Space

(Note: Fun, interactive websites can be found at the end of this wikipage!) Teacher Unit Plans - Year 7 ** **__Classifying quadrilaterals according to features__** ** (VELS 4.25) ** This activity uses the pdf. worksheet that is listed below. You might choose to copy the sheet for each student or laminate sheets for repeated use. You might need to explain the symbols for 'equal' or 'parallel'. The shapes are labelled A - X to facilitate discussion. Students cut up the sheet so that they can arrange the quadrilaterals into groups according to various criteria suggested by the teacher or the students. For example, on the basis of the marked properties, the quadrilaterals can be sorted according to: Space
 * Space
 * number of equal sides
 * number of pairs of equal opposite sides
 * number of pairs of parallel sides
 * number of right angles

Divide students into groups and allocate each group one of the definitions from the table below. The task for students is to: Examples of important points for a discussion: > There will be other examples of this; e.g. Definition 3 students may initially want to specially identify the squares in their set, not including them in the set of rhombuses. Using the formal geometric terms, students could now answer the following: Answers: The above ideas could also be used with triangles.
 * __Classifying quadrilaterals according to definitions__ **** (VELS 4.25) **
 * select all the quadrilaterals from the worksheet that is listed below that fit their definition
 * make a list of their common features [[image:rectangle.jpg width="150" height="63" align="right"]]
 * give their set of shapes a good name, and
 * display their set for the subsequent discussion
 * Definition 1 || Is a quadrilateral with all angles 90°. ||
 * Definition 2 || Is a quadrilateral with both pairs of opposite sides parallel. ||
 * Definition 3 || Is a quadrilateral with all sides equal. ||
 * Definition 4 || Is a rectangle with all sides equal. ||
 * Definition 5 || Is a quadrilateral with one pair of opposite sides parallel. ||
 * Definition 6 || Is a quadrilateral with two pairs of adjacent sides of equal length. ||
 * Definition 7 || Is a quadrilateral with at least one acute angle. ||
 * Definition 8 || Is a quadrilateral with equal diagonals. ||
 * Definition 1 students might want to name their shapes as 'rectangles and squares'.Take this opportunity to point out that a square is a special rectangle.
 * Students may be surprised that Definition 3 quadrilaterals (chosen on equal sides) also have parallel sides. This highlights that not all the features of shapes have to be specified in a definition.
 * Definition 8 and Definition 1 result in the same sets, which highlights that there are alternative definitions.
 * Definition 7 results in the set of non-rectangles, the complement of Definition 8 and Definition 1.
 * Is a square a rhombus? (Yes, it is a special rhombus)
 * Is a square a rectangle? (Yes, it is a special rectangle)
 * Every square is a rhombus, but is every rhombus a square? (No)
 * Every square is a rectangle, but is every rectangle a square? (No)
 * Definition 1 || **Rectangle** || Is a quadrilateral with all angles 90 degrees ||
 * Definition 2 || **Parallelogram** || Is a quadrilateral with both pairs of opposite sides parallel. ||
 * Definition 3 || **Rhombus** || Is a quadrilateral with all sides equal ||
 * Definition 4 || **Square** || Is a rectangle with all sides equal ||
 * Definition 5 || **Trapezium** || Is a quadrilateral with one pair of opposite sides parallel. ||
 * Definition 6 || **Kite** || Is a quadrilateral with two pairs of adjacent sides of equal length ||
 * Definition 7 || **All but rectangles** || Is a quadrilateral with at least one acute angle ||
 * Definition 8 || **Rectangles** || Is a quadrilateral with equal diagonals ||

__ **Activity 1: Reflecting shapes (VELS 4.5)** __
This activity uses folding to show the effect of reflection about a line. There are eight figures supplied on the pdf. worksheet below. Each of the two A4 pages has four figures. The individual quarters of the paper should be cut up for the activity. Students will also need a scrap piece of paper on which they have shaded heavily with a soft 2B or 4B pencil, so that the shaded patch is a bit bigger than the figures they are working with. Supplementary shading may need to be added as the activity progresses. For each figure, students fold the quarter of paper along the marked fold line, so that the shape is on the outside. They then lay it down so that the folded paper with the shape uppermost is on top, and the shaded scrap paper is face upwards under the folded paper, as shown below. Students draw over the outline of the shape, pressing firmly, so that the graphite on the scrap paper marks the underside of the folded figure paper. When the paper is unfolded the original figure and its reflected image about the reflection line can be seen (students may want to redraw this image as it may be a bit faint). Students should be encouraged to note the orientation of the image and its distance from the line of reflection. Students can also check that it really is a reflection by looking at the image of the original figure in a mirror placed on the fold line.



