terms enlargement (including scale factors), reflection and rotation from year 8. Hypothesis 1: Congruent shapes cannot be a reflection or rotation of themselves Learning intention: Ø Understand what is meant by triangle congruence and identify congruent triangles and shapes. GP2 to 3 = Demonstrate shapes that have been enlarged and discuss with pupils what scale factors have been used. Definitions of scale factor, congruency, and the transformations reflect, rotate, enlarge with supporting diagrams. GP 3+ = Discuss with pupils how sets of shapes in a question have been transformed, for instance reflected or enlarged; which transformations mean that a shape cannot be congruent and which ones do not matter? GP 2 to 3 = Pupils will recall how to use and find scale factors using a variety of simple problems with sets of enlarged shapes (i.e. non congruent). They will move on to work where they apply this knowledge in order to identify congruent shapes and in

12 particular, understand how to find congruency in triangles by looking at the position of angles, their size and also the lengths of the sides. Pupils need to analyse which triangles are congruent and be able to explain why. GP 3+ = Apply knowledge of the types of transformations (enlargement, reflection and rotation) to analyse congruency in order to gain a concrete understanding of what congruent means. Pupils need to evaluate that for certain types of transformations, shapes can be congruent. Pupils need to look at a variety of pairs of triangles and look at the position of angles and adjacent sides to evaluate congruency. REACH = create a pair of congruent triangles, applying a transformation where possible. Hypothesis 2: Similarity means that shapes only have to have the same number of sides Learning intentions: Ø Analyse similarity in triangles and apply the properties of quadrilaterals to derive conclusions about angles and sides; Ø REACH - Evaluate how to apply Pythagoras theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs GP3 = Quick task to recall how scale factors alter the size of a shape using a multiplier e.g. SF 2 or more difficult, SF ½. GP 3+to 4 = Demonstrate how a shapes side lengths change but their angles remain the same when a shape is enlarged. GP 5 = Examples taught on how to work with more difficult fractional scale factors and how to find the scale factor that has been used in similar triangles. GP 5+ = Demonstrate how to test if 2 triangles are similar by finding the scale factor and testing it on every side. GP 3 = Pupils quickly identify a scale factor that has been used in sets of enlarged shapes. GP 3+ = Pupils solve quick problems where they need to analyse the scale factor that has been used to alter the size of the shape. GP 4 = Pupils will apply this understanding to identify similar shapes with proportions such as twice as large/small etc., by calculating the change in the lengths of its sides. GP 5 = Pupils will work through problems finding the scale factor of the similarity proportion such as 1/3 bigger. GP 5+ = Pupils will apply similarity proportions in order to find the length of a side in both triangles and quadrilaterals given 2 similar shapes. They will calculate the similarity proportion and then use the inverse of this to work out the missing length of one side. Pupils will also have a range of problems where they apply this knowledge to evaluate if 2 triangles are similar. REACH GP6 = Pupils will evaluate how to apply Pythagoras Theorem again to evaluate similarity between a pair of isosceles

13 triangles where the length of missing sides needs to be determined. Use similarity to create a proof to demonstrate the similarity of 2 triangles. Lesson 4: Mid-term/LC mini test Pupils will end the week by completing their Mid LC assessment. The purpose of this short test is to check current understanding and progress in the Geometry units. Home learning: Given every Tuesday, due in by Tuesday each week. Week 4 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 Home learning this week will be to create a video on their ipad showing applications and questions on a topic from the last 3 weeks priority to be put on questions they did not understand in their Mid LC test. Line of enquiry; How do we apply formulae to predict numbers? Lesson 1 of the week: REACH lesson improving my midterm score (30 min) During this time today, pupils will reflect on their mini test and work in groups to go through corrections, practice questions that will help them to improve their score and develop a better understanding of questions they have struggled with. Pupils will also use their strengths to support and teach their peers. Prior learning of types of numbers such as primes multiples and square number will be ascertained which will lead into and support learning in lesson 2. Year 9 will have studied some special types of numbers in LC1 and so this foundation will be recapped and used to develop the lessons this week. Lesson 1 of the week: REACH lesson improving my midterm score (30 min)

