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Syllabus content Welcome back! This is our third issue of The Mathematical Bridge. This issue focuses on the Geometry section of the Measurement and Geometry strand and looks more closely at the progress of Two-Dimensional Space, Angles and Angle Relationships across Stage 3 and 4 Mathematics. We see these connections as important as the links between shapes and their angle properties become foundational knowledge as students develop geometric deductive and reasoning skills. The associated language, symbols, notation and conventions are all essential in developing an appropriate level of understanding. We hope you find these resources useful and we welcome any feedback and/or suggestions. Pedagogy Although it is now separate, the connections between angles and shapes should still be strongly emphasised, particularly in Stage 3 where we begin to introduce properties of shapes, all shapes have angle properties. This will lead into the Stage 4 substrands of Angle Relationships and Properties of Geometric Figures. These connecting concepts are also further developed as we link measurement and geometry through finding area of shapes and volumes of objects/ solids. The first mention of angles in our new syllabus is actually in Stage 2 in Two-Dimensional Space 1: • recognises the vertices of twodimensional shapes as the vertices of angles that have the sides of a shape as their arm Katherin Cartwright, Mathematics Advisor K-6 and Zdena Pethers, R/Numeracy Advisor 7-12 Getting the right angle In the new NSW mathematics K-10 syllabus Angles is now its own substrand and appears in Stages 2 and 3. We currently teach angles in primary as outcome b in TwoDimensional Space and angles are introduced earlier, in Stage 1. Teaching ideas It will therefore be necessary to explore the concept of angles as a measure of turn in the environment and in shapes prior to expecting students to be able to recognise them as vertices. When developing your scope and sequence of learning in Stage 2, teaching Angles and Two-Dimensional Space together will provide students with a deep understanding of the concept of describing shapes and their features. This is a prior skill to seeing angles as properties of shapes. It is always best to start with the known then move to the unknown. The environment provides students with a wide variety of angles being used in the real world. They can explore, identify, describe, investigate and draw angles from pictures and photographs of familiar places. • identify right angles in squares and rectangles PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 2 Starting with hands on tasks is also important, beginning with concrete examples and activities then applying this knowledge to abstract concepts is essential for all students at every stage of learning from Early Stage 1 to Stage 4 and beyond. This enables students to try a broader range of strategies to solve problems when using geometric thinking and allows students to feel comfortable in taking risks, trialling ideas, testing theories and predictions. A different angle…. As students work mathematically and think like mathematicians, we encourage them to ask and pose questions and prove their reasoning. There are a number of aspects and concepts around angles and lines that would start robust discussion in the classroom. Questions like: How do we know lines are parallel? Can you prove your reasoning? How would you explain what horizontal and vertical lines are? Vertically opposite angles GeoGebra Applet Right Angle Challenge From www.nrich.maths.org/2812 Can students do this without the knowledge of right angles and what perpendicular means? Adjacent angles GeoGebra Applet This activity requires students to manipulate two sticks to make right angles. Egyptian Rope http://www.mathsisfun.com/perpendicularparallel.html From www.nrich.maths.org/982 This activity allows students to use a knotted rope to make various triangles. Students can then investigate angle features of shapes. Teachers can also link angles to time in the hands of a clock or to themselves by looking at angles you can make with your body. There is also much to be explored about angles in sport both with playing fields and also looking at the amount of turn Olympic divers, discus throwers, ice skaters and gymnasts make as part of their sport. In my thinking, right angles and perpendicular lines are a bit of a ‘chicken and the egg’ conversation. It is difficult to explain one without referencing the other. This can be particular difficult when students understanding of right angles (Stage 2 ) does not yet refer to exact measuring of 90 degrees using protractors (Stage 3). These kinds of justifications are not reflected in the mathematics syllabus until Stage 4. However, to assist students in developing sound knowledge and understanding of these concepts, it may need to be discussed from as early as Stage 1. GeoGebra has many applets that are interactive to show students how angles move. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE Angles at a point GeoGebra Applet Angle relationships In Stage 4, there is stronger emphasis on more formal understanding of angle relationships, including the associated terminology, notation and conventions, as this is of fundamental importance in developing an appropriate level of knowledge, skills and understanding in geometry. Angle relationships and their application play an integral role in students learning to analyse geometry problems and developing geometric and deductive reasoning, as well as problem-solving skills. Angle relationships are key to the geometry that is important in the work of architects, engineers, ISSUE JULY 2014 3 designers, builders, physicists, land surveyors etc. as well as the geometry that is common and important in everyday situations, such as in nature, sports, buildings, astronomy, art, etc. (Angle Relationships Stage 4 Mathematics K-10 Syllabus online) In Stage 4, students are expected to use the correct terms and know their meanings. Students should use terms such as complementary, supplementary, adjacent and vertically opposite as they communicate their reasoning in solving problems involving angles at a point. Students are also expected to identify, understand and use angle relationships related to transversals on sets of parallel lines and use the terms alternate, corresponding and co-interior when referring to these angles. They should be able to solve problems involving angles related to parallel lines, and justify why two lines are parallel. A triangle can be classified by its angle relationships as right, scalene, equilateral or isosceles. Note the convention of marking equal sides by identical markers. A right-angled triangle has one angle of 90˚ Alternate angles between parallel lines are equal A scalene triangle has no equal angles and no equal sides. Corresponding angles on parallel lines are equal Complementary angles add up to 90˚ GeoGebra Applet 60 Co-interior angles between parallel lines are supplementary Supplementary angles add up to 180˚ GeoGebra Applet Students should also be proficient in using diagrams and symbols when applying mathematical techniques and reasoning to solve problems involving angle relationships. For example, using the correct notation for right angles and equal angles in diagrams and using capital letters when naming points and intervals. 60 60 An equilateral triangle has all angles of 60˚ and all sides are equal. Students are encouraged to investigate and develop some of these relationships using their knowledge and skills about angle properties from Stage 3 (e.g. vertically opposite, straight angles). Properties of Geometrical Figures Study of angle relationships links smoothly to the investigation of properties of geometrical figures. Angle sum of a triangle is 180 ˚ and angle sum of a quadrilateral is 360˚, and students can use a variety of ways to justify this. They build on their work in Stage 3 relating to the side and angle properties of triangles and quadrilaterals, in a more structured and formal way. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE An isosceles triangle has two equal angles opposite two equal sides. It is important to expose students to different orientations of the special triangles from those shown above. They need to be able to identify them by their properties in ANY orientation. Angle relationships are also important properties of quadrilaterals and together with information about ISSUE JULY 2014 4 their sides, can be used to solve geometrical problems. Students can explore properties of triangles and quadrilaterals through investigations and find unknown angles by developing a series of logical steps. For example: Find the size of ∠ BCE. Note the convention: parallel lines are shown by identical arrows, and a right angle at E is indicated by a square. present different solutions to each other, showing reasoning and justifying their thinking. This deepens their conceptual understanding of angle relationships. Students in Stage 4 should write geometrical reasons without the use of abbreviations to assist them in learning new terminology, and in understanding and retaining geometrical concepts: e.g. 'When a transversal cuts parallel lines, the cointerior angles formed are supplementary'. http://lrrpublic.cli.det.nsw.edu.au/lrrS ecure/Sites/Web/geometer/ Transformations 110˚ E Here is one way a student could solve this problem: Students should also build on their work in Stage 3 on transformations. Translation, rotation and reflection, are called “congruence” transformations as the figures remain identical and side and angle relationships remain unchanged. In enlargements, lengths of sides change but angle relationships remain identical. 1) ∠ ABC = 70˚ since it is co-interior with ∠ DAB between parallel lines AD and BC (co-interior angles are supplementary – add up to 180˚) 2) ∠ BCD = 110˚ since it is cointerior with ∠ ABC between parallel lines AB and DC (cointerior angles are supplementary) 3) ∠ BCE = 70˚ since it is supplementary to ∠ BCD (straight angle) http://www.schools.nsw.edu.au/learni ng/712assessments/naplan/teachstrategi es/yr2013/index.php?id=numeracy/n n_spac/nn_spac_s4b_13 Other Resources www.nrich.maths.org Making Sixty http://www.youtube.com/watch?v=F1 M1MncPq2c Other interesting websites: Another way to solve this problem could be: This activity asks students ti investigate and prove angle properties related to triangles, retangles using knowledge of congruent triangles. Right angles 1) ∠ ABC = 70˚ since it is co-interior with ∠ DAB between parallel lines AD and BC (co-interior angles are supplementary – add up to 180˚) 2) ∠ BCE = 70˚ since it is alternate with ∠ ABC between parallel lines AB and DE (alternate angles are equal) http://www.resources.det.nsw.edu.au /Resource/Access/f9a38f90-8e0d492b-9a5d-4a46dd3f5c22/1 In this activity students explore creating triangles using points around a circle. There are often several ways to solve a geometrical problem and students should be encouraged to PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 Continuum of learning Mathematics K-10 Measurement and Geometry Strand Stage 2 Stage 3 Stage 4 Two-Dimensional Space: A student manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features MA2-15MG Two- Dimensional Space: A student manipulates, classifies