VIEWS: 46 PAGES: 6 POSTED ON: 8/31/2012
YEAR 9: AUTUMN TERM Shape, space and measures 1 (9 hours) Geometrical reasoning: lines, angles and shapes (178–189, 194–197) Construction and loci (220–227) Solving problems (14–17) Teaching objectives for the main activities CORE From the Y9 teaching programme A. Distinguish between conventions, definitions and derived properties. Explain how to find, calculate and use: B. - the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons, C. - the interior and exterior angles of regular polygons. D. Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text. E. Know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by equal divisions of a circle. F. Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS); use ICT to explore constructions of triangles and other 2-D shapes. G. Find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT. H. Explore connections in mathematics across a range of contexts: shape and space. Unit: SSM1 Year Group: 9 Number of 1 Hour Lessons: 9 Class/Set: Core Flexibly use the 1 or 2 lesson structure Oral and Mental Main Teaching (2 lessons) Notes Plenary Objective r Objective A Key Vocabulary Model solutions and notation Using pictures from worksheet See page 179 of framework to distinguish between Definition Assess understanding of 9SSM1a or others, ask one convention, definition and derived properties. Derived conventions. student to describe the shape Also give a practical demonstration as in framework Property Check key vocabulary. using mathematical words etc. but establish it is not a proof. (This will be Demonstration Pose challenging problem for Rest of class try and draw the developed in the mini-pack) Proof students to discuss e.g. pattern/shape described. Transversal Objective D Revisit and strengthen Y8 work using parallel lines and transversals, angles around a point, angles in a a Objective A triangle, vertically opposite angles (perhaps revisit c b Use some of the diagrams from bearings). 9SSMa to discuss conventions. Encourage students to write brief notes to justify a+b=c Label vertices with letters. solutions. (Model this). always Ask question about sides and Assess where weaknesses lie and address them. angles using letter conventions Include diagonals and intersecting lines in polygons. Is a square a rectangle? to describe them. Is and isosceles triangle an equilateral triangle? (and vice versa?) Oral and Mental Main Teaching (1 or 2 lessons) Notes Plenary Objective O and aa and n Objective F Key Vocabulary Take feedback from last exercise. Does 360o divide exactly by 2? Revisit Y8 constructions (Page 221) Bisector Discuss outcomes Extend to ÷ 3, 4, 5, 6, 7, 8, 9, Perpendicular Form generalisations 10 etc. Construct a triangle given R.H.S. Intersection Discuss approaches Establish that with given properties only one Locus. Establish SSS, R.H.S. rules for Discuss methods of division triangle can be constructed. (constructing and Loci constructing triangles. e.g. 360 ÷ 12 cutting out or making with pipe cleaners and straws Hypotenuse Perhaps use AAA in two triangles, extend to factor pairs of 360. could be undertaken). calculate a missing side using ratio. Where does 360o come into our Re-establish S.S.S. rule and explore A.A.A. and work? revisit similarity. Collect ideas. (Page 223) Is it possible to construct triangle ABC such that Set a target of 10 ideas where ………etc. we use 360o. Divide class into pairs – allocate pairs different Objective F starting questions so all questions are attempted. Demonstrate (without comment) constructions. Pupils have to say what you have done OR pupils have to direct you in the construction using precise language. Oral and Mental Main Teaching (1 or 2 lessons) Notes Plenary Objective u Objective G Key Vocabulary Why is the sum of external angle Estimating angles (whiteboard Discuss simple loci in 2 dimensions. Locus in a polygon always 360o. responses) Pupils use constructions (sketch first) to complete Loci What about internal angles in a question on 9SSM1b (loci) and discuss in pairs first. Sphere polygon? OR Plane Ask questions on conventions. Mini plenary Discuss different types of locus T = 2n – 180 Discussion about how loci of multiple points in a and phrases used – ‘equidistant Substitute for different values plane (2D shapes) can form 3D images might be Dynamic geometry from point-line’ etc. of n. Pupils calculate to find T. appropriate before attempting 9SSM1c package could be used. Perpendicular to .. etc. (Use negative fractions, Pupils in 2s or 4s discuss further question on Pupils model loci. decimals etc.) 9SSM1c on loci and try and sketch or describe loci. Using integers show Mini plenary relationship to sum of internal angles in a polygon. (Use regular polygons to demonstrate) Proof comes later in scheme of work. Oral and Mental Main Teaching (1 or 2 lessons) Notes Plenary Objective K Objective E Key Vocabulary When is a segment a sector? How would you do the Ask – what is a circle? – relate to locus. Plane (when it’s a semi circle!!!!) following in your head? Ask pupils to chant ‘A circle is the locus of a point Equidistant Test on names as you point to a 398 + 1252 moving equidistant from another fixed point in a Cyclic master diagram or draw in lines on 648 – 329 plane’. a circle. 17 x 25 How can we draw/construct a circle? Why are all regular polygons 18 x 2.5 Discuss types of equipment particularly string used cyclic? 46.2 ÷ 0.2 by grounds men to construct field markings. Explore some ideas on circle 83 ÷ 0.5 Ask pupils to imagine the line moving as below. theorems. 21 ÷ 1.5 Offer each question separately, followed by collecting answers and methods. If methods are ‘new’ to some students set a similar question Use to establish tangent, chord arc, segment semi to practise. circle, diameter. Establish radius and sector.(mention major and minor segment and sector) Establish how regular polygon can be constructed using a circle (See page 195) Construct regular polygons particularly a hexagon (introduce cyclic). Produce a master diagram/poster identifying key parts of a circle. Oral and Mental Main Teaching (1 lesson) Notes Plenary Objective A and aa Objective A & C Key Vocabulary Note down findings. Ask pupils to sketch a nonagon. Establish convention for exterior and interior angles Regular Establish understanding of of a polygon. Establish that exterior angles can Irregular convention for interior and Now score the nonagons using never by reflex. Address this misconception. Polygon exterior angles of a polygon. the following: (names) Model solutions to difficult Each internal acute angle = 20 questions or set a difficult question points. and ask for ideas for a method or Each right angle 15 points. solution. Each pair of perpendicular lines Check names of polygons. 5 points (they don’t have to Check vocab. for angles work. meet or cross) Could use logo to draw Check scores. regular polygon. Using exterior angle and side Now try and produce the length. nonagon with maximum points? Model a ruler turning through each exterior angle of a polygon. Note the ruler always rotates 360o. Discuss outcomes Establish the sum of exterior angles = 360o. What about interior angles? Regular polygon and exterior angles – explore. Solve problems and questions using properties of shapes and exterior interior angles of polygon. Consolidate with SATs questions if time available