MEP: Primary Demonstration Project Week 17 R: Shapes Lesson Plan Y6 C: Reflection (in a line/point). Line and rotational symmetry E: What is the rule? Different geometric transformations 81 Activity Notes 1 Factorisation Individual work, monitored Factorise these numbers in your exercise book and list their positive (or whole class activity) factors. T sets a time limit of 5 minutes. BB: 81, 256, 431, 1081 Review with whole class. Ps come to BB or dictate to T, explaining Calculators allowed. reasoning. Class agrees/disagrees. Mistakes discussed and corrected. Reasoning, agreement, self- Elicit that: correction, praising • 81 = 3 × 3 × 3 × 3 = 34 (= 9 × 9 = 92 , so a square number) e.g. 81 Factors: 1, 3, 9, 27, 81 9 9 • 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 28 3 3 3 3 × 2 256 2 (= 16 16 = 16 , so it is a square number) 128 2 Factors: 1, 2, 4, 8, 16, 32, 64, 128, 256 64 2 32 2 • 431 is a prime number Factors: 1, 431 16 2 (as not exactly divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23 and 82 29 × 29 > 431) 1081 23 42 47 47 2 2 • 1081 = 23 × 47 Factors: 1, 23, 47, 1081 1 1 7 min 2 Lines and angles Quick individual activities but Ps have rulers (and set squares if possible), or allow freehand drawing. the whole class kept together T gives instructions on what Ps should draw and label. After each T monitors, helps, corrects. instruction, T quickly monitors all pupils and asks a P to show an After each drawing, Ps say example on the BB. Class agrees/disagrees. Mistakes corrected. what they know, or T elicits: a) i) Draw a curved line. BB: e.g. • straight lines extend in both directions to infinity and the ii) Draw a straight line. ends never meet. b) Draw and label appropriately: e • lines are usually labelled i) a straight line with small letters and points f with capital letters. ii) a half line or ray. A • a ray extends from a point iii) a line segment A B to infinity in one direction. c) Draw a line, e, and mark a point, A, on it. e.g. f • line f extends beyond A Draw a line perpendicular to line e at point A. • each of the 4 angles formed How can we show that they are perpendicular? A is 90°. (Mark the angle with a square.) e f d) Draw and label 2 parallel lines 3 cm apart. e • the distance between two How can we show that they are parallel? 3 cm lines is the perpendicular (Mark with single arrows.) distance between them; parallel lines never meet, e) i) Draw two lines, e and f, which however far they are intersect one another. extended. e f ii) Draw two line segments, AB and CD, which • intersect means 'cut or 'cross'. intersect one another. D Ps mark the equal angles on What do you notice about the angles formed? BB and on own drawings. (The opposite angles are equal.) B (1 arc for 1st pair, 2 arcs for A C 2nd pair) © CIMT, University of Exeter MEP: Primary Demonstration Project Week 17 Y6 Lesson Plan 81 Activity Notes 2 (Continued) Elicit that angles are usually f) Draw: i) an acute angle BB: e.g. α β labelled with Greek letters. ii) a right angle, α (alpha), β (beta), iii) an obtuse angle δ γ γ (gamma), δ (delta) iv) a reflex angle. T asks Ps for examples of sizes of angles for each type, then elicits Which types of angles are their limits. missing? BB: 0° < acute angle < 90°, right angle = 90°, (null angle = 0°, 90° < obtuse angle < 180°, straight angle = 180°, 180° < reflex angle < 360° whole angle = 360° ) 15 min 3 Reflection Whole class activity In a PE lesson, Ps were put in pairs and told how to stand in a certain relationship with one another. What could the relationship be? Where Drawn (stuck) on BB or use should the missing pupil from each pair stand? enlarged copy master or OHP Ps study the diagram to find the 'rule' then come to BB to mark the (or use real Ps and a line or missing points. Class agrees/disagrees. Elicit what the rule is and the point in the classroom to form main points about it. (T draws the dotted lines and squares on diagram.) the patterns) BB: Note: The points circled are not given but added by Ps. a) b) A A' E T' ee T helps with the drawing (or B' B eF placing if using real Ps) if S' necessary, with the aid of a CC'C BB ruler or metre rule. S D' D In good