14 Hypothesis 1: Types of numbers do not generate sequences Learning intentions: Ø Recognise, recall and continue sequences of triangular, square and cube numbers, simple arithmetic progressions and Fibonacci type sequences. Ø Understand how to generate terms of a sequence from either a term-to-term rule. GP 1 to 2 = Demonstrate place value columns and discuss how each digit in a number has a value. GP 2 = Provide a series of sequences including special types of numbers such as square, triangle, prime etc. Discuss with pupils how they are made and how to find the next one. Provide pupils with sequences to discover and work out how they are

15 generated from one term to the next term. GP 3 to 4 = Show sequences made from diagrams and discuss with pupils how they are made and how the next one is generated. Demonstrate how this produces numbers that can be put into a table. GP 1 to 2 = Pupils will answer quick questions to recall how to show methods for ordering numbers such as large quantities, negatives and decimals. They will use place value to demonstrate their understanding of how to write and read larger numbers and how to order very similar decimal numbers and fractional negative numbers. GP 2 = Pupils will complete the next number in a linear sequence in a range of problems. They will need to understand the rule and analyse how they continue through description. They will be given problems where they need to recognise the type of sequence. GP 3 = Pupils will analyse diagrams to find the next term in a diagrammatical sequence, and then draw the next 2 patterns. GP 3+ = Pupils will complete a table of values for a diagrammatical sequence, create their own pattern and find the quantity needed for the 10 th pattern. Pupils will generate these sequences from rules and diagrams. GP4 = Pupils can move on to analyse the rule by describing and explaining the rules that the sequences follow and apply their understanding to evaluate what the missing numbers are in the middle of a sequence where only the first and last terms are provided. Hypothesis 2: Algebraic expressions are useful when finding the 100 th term of a sequence Learning intention: Ø Deduce expressions to calculate the nth term of linear sequences (position to term rule); analyse how to find any term in a sequence; evaluate how the nth term generates 5 terms of a linear sequence. GP 4 = Recall with the pupils how to continue linear sequences based on questions from the previous hypothesis and define linear sequences. Count on and back in multiples. Demonstrate how other sequences can go up in 3 s or some numbers, but are not necessarily the multiples e.g. 2, 5, 8, 11 GP 5 = Demonstrate that pupils should write the multiples that the sequence is related to below, from here they can analyse the relationship and see how the first term was created. This will lead them to discover the Nth term (position-to-term rule) and how it works to create the numbers. Provide a quick demonstration of how to use the Nth term to generate 5 terms of a sequence, and how it can be used to find any term such as the 100 th or 20 th terms. GP 5+ = Count back with the class in multiples using the number line to see how they can still work as a negative times tables.

16 GP 4 = Pupils will understand how multiples are linked to linear sequences and find the relationship by working out the difference between each term. Analyse the link between a variety of sequences and the times tables. GP 5 = Pupils will have problems which will require them to apply their knowledge of sequences to discover the nth term formula from a variety of linear sequences. Pupils will therefore understand how to find the nth term of any linear sequence; this will allow them to then analyse how to generate sequences from the nth term formula such as to create the first 5 terms of a sequence whose Nth term is 2n+1. Pupils will need to evaluate how the formula links to the first term and zero term of the sequence as another method and way of checking their work. Pupils will use the Nth term formula to find any term of the sequence. GP 5+ = Pupils will investigate, again using multiples linked to sequences, to determine the nth term for descending negative sequences such as 5, 2, -1, -4. They need to realise that multiples can also go backwards into negative numbers.. Hypothesis 3: The Nth term formula is not suitable for diagrammatic sequences Learning intentions: Ø Evaluate how to find the nth term for diagrammatical sequences Ø REACH: Recognise and develop the nth term for quadratic sequences, generate quadratic sequences GP 4 = Recall with pupils how patterns can be created not just with numbers but with diagrams. Quick recall task delivered finding the nth term of linear numerical sequences. Demonstrate a pattern of dots or lines that creates a linear sequence. GP 5 = Discuss with pupils how the numerical sequence links again to multiples. Example given on how to get from a diagrammatical pattern to a numerical sequence to the discovery of the Nth term. Then pupils can be shown how to find the number of dots or lines required for the 10 th diagram (term). GP 6 = Revise the sequence of square numbers with the groups moving on. GP 4 = Pupils will do a quick revision task to recall how to write a numerical sequence from patterns an how to find the Nth term. They will be given a variety of diagrammatical sequences where they need to write down the numerical values of each term. Pupils can use the table or simply write them. GP5 = Pupils will follow the example and discussion to evaluate and deduce how the Nth term can be used to predict patterns made from a variety of diagrams.