and draws twodimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties MA3-15MG Properties of Geometric Figures: A student classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles MA4-17MG Part 1 Identify and describe shapes as ‘regular’ or ‘irregular’ Part 1 Identify, name and draw right-angled, equilateral, isosceles and scalene triangles Part 1 Classify and determine properties of triangles and quadrilaterals ISSUE 1 | FEBRUARY 2014 Describe and compare features of shapes, including the special quadrilaterals Explore angle properties of the special quadrilaterals and special triangles Classify and draw regular and irregular two-dimensional shapes from descriptions of their features Identify line and rotational symmetries Determine the angle sums of triangles and quadrilaterals Use properties of shapes to find unknown sides and angles in triangles and quadrilaterals giving a reason Part 2 Identify congruent figures Identify congruent triangles using the four tests Note: the key ideas listed above for Two-dimensional Space are only those that relate to angles, this is not a list of all key ideas for Two-Dimensional Space Angles: A student identifies, describes, Angles: A student measures and Angle Relationships: A student compares and classifies angles constructs angles, and applies angle identifies and uses angle relationships, relationships to find unknown angles including those related to transversals MA2-16MG on sets of parallel lines MG3-16MG MA4-18MG Part 1 Part 1 Use the language, notation and conventions of geometry Identify and describe angles as Recognise the need for formal units to measures of turn measure angles Apply the geometric properties of angles Compare angle sizes in everyday at a point to find unknown angles with Measure, compare and estimate angles situations appropriate reasoning in degrees (up to 360°) Identify ‘perpendicular’ lines and ‘right angles’ Record angle measurements using the symbol for degrees (°) Part 2 Draw and classify angles as acute, obtuse, straight, reflex or a revolution Construct angles using a protractor (up to 360°) Describe angle size in degrees for each angle classification Part 2 Identify and name angle types formed by the intersection of straight lines, including ‘angles on a straight line’, ‘angles at a point’ and ‘vertically opposite angles’ Apply the properties of corresponding, alternate and co-interior angles on parallel lines to find unknown angles with appropriate reasoning Determine and justify that particular lines are parallel Solve simple numerical exercises based on geometrical properties Use known angle results to find unknown angles in diagrams PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 6 Stage 2 Teaching Ideas- Two-Dimensional Space and Angles These lesson ideas are specifically for Stage 2 and form prior knowledge that is required for students in Stage 3, as angles has its foundation in their relation to Two-Dimensional shapes. You may like to explore these concepts with your Stage 3 students to gain knowledge of their current understandings. Strand: Measurement and Space Substrand: Two-Dimensional Space 1 Outcomes: WM2-1WM uses appropriate terminology to describe, and symbols to represent, mathematical ideas WM2-3WM checks the accuracy of a statement and explains the reasoning used MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features Students: Compare and describe features of two-dimensional shapes, including the special quadrilaterals recognise the vertices of two-dimensional shapes as the vertices of angles that have the sides of the shape as their arms identify right angles in squares and rectangles group parallelograms, rectangles, rhombuses, squares, trapeziums and kites using one or more attributes, eg quadrilaterals with parallel sides and right angles identify and describe two-dimensional shapes as either 'regular' or 'irregular', eg 'This shape is a regular pentagon because it has five equal sides and five equal angles' To be taught in conjunction with… Strand: Measurement and Space Substrand: Angles 1 Outcomes: WM2-1WM uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA2-16MG identifies, describes, compares and classifies angles Students: Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064) identify 'angles' with two arms in practical situations, eg the angle between the arms of a clock identify the 'arms' and 'vertex' of an angle Activity 1: Exploring angles on shapes Pose questions to students to gain understanding of their knowledge of shapes and if they can identify angles in two-dimensional shapes T: What do these shapes have in common? S: All 2D shapes, all have straight lines/ sides, all regular shapes, all ‘flat’, all have ‘corners’, all have vertices… T: When we look at the vertices, do you know another name or way of describing them? Note: If students do not say ‘angle’ or ‘right angle’ show them the next image Where else can you see them in the other shapes? See if the students can also locate angles in the classroom, in pictures, photos and on objects PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 7 Activity 2: Sorting and grouping shapes Provide students with an assortment of quadrilaterals (shapes cut out of paper) use both regular and irregular shapes Have students work in pairs to sort the shapes into piles and share their reasons for sorting the shapes. Do students only sort shapes according to ‘squares’ ‘rectangles’ etc or do students look at other features like angles or length of sides? You may need to prompt students to expand or explore other ways to sort the shapes Could you sort the shapes into group of those with right angles and those without? What about shapes that have