__** Activity 2: The last Word on reflections and rotations (VELS 4.5) **__
This activity lets students explore vertical and horizontal reflections and rotations using the simple transformation tools in Microsoft //Word.// Give students a copy of the file which is below as a WORD document and which contains a table of shapes. The first column contains original shapes. The second column contains copies of the shapes from the first column AFTER a rotation or reflection transformation has been applied. Students should select a shape from the first column, copy it, and then apply the appropriate reflection or rotation in order to get their copied shape looking like the one in the second column Instructions on how to use //Word's// reflection and rotation tools are available below (Producing reflections and rotations in Word.doc) It is important to note that //Word// uses its own reflection lines and point of rotation (i.e., the user cannot choose them). The reflection lines run through the middle of the shapes (and only horizontal and vertical are possible in //Word//), and the centre of rotation is at the 'centre' of the shape. //NOTE:// with purpose-built graphics illustration software it is possible to do more extensive activities than the ones presented here. Students interested in graphic design may use the reflection and rotation tools quite often when working with such software.



__** Activity 3: Rotations and symmetry (VELS 4.5)   **__
 In this activity students investigate rotational symmetry. There are two resource sheets for this activity. The pdf. file below allows students to explore exactly what rotational symmetry means. Each student will need two copies of the sheet, and should cut out the shapes on the first copy. After positioning one of the cut-out shapes on the corresponding shape on the second sheet, they should use a pin or pen-tip on the marked axis of rotation and rotate the cut-out over the top of the shape below. Students should also record the smallest angle (or fraction of a turn) that shows rotational symmetry. The second resource sheet, pdf. file "Testing Symmetry" below gives students practice (or testing) on identifying mirror (or fold) lines of symmetry and turn fractions for rotational symmetry.
 * A shape has //reflection (or mirror) symmetry// if it can be reflected/flipped about a line in such a way that it looks exactly the same as it did before reflecting.
 * A shape has //rotational (or turn) symmetry// if it can be rotated through a fraction of a full turn and ends up looking //exactly// the same as it did before the rotation (and by 'exactly the same' we mean that it even appears to have the same orientation).



Transformations - Explore transformations of shapes such as rotation, translation or reflection. Identify which transformations have been applied to circles and polygons to produce new images. http://www.eduweb.vic.gov.au/dlrcontent/4c36353635/index.html

Angles - to construct and measure acute & obtuse angles accurately(computer/IWB). Try this computer task: Atudents use a protractor to find the angle measurements at http://www.eduweb.vic.gov.au/dlrcontent/4c4f495f416e676c65204d656173757265203120416375746520616e64204f6274757365/Index.html

Angles - to construct and measure reflex angles accurately (computer/IWB). Try this computer task: http://www.eduweb.vic.gov.au/dlrcontent/4c4f495f416e676c65204d6561737572652032205265666c6578/Index.html

Angles - learn how to recognise acute, obtuse and reflex angles (computer/IWB). Try this computer task" http://www.eduweb.vic.gov.au/dlrcontent/4c4f495f616e676c655f7479706573/index.html

** Year 8  **

__** Activity 1: Desk map (VELS 4.75)   **__
     Students should make a careful scale map of some region, taking care with initial measurements, conversion calculations, and the final drawing. This map could be of an outside area or the classroom, but a quick and simple approach is to get students to make a 'map' of their desktop. This is a small area that can be measured quickly and accurately, and it is likely that there will be very few difficult angles. Get students to place three or four objects on their desk. The map will be easier if the desk is rectangular and most of the objects are oriented parallel to the edges of the desk. Students take relevant measurements to draw a map of the desk top. To make it simple to begin with, a 1:10 scale could be used, with 1 cm on the map representing 10 cm of the desk top. To help students appreciate what the scale is doing and how the numbers are used in calculating, the teacher may give students a 10 cm × 25 cm rectangle of paper to be one of the objects on the desk. This gives students one object for which it is easy to work out what the scaled version is; they may be able to generalise this to their other objects with more awkward dimensions. A second map using a different scale could then be produced, perhaps 2 cm = 5 cm (which is 1:2.5).  If students work out how to scale the 10 cm × 25 cm rectangle they will be able to use the same calculations in general. Graph paper may help students in drawing their maps.  Having made the map, its accuracy can be tested by using the map to calculate a distance that hasn't actually been measured before now, such as between the corners of two of the objects. Students should measure this on their map, convert this measurement to a real-world distance, and then check by measuring on the desktop itself. Students could also check each others' maps in this way.

