The KING’S Medium Term Plan – Mathematics

Y9 LC2 Programme 2014-2015

Module Geometry and Algebra (Angles, shapes and lines, Sequences, Algebraic Graphs and functions). Pupils will cover all objectives, but the depth at which they will study the objectives and each hypothesis is dependent on their end of year target grade point. Key objectives are taken from the AQA GCSE Specification for the new curriculum.

Building on prior learning

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.

Overarching subject Challenge question

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

Lines of Enquiry

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 Topic Statement

By the end of LC2 in Mathematics SWBAT: Geometry (AQA 3.4.1 – G1, 3, 4, 6, 19, 20) Weeks 1-3 In this unit pupils will study the relationship between angles and 2D shapes. They will apply the properties of triangles and quadrilaterals in order to calculate missing angles in a variety of problems. This will develop into calculating angles on sets of parallel lines and pupils will understand the terms alternate and corresponding. Pupils will then analyse how to find the interior and exterior angles of any polygon and evaluate how they can demonstrate a proof. They will look at the meaning of congruence in shapes by applying their knowledge of shape properties and angle facts. Those pupils aiming for higher

targets (GP5+) will apply Pythagoras’ Theorem to evaluate the congruency of triangles. Algebra – sequences (AQA 3.2.4 – A23, 24, 25) Weeks 4 In this unit pupils will study how sequences work and develop. They will look at basic rules moving from one term to the next and apply this understanding to sequences made of diagrams and patterns. This knowledge will develop further into using multiples to find the nth term which will be used to find any term in a linear sequence. Those that have targets of GP4 and above will generate sequences using the nth term and those capable of GP 5 or higher will apply this to quadratics sequences linked to square numbers. Algebra – graphs (AQA 3.2.2 – A8,9,10,12,14) Week 5 In this unit pupils will learn how to use the equation of a straight line in order to plot them. This will require them to recall knowledge on substituting values into a formula looked at in LC1 and also rearranging formulae. This will develop into their understanding of gradient and the intercept of the lines. Once their understanding of how the equation of the line works they will analyse how to draw and identify parallel lines and calculate the gradient of a line. The ultimate goal is for pupils to find a line’s gradient and intercept in order to find a line’s equation. Those that have high targets will evaluate negative gradient, and investigate perpendicular straight line graphs. Week 3 will be a mid LC assessment to check current progress.

Assessment in week 6 will be against the above objectives.

Gap teaching from analysis of assessments in week 7 after the half term.

Medium Term Plan

How each week looks;

1) 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.

2) Learning Intentions: These are the key objectives laid out by the exam board.

3) Weekly success criteria for completion across 4 lessons; 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 we use our knowledge of 2 dimensions to calculate angles? 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 Knowledge: 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). 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.

Success criteria:

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. REACH: Apply their knowledge of algebra to solve angle questions and real life problems. 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

Knowledge: 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. Success criteria:

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. 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. REACH: Apply their knowledge of algebra to solve angle questions and real life problems.

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.

Knowledge: 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? Success criteria:

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. They will need to show applications of shape and angle properties learned throughout the week so far. REACH: Apply their knowledge of algebra to solve angle questions and real life problems. Hypothesis 4 – Parallel lines cannot create angles Learning intention:

Ø Understand and use alternate and corresponding angles on parallel lines. Knowledge: 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. Success criteria:

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. REACH: Apply their knowledge of algebra to solve angle questions and real life problems. Home learning: Given Monday of each week and due in by Monday the following week.

Week 2

Line of enquiry; How can I use 2D shapes to prove the special properties of other shapes?

REACH (1H) (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so as to learn from mistakes done the week before. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong in the baseline assessment. 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 and irregular polygons. Knowledge 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.

Success criteria: 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. 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.

REACH: Apply their knowledge of algebra to solve angle questions and real life problems.

Hypothesis 2: 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.

Knowledge 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. Success criteria: 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.

Hypothesis 3: 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. Knowledge 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? Success criteria: 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 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 transformations and their knowledge of angles where possible.

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

Week 3

Line of enquiry; Can ratio and proportion help us to discover similarity between objects?

REACH (1H) (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so as to learn from mistakes done the week before. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong in the baseline assessment. Hypothesis 1: 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 Knowledge 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. Success criteria: 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. GP6 = Pupils will evaluate how to apply Pythagoras’ Theorem again to evaluate similarity between a pair of isosceles triangles where the length of missing sides needs to be determined. Use similarity to create a proof to demonstrate the similarity of 2 triangles. Hypothesis 2: Two shapes have similar areas if both areas are measured in cm2. Learning intentions:

Ø Analyse similar areas in 2D shapes. Knowledge GP3 to 4= Master similarity in lengths and investigate what happens when it comes to similar areas. GP 5+ = Examples taught on how to identify similar areas, understanding the link to similar lengths. Success criteria: 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 investigate similar areas by calculating them and seeing what happens with the scale factor. GP 5+ = Pupils will work through problems finding the scale factor of the similarity proportion such as 1/3 bigger. GP 5+ = Students will analyse what happens with 2D areas and will evaluate if they are similar or not by finding the scale factor. REACH: Pupils will still analyse 2D scale factors but using more complex 2D shapes and algebra. Hypothesis 3: Two 3D shapes are similar if the formula to calculate their volume is the similar for both.

Learning intentions: Ø Calculate similar volumes in 3D solids.

Knowledge GP3 to 4= Master similarity in lengths and investigate what happens when it comes to similar areas. GP 5+ = Examples taught on how to identify similar volumes, understanding the link to similar lengths and areas. Success criteria: 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 investigate similar volumes by calculating them and seeing what happens with the scale factor. GP 5+ = Students will analyse what happens with 3D solids and will evaluate if they are similar or not by finding the scale factor. REACH: Pupils will still analyse 3D scale factors but using more complex 3D solids and algebra. MIDTERM to test key knowledge so far on modules covered will be done this week. Home learning: Given Monday of each week and due in by Monday the following week.

Week 4

Line of enquiry; How do we apply formulae to predict numbers? REACH (1H) (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so as to learn from mistakes done the week before. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong in the baseline assessment. This week, improvements will be based on the midterm. Hypothesis 1: Algebraic expressions are useful when finding the 100th 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.

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. Knowledge 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 100th or 20th 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. Success criteria: 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 2: 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

Knowledge 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 10th diagram (term). GP 6 = Revise the sequence of square numbers with the groups moving on.

Success criteria: 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. 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 (n2+1).

Hypothesis 3: Quadratic sequences have two differences that are the same. Learning intentions:

Ø Evaluate how to find the nth term for quadratic sequences as well as generating them. Knowledge 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. Keep mastering patterns and linear sequences. GP 5+ = Understand how a quadratic sequence works as well as how to calculate its nth term. Success criteria: 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 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 (n2+1). Home learning: Given Monday of each week and due in by Monday the following week.

Week 5

Line of enquiry; How can algebraic sequences be applied to straight line graphs? REACH (1H) (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so as to learn from mistakes done the week before. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong in the baseline assessment. 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.

Knowledge 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. Success criteria: 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.

Knowledge 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. Success criteria:

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 co-ordinates 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 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, Knowledge 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. Success criteria: 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 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 = x2. GP 6+ = Plot quadratic functions, analyse how to use the graphs to solve equations for the solution of x.

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

Week 6 REACH (1H) (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so as to learn from mistakes done the week before. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong in the baseline assessment. 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

REACH (1H) (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so as to learn from mistakes done the week before. Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong in the baseline assessment. This week the results from the LC2 assesssments in Week 6 will be analysed and individual work will be produced for students to do in lessons.

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.