Loci Lesson on Ants' Behavior
In this engaging lesson presented by Kipkirui Towett, students explore loci through a story about ants following their boss's commands. They discover how to avoid hearing different bosses' voices and understand equidistant points. The lesson progresses with multiple scenarios challenging students' understanding of loci, leading to problem-solving involving walking within specific boundaries. Students of varying proficiency levels can excel by drawing loci paths and solving advanced loci problems.
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Presentation Transcript
Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett Before you begin make sure you have the following equipment: A ruler marked in cm and mm A protractor A sharp pencil A pair of compasses
STARTER Form 4 Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett A story about Ants An army of ants work very hard all day long. They do everything their boss tells them, all the time. Every now and then he barks a random order at them just because he can. If the ants hear the boss order, they must obey The boss voice travels exactly 1metre from where he stands Where are the ants safe to stand to avoid hearing the boss voice? BY: KIPKIRUI TOWETT.
Form 4 Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett BY: KIPKIRUI TOWETT.
Form 4 Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett d p q BY: KIPKIRUI TOWETT.
Form 4 Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett Lets go back to our ants The boss is not happy now that the ants have worked out how to avoid doing his orders, so he hires in another boss to help him He also invests in two Megaphones so both bosses can be heard anywhere Each ant must follow the orders of whatever boss they are standing closest to. Now the ants only way of avoiding work is to be exactly the same distance away from each boss So now where should the ants stand? BY: KIPKIRUI TOWETT.
Form 4 Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett And the only option they had was to align themselves in this order BY: KIPKIRUI TOWETT.
Form 4 Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett This line represent points This line represent points equidistant from the two points equidistant from the two points A and B A and B A B p BY: KIPKIRUI TOWETT.
Form 4 Friday, 28 February 2025 Loci Presented by: Towett Kipkirui Loci Lesson Objectives: Loci is the plural of Locus . Developing students will be able to draw simple loci. A Locus is the path you would follow if you were given certain instructions. Secure students will be able to solve problems involving multiple loci. Eg. You must walk so that you are always 5 metres inside the fence surrounding the school fields. Where must you walk? Excelling students will be able to solve worded problems involving loci. Eg. A goat is tethered to a rope that is 4 metres long. Show the region the goat can reach. Keywords Loci, distance, bisect, perpendicular, angle, line, construct, radius, centre, equidistant, region
Form 4 Friday, 28 February 2025 Loci Presented by: Towett Kipkirui Lesson Objectives: Loci Developing students will be able to draw simple loci. There are only FOUR loci. (1)A fixed distance from a fixed point. Secure students will be able to solve problems involving multiple loci. (2)A fixed distance from a fixed line. (3)The same distance from two fixed points. (Perpendicular bisector) (4) The same distance from two fixed lines. (Angle bisector) Excelling students will be able to solve worded problems involving loci. Lets look at the four loci individually Keywords Loci, distance, bisect, perpendicular, angle, line, construct, radius, centre, equidistant, region
Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett 1. A fixed distance from a fixed point If a point is at a fixed distance from a fixed point, the locus of the point can be illustrated as shown r We end up with a circle of radius r
Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett 2. A fixed distance from a fixed line The locus of a points equidistant from a fixed line can be illustrated as below. This can be well represented as below We end up with parallel lines. But what about at the ends?
Form 4 Friday, 28 February 2025 Loci Presented by: Kipkirui Towett 3. The same distance from two fixed points Step 1 Open a pair of compasses to a distance that is slightly greater than half the distance between the points. From one point draw two arcs, one above the points and one below. Repeat this from the other point. Join where the arcs cross together. Step 2 Step 3 Step 4
