Loci Aim I can use Loci to solve

Loci. Aim: I can use Loci to solve real-life problems. Starter: Complete Captain Whizz’s Problem that is on your desks. X 12 11 8 If you finish that, 12 complete this 9 x multiplication grid: 3 y 6 x

Achievements GOOD GREAT Understand what Loci is and how to draw it around a point. Know how to draw Loci that intersect. Know how to use Loci to solve problems. HERO

The locus of points from two fixed points Imagine placing counters so that they are always an equal distance from two fixed points P and Q. P Q Describe the locus made by the counters. The locus is the perpendicular bisector of the line joining the two points.

The locus of points from a fixed point Imagine placing counters so that their centres are always 5 cm from a fixed point P. 5 cm P Describe the locus made by the counters. The locus is a circle with a radius of 5 cm and centre at point P.

Combining loci Suppose two goats, Archimedes and Babbage, occupy a fenced rectangular area of grass of length 18 m and width 12 m. Archimedes is tethered so that he can only eat grass that is within 12 m from the fence PQ and Babbage is tethered so that he can only eat grass that is within 14 m of post R. (On your diagram 1 square = 1 m) How we could find where the area is that both goats can graze?

The intersection of two loci Suppose we have a red counter and a blue counter that are 9 cm apart. 6 cm Draw an arc of radius 6 cm from the blue counter. 5 cm Draw an arc of radius 5 cm from the red counter. 9 cm 6 cm 5 cm How can we place a yellow counter so that it is 6 cm from the blue counter and 5 cm from the red counter? There are two possible positions.

What have we achieved so far? GOOD GREAT Understand what Loci is and how to draw it round a point. Know how to draw Loci that intersect. Know how to use Loci to solve problems. HERO

Seating Problem. . . I have a problem with my year 9 seating plan, and I need your help. 3 of the girls in the class have been bullying another girl in the class, they are labelled by A, B and C on your copy of my seating plan. Now, the girl that was being bullied was originally sat next to girl A, so I need to move her. Miss N (Head of Year 9) has given me the following rules: 1) She cannot sit closer than 2 metres from girl A. 2) She has to be at least 3. 5 m from girl B. 3) Girl C has to be 2. 5 m from her. Where can I sit her in my lesson? Now, she has to also be as close to the front as possible, because she always forgets to wear her glasses.

B A C FRONT OF THE CLASS

You have had enough of my wonderful teaching and decide to hide on the South Yard rather than enjoy another interesting Maths lesson! However with 3 teachers watching the South Yard and 2 cameras where will you stand? 2 1 Cam 2 Scale: 1 cm : 2 m Cameras can see 7 m in any direction 3

How far can the teacher’s see? There is a wall across the yard (top to bottom), 24 metres across from where teacher 1 is stood. Teacher 2 can see everything within a 10 metre radius from where they are stood, including over the fence. Teacher 3 can see everything in front of the wall on their side. Teacher 1 can see everything 20 metres in front of them. Where is best to hide away?

You have had enough of my wonderful teaching and decide to hide on the South Yard rather than enjoy another interesting Maths lesson! However with 3 teachers watching the South Yard and 2 cameras where will you stand? 2 1 Cam 2 Scale: 1 cm : 2 m Cameras can see 7 m in any direction 3

How do I feel about the lesson? What do I understand? Objectives Understand what Loci is and how to draw it round a point. Know how to draw Loci that intersect. Know how to use Loci to solve problems.

Have we achieved our objectives? GOOD GREAT Understand what Loci is and how to draw it round a point. Know how to draw Loci that intersect. Know how to use Loci to solve problems. HERO

Seating Problem. B A C FRONT OF THE CLASS

You have had enough of Miss Mather’s wonderful teaching and decide to hide on the South Yard rather than enjoy another interesting Maths lesson! However with 3 teachers watching the South Yard and 2 cameras where will you stand? 2 1 Cam 2 Scale: 1 cm : 2 m Cameras can see 7 m in any direction 3

How do I feel about the lesson? What do I understand? Objectives Understand what Loci is and how to draw it round a point. Know how to draw Loci that intersect. Know how to use Loci to solve problems.