parallel sides? What about shapes with all sides equal? What do you notice about shapes that have all sides equal? Specifically about their angles You could pose the statement that ‘all shapes that have all sides of equal length have all angles of equal size’ Allow the students to investigate this and prove it to be true or false. Providing reasons and discussing strategies and the processes they used to explore the problem. Students may like to pose their own investigations about angles and shapes. Activity 3: Angle Arms Many students have the misconception that the length of the angle’s arm influences the size of the angle. E.g. ‘the longer the arms of the angle, the greater the angle size’ Draw a right angle on the board or IWB Now draw another one (with longer arms) Ask the students: Which angle is larger? How do you know? Why do you think that? Where do we measure the angle? How could we check? What could we use to check? (Students may suggest a square pattern block, a piece of paper) Does it matter how long the arms are? Does this change the size of the angle? Provide students with a square pattern block (the orange one) or a square of Brennex paper to take around the class and outside to find right angles where the arms are different lengths or in different orientations. Many students also believe there must be a ‘left’ angle if there is a right angle, for this reason it is important to provide examples in different positions and orientations, including on the diagonal. Also allow them to find right angles in different locations. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 8 Stage 3 Teaching Ideas- Angles Start with concrete and then move to abstract This lesson is from the Teaching Space and Geometry K-6 CD, this resource is currently being updated to align to the new mathematics K-10 syllabus outcomes and will be available online for NSW DEC teachers in the future. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 9 Stage 3 Teaching Ideas- Angles Creating angle testers is one way of allowing students check and justify their angle estimations accurately without using a commercial protractor. Students in the stages before Stage 3 may have had experience with using bendable straws, a pipe cleaner in a straw, to look for angles smaller than or larger than a right angle. With this angle tester, students can find a greater variety of angles and can also explore the angle properties of two-dimensional shapes, specifically triangles. This lesson is by Azim Premji Foundation and can be found here http://www.teachersofindia.org/en/activity/handmade-math-tools-protractor PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 10 Stage 3 Teaching Ideas- Angles This activity is one of many that can be accessed via the NAPLAN Teaching Strategies website. There are a number of activities to the teaching of angles. Strand: Measurement and Space Substrand: Angles 1 Outcomes: WM3-1WM describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-16MG measures and constructs angles, and applies angle relationships to find unknown angles Students: identify that a right angle is 90°, a straight angle is 180° and an angle of revolution is 360° identify and describe angle size in degrees for each of the classifications acute, obtuse and reflex use the words 'between', 'greater than' and 'less than' to describe angle size in degrees (Communicating) Activity: Angle Card Matching PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 11 Stage 3 Teaching Ideas- Angles Strand: Measurement and Space Substrand: Angles 2 Outcomes: WM3-1WM describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-16MG measures and constructs angles, and applies angle relationships to find unknown angles Students: identify and name angle types formed by the intersection of straight lines, including right angles, 'angles on a straight line', 'angles at a point' that form an angle of revolution, and 'vertically opposite angles' recognise right angles, angles on a straight line, and angles of revolution embedded in diagrams (Reasoning) identify the vertex and arms of angles formed by intersecting lines (Communicating) recognise vertically opposite angles in different orientations and embedded in diagrams (Reasoning) Activity: Identifying angles (lesson idea by Nagla Jebeile) This activity requires students to identify angles in the environment in pictures. We have used a sample photo. You may find it more useful to use images that the students take of the school, school community or home environment. Choosing images that display a variety of angles (including vertically opposite angles, adjacent angles and angles at a point) is important as these are all new angle types for students in Stage 3. The Ferris wheel is a great image to explore for vertically opposite angles, adjacent angles and angles at a point. Scissors are also a good example of vertically opposite angles that provide a concrete example for students. What types of angles can you see? Draw the different types of angles you can find Adjacent Acute Obtuse Right Vertically Opposite Straight Line Reflex http://upload.wikimedia.org/wikipedia/commons/9/9f/Luna_Park-Sydney-Australia.JPG PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE Revolution ISSUE JULY 2014 12 Stage 3 Teaching Ideas- Angles in Two-Dimensional Space Strand: Measurement and Space Substrand: Two-Dimensional Space 1 Outcomes: WM3-1WM describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions WM3-2WM selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations WM3-3WM gives a valid reason for supporting one possible solution over another MA3-15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties Students: Classify