1. Which rectangle is bigger – A or B? Why?
For you all to think about as we get started…… A B
Which rectangle is bigger – A or B? Why?

2. Starter – Using Scales…..
A scale on a map says:
1cm = 10km
How far (in km) is a distance measured as 4 cm on the map?
What about 0.5 cm?
How far on the map (in cm) is 15km?

3. Starter – Using Scales…..
A scale on another map says:
1cm = 4km
How far (in km) is a distance measured as 7 cm on the map?
What about 1.5 cm?
How far on the map (in cm) is 20km?

4. Starter – Using Scales…..
A scale on another map says:
5cm : 20 km
How far (in km) is a distance measured as 25 cm on the map?
What about 11 cm?
How far on the map (in cm) is 28 km?

5. ANSWERS – Using Scales…..
1cm = 10 km
40 km
5 km
1.5 cm
1cm = 4km
28 km
6 km
5 cm

6. ANSWERS – Using Scales…..
5cm : 20km
100 km
44 km
7 cm

7. Loci and Constructions

8. By the end of this lesson you should:
Know the meaning of the words LOCUS and LOCI (ALL)
Have mastered 2 of the four construction skills (ALL)
Have mastered 3 of the four construction skills (MOST)
Have mastered all four construction skills and be able to describe the steps (SOME)

9. Key Questions:
Be prepared at the end of the lesson to describe to the class the method you have used to draw two of the four constructions we will have looked at today.
I will be choosing which pupils will share their methods – so be clear and be prepared!

10. LOCUS
Imagine a point moving and leaving a path behind it as it moves. •
This path is called the Locus of the point. It can be a curve, or even a circle!
If we have two or more paths, we use the word Loci. This is the plural of Locus.

11. We are now going to look at four different LOCI
We will also learn the four skills needed to draw (or construct) them.

12. A CIRCLE ….. With a radius of 4cm
Skill 1
A point moves so that it always stays the same distance away from another fixed point
On your sheet mark the locus you get if the moving point always stays exactly 4cm from the x
What will your locus look like? What equipment will you need to draw it?
A CIRCLE ….. With a radius of 4cm
Title: Same distance from a point

13. Same distance from a point
4 cm x

14. Skill 2
A point moves so that it always stays the same distance away from a fixed line
On your sheet mark the locus you get if the moving point always stays exactly 2cm from the line
What will your locus look like? What equipment will you need to draw it?
A Parallel line … and ?
Title: Same distance from a line

15. Same distance from a line

16. Skill 3 COMPUTER SIMULATION
A point moves so that it always stays the same distance away from two fixed lines (which meet at an angle)
Title: Same distance from two lines
What do you think the locus will look like? What equipment will you need to draw it?
COMPUTER SIMULATION

17. The locus you have drawn should have cut the angle exactly in half
This line is called the ANGLE BISECTOR
Working with your partner, write a description of the method you used to draw this locus.

18. Skill 4 COMPUTER SIMULATION
A point moves so that it always stays the same distance away from the points at each end of a fixed line
Title: Same distance from two points
What do you think the locus will look like? What equipment will you need to draw it?
COMPUTER SIMULATION

19. The locus you have drawn should have cut the line exactly in half and at 90°
This locus is called: The
PERPENDICULAR BISECTOR of the line.
Working with your partner, write a description of the method you used to draw this locus.

20. Practice Tasks
In your pairs, draw an angle, any size and any way around, on the reverse of your skills sheet.
By helping each other, bisect this angle using the method you have been shown.
Now draw two points and a line joining them.
Again, helping each other, construct the perpendicular bisector for this line.
Repeat 1 to 4, but swapping roles.

21. Key Questions:
Describe to the class the method you have used to draw two of the four constructions we will have looked at today. Use the descriptions of the methods that you wrote to help you.
I will be choosing which pupils will share their methods – so be clear!!