Oral and mental starter
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1 Lesson 8 Objectives Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes (Y7) Vocabulary parallel, perpendicular, transversal, intersecting, vertically opposite, supplementary, complementary, alternate, corresponding, interior, exterior, equidistant, convention, definition Resources Whiteboards (if available) Objectives Solve geometrical problems using side and angle properties and explaining reasoning with diagrams and text (Y8) Vocabulary parallel, perpendicular, transversal, vertically opposite, supplementary, complementary, alternate, corresponding, interior, exterior, equidistant, prove, proof, convention, definition, derived property Resources OHT of M8.1 OHT of M8.2 (for plenary) Whiteboards (if available) Mixed set of questions drawn from the Framework By the end of the lesson pupils should: know and use the angle properties of parallel and lines, and of triangles and polygons be able to justify and explain reasoning with diagrams and text Framework supplement of examples, pages 16, 17, 183 Levels 5 and 6 Lines and angles Oral and mental starter 10 minutes Ask pupils to listen to the following instructions, and sketch and label the diagram: Draw an isosceles triangle ABC. Mark the equal angles and sides. Mark and shade angle ABC. Extend line AB to point D, and mark the exterior angle of the triangle. Discuss different orientations of the triangle. Now ask pupils to do the same for these instructions: Draw a pair of parallel lines with an intersecting transversal. Label the parallel lines. Label a pair of corresponding angles with the letter c. Label a pair of alternate angles with the letter a. Label a pair of vertically opposite angles with the letter v. Discuss pupils answers and the relationships between the angles: Which are equal? Do any add up to 90 (complementary)? add up to 180 (supplementary)? Main teaching 40 minutes Tell pupils that they are going to use their knowledge of lines and angles to solve geometrical problems. Model how to solve the problem on OHT M8.1. ABCD is an isosceles trapezium with AB parallel to DC. P is the midpoint of AB, and AP = CD, AD = DP. DAP = 75. Calculate the sizes of the other angles. Ask pupils to draw and label the diagram and discuss the question in pairs. Q What information can you add to the diagram? Label AB and CD as parallel. Label AP = PB = CD. Label BC = AD (isosceles trapezium). Label DAP = PBC = 75 (isosceles trapezium). Q Which angles can you calculate first? Justify your answers. Discuss pupils solutions and model the use of correct language and geometrical reasoning. DAP = APD = 75 (triangle APD is isosceles) ADC = (interior angles, AB and DC are parallel) ADP = (angle sum of triangle is 180 ) and so on Ask pupils to solve a selection of mixed problems involving lines and angles. Use the Framework supplement of examples, pages 16, 17 and 183, and examples from previous Key Stage 3 test papers. Check pupils knowledge of interior and exterior angle properties of polygons. Plenary A D P C B 10 minutes Show OHT M8.2, developed from a 1999 test question. Ask pupils to discuss in pairs how to solve the problem and to explain their reasoning. k = (interior angles) 3(m + 70) = 360 (angles at a point total 360 ) Demonstrate how pupils should show their working concisely. Year 9 booster kit: mathematics 73
2 74 Year 9 booster kit: mathematics
3 Isosceles trapezium M8.1 A P B D C ABCD is an isosceles trapezium with AB parallel to DC. P is the midpoint of AB, and AP = CD, AD = DP. DAP = 75. Calculate the sizes of the other angles. Year 9 booster kit: mathematics Crown copyright
4 76 Year 9 booster kit: mathematics
5 Star M8.2 The shape below has three identical white tiles and three identical grey tiles. The sides of each tile are the same length. Opposite sides of each tile are parallel. One of the angles is 70. OHT M8.2 k 70 m Not to scale (a) Calculate the size of angle k. Give a reason for your answer. (b) Calculate the size of angle m. Give a reason for your answer. Year 9 booster kit: mathematics Crown copyright
6 78 Year 9 booster kit: mathematics
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