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

B

A

Which rectangle is bigger – A or B? Why?

For you all to think about as we get started……

Starter – Using Scales…..A scale on a map says:

1cm = 10km1. 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 = 4km1. 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 km1. 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 = 4km1. 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: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!

LOCUSLOCUSImagine 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 1Skill 1A 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 4cmA CIRCLE ….. With a radius of 4cmTitle: Same distance from a point

Same distance from a point

x 4 cm

Skill 2Skill 2A 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 ? A Parallel line … and ? Title: Same distance from a line

Same distance from a line

Skill 3Skill 3A 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 SIMULATIONCOMPUTER SIMULATION

The locus you have drawn should have The locus you have drawn should have cut the cut the angleangle exactly in halfexactly 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 4Skill 4A 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 SIMULATIONCOMPUTER SIMULATION

The locus you have drawn should have The locus you have drawn should have cut the cut the lineline exactly in half and at 90exactly 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 TasksPractice Tasks1. 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: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!!