This term I am introducing geometrical reasoning in key stage 3 to Year 7. I was thinking about where to start the topic, what the key objectives should be and how I can challenge the various abilities.
We start the topic learning how to measure and draw acute and obtuse angles with a 180° protractor. Students have lots of practice to learn how to position the protractor correctly.
Understanding the types of angles is also key. If they can identify whether an angle is acute or obtuse they are less likely to use the wrong scale when measuring so 40° is not measured as 140°.
To challenge these students I would teach them how to draw and measure reflex angles using a 180° protractor. By separating the angle into a straight line and an acute or obtuse angle. Some students are able to subtract the interior angle from 360°.
Calculating missing angles on a straight line and about a point is also a key skill
Middle ability students begin with applying angle properties, such as angles on a straight line, vertically opposite and angles in a triangle. Little, if any time, is given to measuring or drawing angles. Although I do make sure their knowledge with this is secure.
To challenge the middle ability students I like to introduce proof. A nice way of doing this could be to prove vertically opposite angles are equal and move on to prove angles in a triangle using parallel lines.
More able students start the first lesson by recapping angles on a straight line. Moving on to the proof of vertically opposite angles being equal and why angles about a point have a sum of 360°. We then move on to proving angles in parallel lines and angles in a triangle. Every angle question would involve at least two angle properties and emphasise the need to explain which angle properties apply.
Knowing where the angle properties originate from and being able to prove them is key for this ability. Introducing proof at this point in their mathematics education ensures they are much more likely to prove formulae like the Cosine Rule or Quadratic formula at GCSE.
For further examples of proof with geometry check out my YouTube videos.
Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values. Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]
In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]
Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]