17 GP 5+ = Pupils will have creative freedom to generate a pattern given an Nth term formula with which it would fit. For instance, create a diagrammatical sequence to fit the Nth term 3n+1. REACH - GP 6 = Pupils able to move on will investigate quadratic sequences and the steps needed to find the Nth term formula by looking at the link to square numbers. For instance, 2, 5, 10, 17 Square numbers plus 1 (n 2 +1). Challenge question - A discussion on what we have done so far this LC and how it helps to answer the LC Challenge Question. Pupils will also reflect on the weekly lines of enquiry in books. Home learning: Given every Tuesday, due in by Tuesday each week. Week 5 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 Home learning this week will be a targeted worksheet generating and solving sequences. Line of enquiry; How can algebraic sequences be applied to straight line graphs? Lesson 1 of the week: REACH lesson improving my knowledge of sequences Pupils will use this session to respond to comments in their books. They will be given instructions as to how they can improve work, how to correct work and how to carry out further REACH work to stretch them beyond target grades. Today will see a much fuller and deeper reflection as to their progress, improvements and confidence levels in certain topics. Prior learning will be ascertained in the lesson recalling and understanding how to plot vertical and horizontal lines on a set of axes, from work done in year 8 LC5. Hypothesis 1: Horizontal lines are parallel to the x axis Learning intentions: Ø Recall how to work with coordinates in all four quadrants; understand how to plot horizontal and vertical lines and name their equation. GP 1+ = Through demonstration and discussion, recall with pupils how to plot co-ordinates in all 4 quadrants focusing on the order of direction. GP 2+ = Define midpoint then demonstrate a line plotted between 2 points on a set of axes and discuss with pupils where the midpoint would be and how they can be sure. Provide and work through an example of how to accurately find the midpoint of a line and write as a co-ordinate. GP 3 = Demonstrate how plots in a vertical or horizontal line have their own equation such as y = 5. Discuss the reason for this name and that vertical lines have an equation such as X = 3.

18 GP 1+ = Pupils have a set of axes to plot a co-ordinates in all 4 quadrants and to complete a square by finding the correct plot. They need to demonstrate their understanding of the order of direction particularly with negative co-ordinates. GP 2+ = Pupils will understand how to apply and use co-ordinates to find the midpoint of a straight line on a set of axes (through the method shown on a range of problems). Pupils therefore evaluate how to find the midpoints of the lines/sides on a shape such as a parallelogram. GP 3 = Pupils will develop their understanding of shapes and co-ordinates through plotting points that a line in order to complete a given shape such as a parallelogram or isosceles trapezium; They will practice finding the equation of vertical and horizontal lines by plotting points; pupils will therefore deduce the equation of the vertical or horizontal lines in the shapes they have plotted, for instance x = 2 or y = 5. Hypothesis 2: Lines with larger values of x are steeper Learning intention: Ø Understand how to plot graphs of equations that correspond to y=mx+c; apply y = mx + c to identify parallel lines. Ø Begin to analyse how to evaluate and interpret gradients (m) and intercepts (c) of linear functions. GP 3 = Recall with pupils how to plot points on a grid, look for relationships between the x and y co-ordinates. GP 4 = Demonstrate how a table of co-ordinates can be generated from the equation of a line such as y = 2x + 1. Discuss that the equation of a line always follows the form y=mx+c. Help pupils understand how to plot the co-ordinates from the table of values. Show the effect of changing the value of C. GP 5 = Teach pupils how to plot graphs such as y=2x, y=3x etc. on the same set of axes and discuss how they are different and why. Look at the relationship between the x and y co-ordinates and what happens to a line when we change the value of M. GP 3 = Pupils will look for the relationship between the x and y co-ordinates to understand how they create and satisfy the equation of the line y = x (1,1) (2,2) (3,3); pupils should analyse and investigate the relationship between similar sets of coordinates provided to find the equations of linear functions and lines such as y = x + 1 etc (2,1) (3,2) (4,2). GP 4 = Pupils will understand how to complete a tables of values for x co-ordinates given the equation, such as y = 2x + 1; then apply knowledge in order to plot the straight line graph; analyse therefore how the equation of a line is written in the form