humour, at a quick F' e pace E' E E' Discussion, agreement, T a praising Feedback for T Reflection in the line a. Reflection in the point C. A and its mirror image A' are E and its mirror image, E', the same perpendicular distance are an equal distance from on line e , from line a. point C on line e. c) d) e) E' P P' C Q' C' E P' Q' P D' S Q R' A Q S' A' D R' R B' S' S R e a B Translation by the same A' is half as far from line a as A P' is half as far from line e as P distance to the right and up (or on the same perpendicular line on the same perpendicular line by the same angle) each time. as A and on the same side of as P but on the opposite side of The lines PP', QQ', RR' and SS' line a as A. line e . are all parallel. 24 min © CIMT, University of Exeter MEP: Primary Demonstration Project Week 17 Y6 Lesson Plan 81 Activity Notes 4 PbY6b page 81, Q.1 Whole class activity Read: What has been done to Triangle 1 to form the other shapes? Drawn on BB or use enlarged Describe each transformation in your exercise book copy master or OHP Ps come to BB to point out the relevant pairs of triangles and explain If possible, T has Triangle 1 the transformations. Class agrees/disagrees. Ask Ps to draw the cut out to show the actual mirror lines or points of reflection, to say the scale of enlargement or movements to the class. reduction and to give the angle of rotation where relevant. At a good pace. Agree on a good way to list the transformations in Ex. Bks. Discussion, reasoning, T suggests the form below if no P has an idea. After agreement, Ps agreement, demonstration with write the transformation in Ex. Bks. model where possible Extension Ask Ps to point out other relationships too (e.g. 7, 8, 9 and 10) and to Elicit that in a reflection, the show congruent and similar triangles. corresponding points on the original shape and its mirror Solution: image are the same f perpendicular distance from 3 the mirror line or axis. 1 2 7 9 Praising, encouragement only e Expect only the name of each g C 4 11 transformation from less able 5 6 10 Ps, but some details from the 8 more able Ps. e.g. 1 → 3: we say that the ratio of reduction is 1 : 2 ( the value 1 → 2: translation (4, 0) 1 → 3: reduction, reflection, translation of the image is given first); → → 1 4: enlargement (2:1), translation 1 5: reflection in line e or we say that it is a reduction 1 → 6: reflection in point C 1 → 7: reflection in line f by scale factor 1 half, 1 → 8: reflection in horizontal axis, rotation by 90°, translation i.e. triangle 3 is half the size 1 → 9: reflection in vertical axis and rotation by – 90° (i.e. clockwise) of triangle 1; → 1 → 10: reflection in line g , then translation by (16, 0) 1 4: we say that the ratio of enlargement is 2: 1, or it is → 1 11: stretch vertically (same width but 3 times as high) enlargement by scale factor 2. 30 min 5 PbY6b page 81, Q.2 Individual work, monitored, Read: Draw the lines of symmetry and mark the centres of rotation. helped Set a time limit of 3 minutes. Expect only rough freehand drawing Use enlarged copy master or first and then discuss afterwards with the whole class how to draw the OHP lines of symmetry and mark the centres of rotation accurately. Discussion, agreement, self- Review with whole classs. Ps come to BB to draw, mark and label. correction, praising Class agrees/disagrees. If no P shows the accurate method, demonstrate Extra praise for Ps who with BB compasses and ruler, involving Ps where possible. remember how to construct Solution: the lines/points accurately. a) b) c) (Instructions given on following page.) m C C e) The dog looks symmetrical d) e) f) at first sight but on closer inspection, the RHS of the m dog is not exactly a mirror Not symmetrical! m image of the LHS. 34 min © CIMT, University of Exeter MEP: Primary Demonstration Project Week 17 Y6 Lesson Plan 81 Activity Notes To Ts: To draw a line of symmetry e.g. Choose a point on the shape and its corresponding mirror image. Set compasses to the distance between them. Put the compasses on ) one chosen point and draw arcs above and below it. Repeat with the other chosen point. Draw a straight line through the points where the arcs cross.