__ **Activity 2: Finding what to do by using easy numbers (VELS 4.75)** __
One way to help students decide what operation and what factor to use is to get them to generalise from a simple case where the operation is obvious. Suppose, for example, that on a map where the scale is 5 cm = 1 km and the distance between two towns is 27.8 cm. How far this is in the real world? Some students may struggle to work out what operation to use. Here is a procedure, working first with sample numbers. Forget the 27.8 for a moment, and just look at the ratio, 5 cm = 1 km. By using simpler numbers it should be possible to work out what operation to use. If the measurement was 10 cm it's pretty obvious that the real world amount would be 2 km (//assuming// fluency with the 5 times table!). What's the relationship between 10 and 2? Well, 10 ÷ 5 = 2. If the measurement was 15 cm, then that's 3 km, and note that 15 ÷ 5 = 3. If it was 20 cm, then it's 4 km because 20 ÷ 5 = 4. This helps to establish that dividing by 5 is what turns the measured lengths in centimetres into real world lengths in kilometres. Some students may not need such a step by step approach; just asking what they would do if the length measured was 20 cm (instead of 27.8 cm) might be enough to trigger the required operation and factor. ==== **__Activity 3: Mini island__ (VELS 4.75) **  This activity gives students the opportunity to work with different scales and convert distances, and allows them to check their answers on the 'real world' object. The Mini Island pdf. file below, has two pages and it is important that the sheets are printed on A4 paper, with no enlargement or reduction. One page contains a picture of a 'Real World Island', which is a mini island represented at its actual size. The second page contains maps of the island, produced at different scales (and each map uses a different way of representing the scale). Students are asked to use the maps, with their scales, to work out the real world distances between various points on the island, and then they check their answers by taking the actual measurements on the Real World Island. In addition to straight line distances, students are also asked to work with curved lines. As an alternative, the classroom teacher could prepare some different scale maps of the students' classroom so that the environment is more real for the students. To assist in producing multiple scale maps, calculated use of the reduction features of a photocopier can be applied to some original scale map drawn by the teacher (perhaps draw the first map at 1:50 (i.e., 1 cm = 0.5 m), and then reduce or enlarge this on the photocopier and work out the corresponding new scale). Get students to use the maps to determine distances between points of interest in the classroom, and then check the reality by actually measuring. If the measurements are left until the very end of the lesson, students' calculations could be recorded on the board, and incentives offered for those closest to the real distances (this relies, of course, on the teacher's maps being accurate!). ====

__** Activity 4: Scale conversions (VELS 4.75) **__
The Scale Conversion pdf. file below provides students with some practice converting among the different ways of describing the scale, and also converting distances.

<span style="FONT-FAMILY: 'Times New Roman', Times, serif">** __Activity 5: Know your district__ (VELS 4.75) **
Look at different scale maps of your district, or other familiar area. Explore how changes of scale affect the length measured on each type of map. In Melbourne, the Melway (or other similar publication) has sets of pages at different scales, especially depicting the central business district. In the case of the Melway, these sets of pages are bordered by different colours. There is usually a graphical (graticule) scale at the top of each page, and the Map Symbols page also indicates the ratio scale. __

Angles - To explore the sum of interior angles of a triangle try this task (computer/IWB): http://www.eduweb.vic.gov.au/dlrcontent/4c36353535/index.html
 * INTERNET TASKS specifically related to Year 8's: **

Geometric Shapes - Explore dilations by transforming shapes such as triangles and rectangles. Choose a scale factor and position a shape and dilation centre. Notice how the coordinates of the dilation image are related to the original image. (computer/IWB) http://www.eduweb.vic.gov.au/dlrcontent/4c36353636/index.html

Exploring quadrilaterals - Examine the sides and angles of a four-sided shape. Identify its geometric properties such as the number of sides of equal length. Classify the shape as a parallelogram, rhombus, square, rectangle, kite or trapezium. Notice that some quadrilaterals can be classified in different ways. (computer/IWB) http://www.eduweb.vic.gov.au/dlrcontent/4c36353632/index.html

Exploring relationships of angles - Explore angles formed by a transversal line intersecting parallel lines. Look at illustrations showing pairs of angles: vertically opposite, corresponding and alternate angles. Name pairs of angles to score points and help a monkey drive to the supermarket to buy food. (computer/IWB) * This task looks fun! http://www.eduweb.vic.gov.au/dlrcontent/4c36353534/index.html

**Year 7 or Year 8** 2D Geometry Quiz (computer/worksheets): http://www.bbc.co.uk/skillswise/numbers/measuring/2d_shapes/quiz.shtml

Basic Angles Powerpoint Quiz(IWB): http://pds.hccfl.edu/it3/TResources/MMInstruct_tools/ms/Math/angles.ppt

Choose from a Maths activity or a quiz about Angles(computer/IWB): http://www.bbc.co.uk/schools/ks2bitesize/maths/revision_bites/angles1.shtml

How many angles can you find in this photograph?(computer /IWB/worksheet) Name, count and record the different types of angles in your workbook. http://community.webshots.com/photo/fullsize/2522357870012195579NdeCqt

Symmetry artist-have a bit of fun making your own symmetrical drawings(computer/IWB): http://www.mathsisfun.com/geometry/symmetry-artist.html

Find out about all kinds of Geometry at this web site(computer/IWB): http://www.mathsisfun.com/geometry/index.html

Try the Geometry activities at Mathletics(computer?IWB/worksheets): [|www.mathletics.com.au]