19 y=mx+c. Explain what happens when the intercept C is changed; pupils should identify parallel lines from equations. GP 5 = Pupils need to evaluate how the value of x alters a line s gradient (steepness) such as y=2x compared to y=3x or y=0.5x. They will describe how it alters the line and write about which one is steeper. Extension to this hypothesis = GP 5 - Analyse how to plot a graph without being provided the table of values given the range for the x-axis. Hypothesis 3: Lines with different intercepts can be parallel. Learning intentions: Ø Analyse how to evaluate and interpret gradients and intercepts of linear functions, Ø Apply y=mx+c to find the equation of the line through two given points or through one point with a given gradient Ø Evaluate how to identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically, GP 4 to 5 = Recall how the value of x alters a line s gradient (steepness) such as y=2x compared to y=3x or y=0.5x and that the value of C determines the intercept of a line on the y axis. Discuss how we know if lines would be parallel before plotting them. GP 5 = Teach pupils how to multiply and add/subtract where negative values are involved. Create a table of co-ordinates using these negative values and for equations such as y = -3x + 2 (M is negative). GP 5+ = Teach pupils how to use 2 points along the line to calculate the gradient of the line, then look for the intercept. Show how these vales for M and C can then be used to write down and interpret the equation of the straight line graph. GP 4 to 5 = Pupils will develop their understanding of the terms gradient and intercept in relation to a straight line graph and its equation. They will be asked how to identify parallel lines and to sketch parallel lines from their equations, e.g. y=2x+5 and y=2x+1. GP 5 = Pupils will use co-ordinates tables to create and plot graphs in order to evaluate what happens with equations such as y = -3x + 2 (negative value of x). They will report on the effect of a negative gradient but. GP 5+ = Pupils will work through problems in order to evaluate and interpret through calculation, the gradients and intercepts of linear functions from their equation and from the line; apply this in order to find and use the equation of a straight line already

20 plotted in the form y=mx+c; Extension to this hypothesis = GP 6 - Rearrange the equation of a line to plot a line, for instance 2x + y = 5. REACH GP 6 = Pupils will evaluate how to plot quadratic functions such as y = x 2. GP 6+ = Plot quadratic functions, analyse how to use the graphs to solve equations for the solution of x. Answer the overarching challenge question: How do Algebra and Geometry help us to make sense of the world we live in? Home learning: Given every Tuesday, due in by Tuesday each week. Revision of unit for exams next week. Pupils will be provided with online resources, videos and booklets where requested. Week 6 Lesson 1 of the week: REACH lesson General revision of improvements needed from everything learned in LC2 Pupils will use this session to respond to comments in their books. They will be given instructions as to how they can improve work, how to correct work and how to carry out further REACH work to stretch them beyond target grades. Today they will use all their personal reflection to begin revision prioritising the topics they need to work on. Resources will be provided to allow for personalised, independent and structured revision. Lesson 2 and 3: Revision using levelled booklets followed by assessments. This time will also be used to complete revision from year 8 work done on distance time graphs. Lesson 4: End of LC2 exam Gap Analysis Reinforcement Week 7 Gap Reinforcement As seen in the lesson activities each week, gap teaching will not just be at the end of the LC2 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.

21 Extended Learning This will be in the form of REACH questions to challenge pupils in lessons beyond their target grade. They will be required to apply their knowledge from each week in order to solve these problems. Extended learning will also come in the form of access to websites, revision videos and additional independent assignments set at the right level, yet will challenge them to reach further. Examples of GCSE questions These are an example of how the level of difficulty can vary between Foundation and Higher. Pupils will be given work to suit their target level, those studying the Higher curriculum will work towards these more difficult types of problems in year 10 but will have chance to try them in REACH.