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Time: 5 hours
Level: Introductory
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 Introduction Resource- This unit looks at various aspects of shape and space. It uses a lot of mathematical vocabulary, so you should make sure that you are clear about the precise meaning of words such as circumference, parallel,...
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- 1.1 Angles, notation and measurement Resource
- In everyday language, the word ‘angle’ is often used to mean the space between two lines (‘The two roads met at a sharp angle’) or a rotation (‘Turn the wheel through a large angle’). Both of these senses...
- 1.2 How to measure an angle Resource
- To measure an angle you need a protractor. The protractor shown here is a semicircle that is graduated to measure angles from 0° to 180°. It is also possible to buy circular protractors that measure angles...
- 1.3 Angles, points and lines Resource
- Very often, angles in a shape are determined by the geometric properties of that shape. For example, a square has four right angles. So, when you know a shape is a square, you do not need to measure its...
- 1.3.2 Angles on a line Resource
- Click here for Activity 2.
- 1.3.3 Drawing a pie chart Resource
- You can use the fact that the sum of angles at a point is 360° to draw a pie chart.
- 1.3.4 Vertically opposite angles Resource
- When two straight lines cross, they form four angles. In the diagram below, these angles are labelled α, β, θ and φ and referred to as alpha, beta, theta and phi. The angles opposite each other are equal....
- 1.4 Parallel lines Resource
- Two straight lines that do not intersect, no matter how far they are extended, are said to be parallel. Arrows are used to indicate parallel lines.
- 1.4.1 Corresponding angles Resource
- If you trace the lines at one of the intersections in the diagram below and place them over the lines at the other intersection, you will find that the two sets of lines coincide exactly. The four angles...
- 1.4.2 Alternate angles Resource
- Other pairs of equal angles can be identified in Example 5. These pairs of angles occur in a Z-shape, as indicated by the solid line in the diagram below. Such angles are called alternate angles.
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- 2.1 Geometric shapes – triangles Resource
- This section deals with the simplest geometric shapes and their symmetries. All of the shapes are two-dimensional – hence they can be drawn accurately on paper.
- 2.2 Geometric shapes – quadrilaterals Resource
- The next few activities explore some properties of quadrilaterals and their diagonals.
- 2.3 Geometric shapes – circles Resource
- All circles are the same shape – they can only have different sizes.
- 2.4 Drawing circles Resource
- Drawing circles freehand often produces very uncircle-like shapes! If you need a reasonable circle, you could draw round a circular object, but if you need to draw an accurate circle with a particular...
- 2.5 Symmetry Resource
- Symmetry is a feature that has been used in the design of objects and patterns in many cultures throughout recorded history. From Greek vases and medieval windows to Victorian tiles and Native American...
- 2.6 Line symmetry Resource
- Look at the shapes below. The symmetry of the shape on the left and its relationship to the shape on the right can be thought of in two ways:
- 2.7 Rotational symmetry Resource
- There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim.
- 2.8 The angles of a triangle Resource
- The sum of the angles of any triangle is 180°. This property can be demonstrated in several ways. One way is to draw a triangle on a piece of paper, mark each angle with a different symbol, and then cut...
- 2.9 Similar and congruent shapes Resource
- Two shapes are said to be similar if they are the same shape but not necessarily the same size. In other words, one may be an enlargement of the other. They may also have different orientations, as in...
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- 3.1 Areas of quadrilaterals and triangles Resource
- You may like to add the area formulas in this section to your Learning Journal for future reference.
- 3.2 Areas of circles Resource
- There are two very famous formulas for circles:
- 3.3 Volumes Resource
- What is a volume? The word usually refers to the amount of three-dimensional space that an object occupies. It is commonly measured in cubic centimetres (cm3) or cubic metres (m3).
- 3.4 Cylinders and shapes with a uniform cross-section Resource
- An important idea when calculating volumes of simple shapes is that of a cross-section. In the case of the rectangular box considered above, it is possible to slice through the box horizontally so that...
- 3.5 Scaling areas and volumes Resource
- In OpenLearn unit MU120_4M5 Diagrams, graphs and charts you saw how a scale is used on plans of houses and other structures. The scale makes it possible to take a length on the plan and calculate the corresponding...
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- 4 OpenMark quiz Resource
- Now try the quiz and see if there are any areas which you need to go over again. Click Open mark quiz.
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| | References and Acknowledgements | |
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