Plan for Year 7 Symmetry and Position

Unit: Symmetry and positionDelivered:Time to deliver:

MPA map for this unit:

From Year 7 From Year 8use conventions and notation for 2-D coordinates in all four quadrants; find coordinates of points determined by geometric information

identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles

identify and use angle, side and symmetry properties of triangles and quadrilaterals; explore geometrical problems involving these properties, explaining reasoning orally, using step-by-step deduction supported by diagrams

use 2-D representations to visualise 3-D shapes and deduce some of their properties

find the midpoint of the line segment AB, given the coordinates of points A and B

identify alternate angles and corresponding angles; understand a proof that:

the angle sum of a triangle is 180° and of a quadrilateral is 360° the exterior angle of a triangle is equal to the sum of the two interior opposite

angles

solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometrical properties

Live content and examples click here!

Audit of Personal Learning and Thinking Skills in this unit:

Where does all this fit in terms of attainment? Click here to see level by level descriptions for this work.

Description of content:

Content Further pointsAt any stage it may be appropriate to give “traditional” reinforcement activities for students to complete in their books, on paper etc.

Support:

Give students cut out card or paper shapes of various different sized rectangles, squares, equilateral, isosceles and scalene triangles. In pairs or small groups they are to sort these into piles with a reason for their sorting. In class feedback start to look for, encourage or prompt use of key words such as equal side, equal angle, lines of symmetry – if these don’t occur could give groups more time to look at shapes again with particular aim of grouping according to symmetry properties. At a more basic level encourage use of clear position vocabulary such as top, next to, etc rather than “this side” etc.

“Classroom coordinates” bit more risky/time consuming but could try the following:

Standing at the back of the class with the desks arranged in rows and columns and with a visual representation of this on your whiteboard that the students are facing. This way every representation is consistent with what they are experiencing.Using desks to describe where you want the line of symmetry getting students to position themselves across the line of symmetry (no need for coordinates/equations). Student recording at the board to ensure that an overview of what this would look like from above.Include generating shapes which overlap after a reflection - how can you make this happen? Could use desks

Open and closed tasks in a variety of contexts that allow them to select the mathematics to use.Pupils plan what to do.

Develop their own lines of enquiry and convincing arguments to support their decisions and conclusions.Think creatively, drawing on their knowledge and understanding of mathematics and identifying the mathematical features that are important.

Evaluate their own and others' work and respond constructively.Work logically towards results and solutions, and to value feedback and learn from mistakes.

Work collaboratively as well as independently to solve mathematical problems.

Work independently on extended tasks that bring together different aspects of mathematical content.

Pupils should be able to develop convincing arguments to influence others and take part in discussions.

as grid again, use a loop of string stretched to a rectangle as the original and another loop stretched to make the reflection of the shape - show that they overlap if you position a line of symmetry appropriately. Student recording at the board to ensure that an overview of what this would look like from above.This is likely to start to lead to the need to name locations so ideal to bring in the coordinate system: determine the origin as the desk in the row nearest to you, on the far left hand side (so if you were standing at the front of the class this would be the back right hand desk) and therefore name or label desks in the conventional way. Start then to get students in certain positions by using the coordinates, or position students and get them to tell you the coordinates. Again, make half a shape and get students to complete it using a line of symmetry (string, several metre rules etc) or use the string loops to make rectangles, triangles etc to position symmetrically.

Now do a similar thing to engage students in translations: how can I move from Bob to Clare? This should start the idea of giving directions as across and up or down and lead to the need to clarify the across direction by using positional words like left and right. Dependent on the group you could even start to use just numbers e.g.

saying “four, two” meaning the column vector Students are sitting on their desks unless they are the

ones who are moving. Could reinforce coordinate knowledge by asking “if the student at (3,2) moves 4 right and then 2 up, who’s table will they be sitting on?”

Could now also use the string loops again to demonstrate that a whole shape can move in a similar way by moving each vertex by the translation given.

Core and Extension:

Any ideas from Support that may be necessary. Diamond mine is a good fast paces game which would check understanding of the four quadrant coordinate system: http://nrich.maths.org/public/viewer.php?obj_id=2760

A few examples of using and describing 3D shapes is in the supplement of examples here http://nationalstrategies.standards.dcsf.gov.uk/downloads/pdf/ma_sf_exmp_198_200_036608.pdf and could be used as a starter / discussion activity when appropriate.

Could use the nRich “Square it” activity to start this by getting students to position the point to make a square so that they start to see how it can be rotated: http://nrich.maths.org/public/viewer.php?obj_id=2526 and then “Eight Hidden Squares” at http://nrich.maths.org/public/viewer.php?obj_id=6280 so that they start to use coordinates in locating points. This could be done whole class or print it out and highlight the red crosses so that students could do it in groups or alone on paper.http://nrich.maths.org/public/viewer.php?obj_id=6288 is a cops and robbers game and although it is not defining shapes you are using the coordinates to help you locate possible places where the robber can be – level 2 uses all four quadrants, levels 3 and 4 make it even more restrictive!

Although tessellation is not in this unit a nice activity now could be to get students to draw a pattern onto a 4 quadrant axis page using a single quadrilateral and showing how it will tessellate:

Origami folding- become each group of three students given instructions on how to make one or two of these shapes by paper folding. Given time limit to become experts in making this shape, then each group given time to teach the rest of the class how to do it. Each student will therefore end up with one of each of the shapes for use in later lessons.Equilateral triangle, Isosceles trapezium, Kite, Isosceles triangle, Parallelogram, Rhombus, Trapezium and rectangle (just an A4 sheet for the rectangle!)

Discover the properties of their shape and then teach the class about the properties (discussion of examples v proof for higher ability)- symmetry (rotational & reflection), parallel, perpendicular, equal lengths, angles etc. These can be shown on the shape – e.g. fold and then draw on lines of symmetry, mark equal angles, and demonstrate rotational symmetry by numbering sides and rotating one shape on top of an identical one.

A good card sort activity is here.