For you all to think about as we get started……
A
B
Which rectangle is bigger – A or B? Why?
Starter – Using Scales…..
A scale on a map says:
1cm = 10km
1. How far (in km) is a distance
measured as 4 cm on the map?
2. What about 0.5 cm?
3. How far on the map (in cm) is
15km?
Starter – Using Scales…..
A scale on another map says:
1cm = 4km
1. How far (in km) is a distance
measured as 7 cm on the map?
2. What about 1.5 cm?
3. How far on the map (in cm) is
20km?
Starter – Using Scales…..
A scale on another map says:
5cm : 20 km
1. How far (in km) is a distance
measured as 25 cm on the map?
2. What about 11 cm?
3. How far on the map (in cm) is
28 km?
ANSWERS – Using Scales…..
1cm = 10 km
1. 40 km
2. 5 km
3. 1.5 cm
1cm = 4km
1. 28 km
2. 6 km
3. 5 cm
ANSWERS – Using Scales…..
5cm : 20km
1. 100 km
2. 44 km
3. 7 cm
Loci and Constructions
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)
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!
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.
We are now going to look at four
different LOCI
We will also learn the four skills
needed to draw (or construct)
them.
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
Same distance from a point
x
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
Same distance from a line
Skill 3
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
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.
Skill 4
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
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.
Practice Tasks
1. In your pairs, draw an angle, any size and
any way around, on the reverse of your skills
sheet.
2. By helping each other, bisect this angle using
the method you have been shown.
3. Now draw two points and a line joining
them.
4. Again, helping each other, construct the
perpendicular bisector for this line.
5. Repeat 1 to 4, but swapping roles.
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!!