![]() When you insert the pencil, line up the point and the pencil to make it easier to draw a line. Like any tool they require practice in setting up and use to achieve high quality results.įirst notice that the compasses have two arms. This unit of work is just one of several approaches that you could take when teaching this topic, and you should aim to adapt the resources to match the ability level of your learners, as well as your school context.Ī pair of compasses are a great tool for drawing accurate arcs and circles. This process usually involves pattern spotting as a first step, but is then followed by making and then proving, or disproving a conjecture based on the patterns they have spotted. In this unity they will develop an understanding of the process of developing a geometrical proof in mathematics. The lessons then build on this to make sure learners understand the link between these angle facts and the circle theorems and can confidently apply a range of facts to derive the circle theorems.Ĭore learners need to be confident and fluent with the angle facts such as angles on a straight line and angle facts related to parallel line and triangles before solving more complex problems involving the the circumference of circles, arc lengths and calculating perimeters and areas of sectors.Īt the extended tier, learners are expected to know and recall a range of angle facts and circle theorems. In this unit we will revisit learners' understanding of angles and the angle facts they may need in solving multi-step geometrical reasoning problems. This unit of work is just one of several approaches that you could take when teaching this topic and you should aim to adapt the resources to match the ability level of your learners, as well as your school context. In this unit they will develop an understanding of the process of developing a geometrical proof in mathematics. Teachers can find the various angle facts difficult to represent and numerous circle theorems can be confusing for learners to recall and apply.Ĭore learners need to be confident and fluent with the angle facts such as angles on a straight line and angle facts related to parallel lines and triangles before solving more complex problems involving the circumference of circles, arc lengths and calculating perimeters and areas of sectors.Īt the extended tier, learners are expected to know and recall a range of angle facts and circle theorems. The unit then builds on this to make sure learners understand the link between these angle facts and the circle theorems and can confidently apply a range of facts to derive the circle theorems. This unit of work revisits learners' understanding of angles and the angle facts they may need in solving multi-step geometrical reasoning problems. I hope you have found this insights video useful to help your learners visualise better the connections between graphs and algebra.In this unit of work we are going to look at circle theorems and their application. ![]() But they need to check that the equation starts with ‘one y’ on the left hand side and if not, organise the equation so that it is ‘one y’ before making the substitutions. ![]() So the equation becomes.Ī common misunderstanding is that learners use the general formula and immediately assume the gradient is the coefficient of x and the intersection is the number on its own. In this case the gradient they have calculated is two and the y intercept point is one. where m is the gradient and c is the value of y where the line crosses the y axis. Then when they have the found the gradient they can use the following formula to find the general equation of a line. Often written as y2 minus y1 over x2 minus x1. So the gradient, how steep the slope is, is four over two, which is two.įrom this, learners will be able to visualise the general gradient formula, the change in y coordinates over the change in x coordinates. And we go ‘along’ from x equals zero to two, an increase of two units. In this example we go ‘up’ from y equals one to five, an increase of four units. This can easily thought of as the amount they go ‘up’ (the y direction) over how far they have to go along (the x direction). Here using the two coordinates ‘x1 and y1’ and ‘x2 and y2’ a straight line is drawn.īut the idea of the gradient - the steepness of the incline - the inc-’line’, is not always appreciated. Many learners are very capable of plotting coordinates and drawing a straight line graph, but are sometimes lost seeing the connection between a line, and an algebraic equation. Welcome to this short ‘insights video’ into helping learners better understand the connections between graphs and algebra.
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