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SCITT Day 6 2018 19

SCITT Day 6 2018 19. GEOMETRY: IDENTIFYING KEY FEATURES OF SHAPE AND SPACE. Today we will…. Be aware of the key ideas underpinning the two strands of geometry in EYFS, KS1 and KS2; Explore challenging practical tasks for applying knowledge in shape and space;

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SCITT Day 6 2018 19

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  1. SCITT Day 62018 19 GEOMETRY: IDENTIFYING KEY FEATURES OF SHAPE AND SPACE

  2. Today we will… • Be aware of the key ideas underpinning the two strands of geometry in EYFS, KS1 and KS2; • Explore challenging practical tasks for applying knowledge in shape and space; • Look at coordinate representation and use of angle; • Be able to teach further aspects of 2D shape, including transformations (translation, rotation, reflection and scaling) Associated issues for teaching Explore aspects of position and movement using ICT. Consider the role of a plenary within any lesson structure What do success criteria look like in mathematics?

  3. Additive Reasoning A problem… Goldilocks Basket Goldilocks had 8 pieces of fruit in her basket. She has given 3 pieces to her favourite family of bears. How many pieces does she have left? Use a bar model to represent the problem… • Build it & act it out (number rods, counters, cubes) • Say it • Draw it • Number sentences – which best fits? C P A

  4. Bar Model representations: (KS1 problems) Additive Reasoning BUILD: • There are 4 yellow flowers and 3 blue flowers – how many altogether? • There are 5 lollies. Jess eats 2. How many are left? • 6 + [] = 17 altogether QUESTION: (Create your own) “John has 7 balls. Mark has 5 more…” “Beth has 6 balls. Emily has 3 less…” • COMPARE: • There are 5 red cars and 3 yellow cars, how many more red cars? • The string is 4cm, the ribbon is 8cm. How much shorter…?

  5. Defining terms ‘Proportion’ 4 16 12 16 “4/16 of the tiles are green ” As a Fraction • “¼ of the tiles are green” As a Percentage • “25% of the tiles are green” As a Decimal • “0.25 of the tiles are green” As a Proportion: “4 in every 16 tiles are green” Or “1 in every 4” are green Compare part-to-whole

  6. Defining terms ‘Ratio’ 4 green parts 12 red parts As a Ratio: “The ratio of green to red is 4 to 12” (Simplify 1 to 3) or “1 green for every 3 red” Proportion ¼ Ratio 1:3 Part-to-whole Part-to-part

  7. Purposeful Plenaries • What are plenaries for? • How have you seen them used? • What features make for a successful plenary?

  8. Mastery in Geometry What’s it all about? What's involved? What would you expect to see re. ‘Big ideas’ in Geometry, across the primary years & in different year groups? What would you expect primary learners to be able to do and understand?

  9. Teaching Point “What pupils need most of all for learning about shape and space is lots of practical experience of colouring shapes, cutting them out, folding them, turning them over, rotating them, looking at them in mirrors, fitting them together, making patterns, matching them, sorting them and classifying them. The approach here can be much less structured than in other aspects of the mathematics curriculum.” [Haylock “Maths Explained…” page 274]

  10. Interactive Teaching Programs(ITPs)

  11. Polygons • Poly comes from the Greek word meaning ‘many’; • gon comes from the Greek word for ‘angles’. • A polygon is, therefore, a flat shape with ‘many angles’. • When we talk about polygons we are talking about shapes with 3 or more straight sides. (Polyhedrons: a solid shape with ‘many faces’)

  12. Glossary Definitions What's the same, what's different? • How would you define these quadrilaterals: • Parallelogram • Rhombus • Rectangle • Square • Oblong • Kite and inverted kite (delta) • Trapezium Triangle, square, rectangle, oblong, quadrilateral, pentagon, hexagon, octagon, circle, semicircle, cube, cuboid, pyramid, cone, cylinder, prism, sphere, hemisphere, face, edge, vertex/vertices, surface, solid, side, straight, curved, diagram, right-angled, symmetrical, 2-D shape, two-dimensional, 3-D shape, three-dimensional, describe, property How do we compare to www.amathsdictionaryforkids.com ?

  13. Sorting • What different properties of shape are expected? • Use Tree, Venn and Carroll Diagrams to sort shapes… [How are these different sorting diagrams linked?]

