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UNIT – ANGLES KEY STAGE 3
TEACHERS NOTES
For every piece of work it is possible to adapt each PowerPoint slide or create new ones in order to develop the
work further. Any opinion about the work would be useful. Contact me at [email protected] or use
the feedback form on the NGfL Cymru website.
1. Rotating Clockwise and Anticlockwise
This section emphasizes how important is it to relate an angle with a revolving object. It’s misleading
for a child to think of an angle as a distance between two lines that touch each other.
This section discusses and revises rotating clockwise through quarter, half, three quarters and a full turn.
The pupils must be directed that there is no need to start from the “northern” position every time (this
can be seen on slide 4 in the exercise).
In the last exercise it is possible to discuss clockwise and anticlockwise movement by travelling from
one site to the next one. Perhaps pupils will remember using the LOGO turtle in primary school.
2. Degree
Starting with revising the necessary vocabulary, this unit develops by showing the pupils how to
measure and create accurate angles. Pupils have great difficulty in knowing when to use the external and
internal scale of the protractor. There are 4 slides emphasising the need to note the measurement’s
direction (clockwise and anticlockwise).
The next two slides (5 and 6) show (visually) the correct method of measuring and creating an angle.
They emphasise the fact that counting should start from an angle of 0° every time, avoiding the problem
of using the incorrect scale.
There are 5 various worksheets, with the last measuring the three angles of a triangle. Completing the
last worksheet will help the pupils’ understanding of angles in a triangle before reaching section 3.0.
This unit ends with the work on calculating angles. It is possible to print the exercise sheets to create
worksheets.
3. Triangles
The first slide shows the traditional test for the total angles of a triangle. Again it is a visual resource if
there is no time to take the test in class. There is a worksheet of exercises available to go with the slide.
The slides that follow are a good way to get pupils to describe the properties of a triangle. They have
been designed so that one property appears on every mouse “click” (or an interactive pen), ending with
the triangle’s name.
The unit ends by calculating the angles in an isosceles triangle. Again it is possible to print the slide to
create worksheets.
4. Parallel lines
This section begins by looking at parallel lines that appear in train lines and when skiing. The next slide
contain visual tricks. Perhaps that it is possible to use a ruler or a straight line from Active Studio to
prove that parallel lines exist in each picture. Slide 5 consists of an example of two cars parking, using
the parallel method. The two video files need to be downloaded to ensure they work correctly. It is
advisable to have Windows Media Player 9 or 10 on your computer.
The next series of slides show visual alternate, corresponding and interior angles as well as
parallelogram angles, showing clearly the position of letters Z, F and C. There are exercise sheets
available to go with every subdivision and it is possible to print them to create worksheets.
Slide 16 is an opportunity to revise the properties of parallel lines and then the transition to
perpendicular lines. Note, as the animation happens it is possible to discuss the properties of two lines
intersecting (Section 2.0), and then in one particular place, every angle is 90 degrees which is where the
two lines are perpendicular.
To end the section there are various types of complex questions to be found where there is a need to use
and mix every rule. The last two slides analyse the four first examples on the worksheets.
5. Structure
Here, many different examples of structures are seen, using only angles. Beginning with the simple
work of creating accurate triangles, the work develops to be very intricate. Perhaps the work on halving
angles is rather ambitious for key stage 3 but it can be an exercise for the most able pupils only.
6. Internal angles
This section focuses on regular polygons only, creating an investigation to find out the general statement
to calculate the size of internal angles.
7. External angles
To go with section 6.0, section 7.0 looks at the external angles of regular and irregular polygons, noting
visually that the total is always 360 degrees. Then finally, the last slide connects section 6.0 and 7.0 to
show that the total of the two add up to 180 degrees. As the number of sides increase, the pupils should
be notified that the interior angle tends towards 180 degrees while the exterior angle tends towards 0
degrees. Further more it should be noted that a regular shape and the number of infinite sides, approach
being a circle.
8. Circle Sector
This section is an extension to the work on the area and circumference of a circle. I have included this
section because quarter and half circles are 90 and 180 drgrees of the full circle.
I have not included the work on area and length of the arc of any angle of the circle because the work is
too complicated for key stage 3. Perhaps it is possible to modify the slides and the animations to create
this.
9. Geometry of a Circle (Key Stage 4)
This is the only section for key stage 4, or it is possible to use the initial section for the higher sets in
year 9. The work builds on the pupils’ understanding of each rule before they embark on various types
of complex questions that use a mixture of the rules.
Again, it is possible to print the exercises to create worksheets.