two-dimensional shapes and describe their features explore by measurement side and angle properties of equilateral, isosceles and scalene triangles explore by measurement angle properties of squares, rectangles, parallelograms and rhombuses Activity: Exploring angles using pattern blocks There are number of great activities that use pattern blocks to look angles and angle relationships of two-dimensional space. Two lessons that explore angles using patterns blocks come from our Teaching about angles Stage 2 book. This book is currently being rewritten to align the lessons to the new mathematics K-10 syllabus outcomes. These two lessons attached are in draft form but can be used in the classroom. We welcome any feedback about the success of these lessons. This book, Developing Mathematics with Pattern Blocks by Paul Swan and Geoff The book can be purchased through AAMT for $40 for members. It has a number of wonderful lessons that use pattern block for angles, other special relationships and also for Fractions. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 13 Stage 4 Teaching ideas – Angle relationships Strand: Measurement and Geometry Substrand: Angle Relationships Outcomes: A student MA4-18MG identifies and uses angle relationships, including those related to transversals on sets of parallel lines MA4-1WM communicates & connects mathematical ideas using appropriate terminology, diagrams & symbols MA4-2WM applies mathematical techniques to solve problems MA4-3WM recognises and explains mathematical relationships using reasoning In Stage 3, students investigate angle relationships in a more informal way, finding different types of angles in their environment, developing a conceptual understanding of what angles are and their relationship to their world. In Stage 4, students are expected to manipulate angles in a more abstract way, formally name them and solve problems that involve angle relationships. Naming practice Excerpt from: Mathematics Stage 4 – Angles (Centre for Learning Innovation) can be found on TaLe – secondary teachers – item code X00LB. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 14 Once students have had a chance to work through activities like those below, a good way to differentiate learning for all students would be to ask them to work in pairs of small groups, and make up diagrams and similar problems for other students. This will deepen their understanding of angle relationships and give all students the opportunity to work at a level that is appropriate to their ability. Using Angle Relationships In each diagram, use the angle given, to find the value of each pronumeral, giving your reasons. Do not measure the angle using a protractor as the diagrams are not drawn to scale. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 15 Excerpt from: Mathematics Stage 4 – Angles (Centre for Learning Innovation) can be found on TaLe – secondary teachers – item code X00LB. Reasoning in geometry X + 61 + 29 + 90 X= PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 16 Page 2 PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 17 Reasoning and parallel lines Excerpt from: Mathematics Stage 4 – Angles (Centre for Learning Innovation) can be found on TaLe – secondary teachers – item code X00LB. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 18 Page 2 Excerpt from: Mathematics Stage 4 – Angles (Centre for Learning Innovation) can be found on TaLe – secondary teachers – item code X00LB. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 19 Stage 4 Teaching ideas – Properties of geometrical figures Strand: Measurement and Geometry Substrand: Properties of Geometrical Figures Outcomes: A student: MA4-17MG classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles MA4-1WM communicates & connects mathematical ideas using appropriate terminology, diagrams & symbols MA4-2WM applies mathematical techniques to solve problems MA4-3WM recognises and explains mathematical relationships using reasoning The following investigation activities could be done in pairs or small groups where students are encouraged to discuss, justify and give reasons for their decisions. Investigation – Angles in quadrilaterals Syllabus PLUS Series Recordings Excerpt from: Mathematics Stage 4 – Properties of geometrical figures (Centre for Learning Innovation) can be found on TaLe – secondary teachers – item code X00L9. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 20 Investigation – Quadrilaterals Excerpt from: Mathematics Stage 4 – Properties of geometrical figures (Centre for Learning Innovation) can be found on TaLe – secondary teachers – item code X00L9. PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014 21 Subscription link DEC Mathematics Curriculum network GeoGebra Institute, GeoGebra applets and teaching ideas Click on this image to be added to our network list for all newsletters and professional learning information Conferences Syllabus PLUS NEW Keep an eye out for the Syllabus PLUS Maths K-6 Series 4 in SchoolBiz Term 3, week 1. Flyer attached. Resources Scootle MANSW NEW MANSW have a new website, their annual conference is also coming up this Term. ‘Wonderland in Wollongong… Curiouser & Curiouser’ 12-14 September at the Novotel Wollongong. See website for registration details. Further information Learning and Leadership Directorate Primary Mathematics Advisor [email protected] Secondary Mathematics AC Advisor [email protected] Secondary Mathematics Advisor [email protected] Level 3, 1 Oxford Street Sydney NSW 2000 9266 8091 Nagla Jebeile 9244 5459 Katherin Cartwright © July 2014 NSW Department of Education and Communities PUBLIC SCHOOLS NSW – LEARNING AND LEADERSHIP DIRECTORATE ISSUE JULY 2014