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Bolwarra Public School Mathematics Learning Sequence Stage 2 Term 2 Unit 2 Outcome/Key Ideas Sample teaching, learning, working mathematically activities SGS2.2a Manipulates, compares, sketches and names two-dimensional shapes and describes their features Ignition Activities Shape Guessing Hold a 2D shape hidden behind a screen. Gradually lift a small part into view. Write down all the shapes children think it could be. Slowly pull the shape up and ask the children to eliminate shapes from their list. Discuss the properties of the shape. Hold the shape at tilted angles to increase difficulty. Note: SmartBoard have a shape program very similar to this and it reveals one square at a time. Can be downloaded for free. 2002 K-6 Syllabus p126 Shape Hunt In manageable groups (3 or 4), children go on a shape hunt in the school grounds. They draw and label each shape they find. Milestones in Mathematics for NSW, Yr 3 & Yr 4 Identify and name pentagons, octagons and parallelograms presented in different orientations (Year 3) Compare and describe special groups of quadrilaterals (Year 4) Language Pentagons, octagons, parallelograms, polygon, orientation, quadrilaterals, features, symmetry, parallel, right, rhombus, square, rectangle, trapezium, kite, adjacent, rotational symmetry, regular, irregular, Polygon: a two dimensional shape having three or more straight sides Quadrilateral: a polygon with four sides Parallelogram: a quadrilateral with opposite sides parallel Celebrity Quadrilateral. (Played like Celebrity heads but with shapes instead)Use hints about parallel sides, right angles and equal sides to identify the quadrilateral. Explicit Mathematical Teaching What is a shape? A polygon (Greek term meaning many angles) is a closed shape with three or more angles and sides. The angles are the focus for the general naming system used for shapes. What is a regular shape? Shapes which have equal angles and sides of equal length. This means that a rectangle is an irregular shape. If you turn (rotate) regular shapes they look the same. There are many more lines of symmetry in regular shapes. There has to be a certain length to sides of shapes to make it a closed shape eg a triangle cannot be constructed from three straws if the sum of the lengths of the two shortest straws is less than the longest straw Shape Word Beginnings-Discuss the fact that many shape words have a beginning element (sometimes a prefix) that has a specific meaning, eg poly (many), octa (eight), tri (three) etc Discuss metalanguage in lessons eg Why is a pentagon called that? What does it have to do with the Pentagon in the US? (five sided building) What does the prefix 'pent-' mean? What other 'pent-' words can you think of? (Pentathlon, pentominoes).Are the following shapes Sarah Rose – Mathematics Consultant K-12 – Hunter/Central Coast Region Differentiation Resources Additional Sample Units of Work, Stage 2, 2D RIC, NSW, Math Assessment Stage 2 Planned Assessment Pre Assessment – Sort a group of shapes based on given criteria eg, number of lines of symmetry, regular/irregular shape, at least one pair of parallel sides (remember that in mathematics 'regular' shapes have all sides equal, and all internal angles equal). 2D shapes Pre Assessment Match up- match the shape name and number of sides to the picture of the shape. Teaching Space and Geometry CD ROM-Stage Two –Exploring Quadrilaterals Unit Lesson Five-(assessment activity) Parallelograms on the Geoboard Using computer drawing tools to create a variety of quadrilaterals QT focus-Deep Knowledge (refer to attached lesson) pentagons? (Yes) Why or why not? What makes a regular pentagon? Extension: Can a regular pentagon have a right angle? Repeat for octagon. Whole Class and Group Teaching Exploring Quadrilaterals Unit of Work –need to be taught in sequence Lesson One What are Quadrilaterals? Discovering the features of quadrilaterals QT focus –metalanguage Lesson Two Four Sided frames Manipulating four-sided frames to create different quadrilaterals QT focus-substantive communication Lesson Three Rigid and Non Rigid Shapes Manipulating shapes to explore their rigidity Lesson Four Computer Quadrilaterals Using computer drawing tools to create a variety of quadrilaterals Show students the 'Quadrilateral tree' attached. Is a square always a rectangle? Why or why not? Is a rectangle always a square? Why or why not? Discuss with students the refinements of a quadrilateral to form the special quadrilaterals. Geoboard Shapes The students are asked to try and make a shape by stretching a rubber band around a geoboard. As each shape is made, the students can discuss and record their observations. Ask questions such as: Sarah Rose – Mathematics Consultant K-12 – Hunter/Central Coast Region Teaching Space and Geometry CD ROMStage Two- Exploring Quadrilaterals Unit of Work (refer to attached lesson sheets) (refer to attached lesson sheets) QT focus-substantive communication (refer to attached lesson sheets) QT focus-student engagement (refer to attached lesson sheets) (refer to attached lesson sheets) How many sides does the shape have? Can you find shapes that look like other shapes? Can you make up names for them? Do your shapes have sharp corners? Blunt corners? What is the smallest number of sides you need to make a shape? Why can’t we have a shape with two sides? Irregular/Regular- Make a regular octagon, now make an irregular octagon. Remember that an irregular shape does not have equal sides. Repeat this with a triangle, and discuss the difference between isosceles, equilateral and scalene triangles. Computer Learning Objects SHAPE OVERLAYS -STAGES 1-3 The Shape overlays series of learning objects requires the student to manipulate 2D shapes, by sliding and overlapping, to create other 2D shapes. DIGITAL GEOBOARD -STAGES 1-3 A digital version of a geoboard which enables a band to stretch around the pegs on the geoboard to form a coloured shape. Sarah Rose – Mathematics Consultant K-12 – Hunter/Central Coast Region BST/NAPLAN Questions to practise 2003 BST-YR 3 2006 BST Yr 5 Sarah Rose – Mathematics Consultant K-12 – Hunter/Central Coast Region 2006 BST-YR 3 and Yr 5 question Reflection Time should be allowed at the end of each class lesson to revise learning outcomes shared and strategies used. Working Mathematically is modelled throughout. Sarah Rose – Mathematics Consultant K-12 – Hunter/Central Coast Region The Quadrilateral Tree Quadrilateral: any four sided polygon Trapezium: at least one pair of parallel sides Kite: at least one pair of adjacent sides equal Parallelogram: two pairs of parallel sides Rhombus: all sides equal Rectangle: four right angles Square Sarah Rose – Mathematics Consultant K-12 – Hunter/Central Coast Region l