  14. Triangles • A 3-sided polygon is called a triangle. • Can you sketch them all? • Right angled • Isoceles • Equilateral • Scalene • Are there any others…? Congruent Shapes which are exactly the same size and shape Similar Shapes that are proportionally equivalent

  15. A 2-piece tangram • Start with a square. Draw a straight line from one corner of the shape to bisect one of the opposite sides. Use this 2-piece tangram to investigate what different 2D shapes you can make by joining the pieces ‘full side’-to- ‘full side’. (No overlapping) • How many different shapes can you make? • Can you identify their properties?

  16. Mastery Read the ‘Big Ideas’ for your year group… What understandings are identified? Do they meet your expectations?

  17. Geometry – D Haylock • Two aspects: • Moving or changing shapes • Classifying shapes • Fundamental concepts: • Transformation • Equivalence We ask learners: “How are they the same? How are they different?” Copy this shape onto a whiteboard… How is your shape compared to mine?

  18. Tetrominoes • What different shapes can you make using four squares joined ‘full-side’ to ‘full-side’? • Can you sketch them? • How many are there? • Convince me!

  19. Explore Discuss and sketch models and images for: • Translation • Reflection • Rotation • Tessellation (and packaging) • Patterning • Matching • Sorting and classifying • Enlargement [Y6 R&P] ‘…similar shapes where the scale factor is known or can be found.’ What other ‘shape’ examples...?

  20. Coordinates-Plotting Coordinates squares on a grid. Draw … • A tick B4 • A cross E3 • A triangle C2 5 4 3 2 1 A B C D E

  21. Coordinates 10 9 8 7 6 5 4 3 2 1 0 Coordinates as points on a plane. What do we know about plotting coordinates? e.g.(3, 2) 0 1 2 3 4 5 6 7 8 9 10

  22. 14 13 12 11 10 Real Life Ordnance Survey Maps Locate ‘interesting features’… give 6 fig coordinates for others to find them. e.g. 042 123 Means X: 04 and 2 ‘tenths’ Y: 12 and 3 ‘tenths’ 04 05 06 07 08

  23. Estimating Angle Makers • Draw round a CD twice. • Cut out the circles. • Find the centre point of each circle by folding. • Cut along a radius of each circle. • Intersect the circles.

  24. Using a Protractor • Can you create Success Criteria to “use a protractor to measure an angle”? (Expectations: to nearest 10° or 5° or 1°) • What are the main teaching points? • How might you model this? Woodlands Junior – “What’s My Angle?” http://resources.woodlands-junior.kent.sch.uk/maths/shapes/angles.html

  25. Robot Instructions • A robot is programmed to walk 3 paces, turn left 90°, then walk another 4 paces and turn right through 90°. It repeats this over and over. Trace out its path on a grid. • Make up another program for the robot to follow... What shapes can you make it draw?

  26. fd 100 bk 100 rt 90 lt 90 cs seth 0 Repeat ? [fd 30 rt 90] pu / pd (pen up/down) pe / ppt (en erase/paint) Create a set of commands to draw a: Square Rectangle Other regular shapes Block letter of the alphabet A spirograph MSWLogo

  27. 2D challenges Tarsia Jigsaw Investigate ITP's – ‘Isogrid’, ‘Polygon’, ‘Area’, ‘Coordinates’ What different shapes can you make by folding A4 paper? Isogrid ‘Dot to Dot’ - use a triangular array of 15 dots to draw different triangles. How many are there? 3D challenges The 12 Pentominoes – Which make the net of an ‘open cube’? Nets Challenge – choose any 3d shape. Create its net to ‘tightly wrap’ it Online searches: ‘Tangrams’/ ‘Tesselations’/ ‘MC Escher’/ ‘Origami’/ ‘Transformations’/ ‘Platonic Solids’ Use the mathematical equipment to accurately draw: equilateral triangle, square, isosceles triangle, hexagon, pentagon…. Nrich - Properties of shape Activities - ‘airnets’; ‘transformations on a pegbd’; ‘a shapely network’; ‘property chart’; ‘making tangrams’ Google– ‘Soma Cube’; ‘Spiral in a square’ Online links: http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/aug/10/attack-on-the-pentagon-results-in-discovery-of-new-mathematical-tile Create a glossary that names and defines the properties of 2d/ 3d shapes You will feedback!

  28. MATHS TASK 5 Prepare 15 maths questions with sketches, diagrams and explanations, working at your own level. This will give an indication of your progress with the subject knowledge audit. In your reflection identify websites and reference materials used and any areas for future study. (Trainees can work independently or within a study group for this task.) LEARNING OUTCOME: To evidence the ability to research any aspects of overt subject knowledge to build on the initial audit.

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