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Q Now suppose that the goat is tethered to the corner, O, of a shed that is 4 metres one way by 6 metres the other way. The diagram in fig 1 shows how this arrangement looks from above – make sure the students appreciate that this is a plan view. The height of the shed is irrelevant, so long as the goat can’t climb over it! teachwire.net/secondary When a goat is tethered to a shed, howmuch of the surrounding area can they reach? Colin Foster explains how this is a rich scenario for exploring circle area calculations... THE TETHERED GOAT Lesson plan: MATHS KS3 In this lesson, students consider the parts of a field a goat can reach if it is tethered to the corner of a shed. The region of grass the goat can access depends on the length of the rope; as the rope gets longer and begins to snag on the corners of the shed, students will need to think hard in order to work out the locus and calculate the total area of accessible grass. STARTER ACTIVITY Q Imagine a goat is tethered by a rope to a post in the middle of an empty field of grass. What shape area of grass can the goat eat? Why? Students should realise that the locus of points in a plane that are a fixed distance from a fixed point is a circle. Since the rope is flexible, the goat will be able to eat all of the grass inside that circle. Encourage students to use precise language and vocabulary to answer the question, and state that the radius of the circle is equal to the length of the rope, and that the centre of the circle is at the base of the post. Q What assumptions do we need to make to answer this question? Students might say many things in response to this – that the rope is not stretchy and doesn’t break; the post is fixed; the ground is flat; the grass in the field is evenly distributed; the field is larger than the area the goat can reach; there is nothing else in the field, etc. How much grass can a tethered goat reach? Q MAIN ACTIVITY 90 WHY TEACHTHIS? This lesson applies students’ knowledge of loci and the area of a circle to solve a problem involving a tethered goat. KEY CURRICULUM LINKS • Make and use connections between different parts of mathematics to solve problems • Calculate and solve problems involving the perimeters of 2D shapes (including circles), areas of circles and composite shapes DOWNLOAD a FREE KS4 lesson plan on using and interpreting bearings teachwire.net/ use-bearings