Straight Line Graphs Homework Sheet

This MEP resource from CIMT is taken from text book 8B which covers the mathematics scheme of work for the second half of year 8.

Straight line graphs covers: coordinates, plotting points on straight lines, plotting graphs given their equations, the equation of a straight line and the equation of a line given two points.

The initial file forms part of the textbook. The activities sheet, extra exercises and mental tests compliment the work covered in the textbook. The overhead slides can be used on an interactive whiteboard.

Alongside the pupils' material there are lesson plans which outline the content of the unit, these are differentiated into three levels, ST, A and E as well as suggested routes through them.

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One of the topics that my pupils struggle with the most, from Key Stage 3 right through to Year 12, is linear graphs.

My bright Year 11s know the rule for finding the gradient of a perpendicular line, but can't work out how to answer a GCSE question like this:
Strangely, I teach this differently at GCSE and A level.  At GCSE my pupils write down

y = mx + c

and substitute values for y, m and x, then solve for c.  Whereas at A level my pupils use the equation

y - y1 = m(x - x1)

Essentially the same method but a slightly different approach. Perhaps I should be more consistent and introduce the 'A level method' at GCSE. I'd like to hear what other teachers do.

In this post I’ll suggest some ideas and resources for teaching linear graphs.

Key words

Let's start with the basics. There's a lot of new vocabulary in coordinate geometry, some of which pupils will have encountered at primary school. This is a nice activity for discussing new words. This topic also lends itself well to a vocabulary knowledge survey as suggested in my earlier post. 

Here's a nice trick for remembering the words parallel and perpendicular (this could be helpful for spellings - parallel is often misspelt): 

and this activity is suitable for Year 6 or 7. 

My blog post 'All about gradient' features ideas and resources for teaching gradient (the post focuses mainly on real-life applications of the concept of steepness, but also features links to gradient worksheets and activities).

Understanding parallel and perpendicular gradients

So here's the key information that pupils need to understand:


If they know how to work out a gradient as 'rise over run' (or equivalent) then pupils should be able to derive the 'negative reciprocal' rule for perpendicular gradients from an activity like this one from MathsPad.

Here's a few activities for a lesson on perpendicular lines:
Bringing it all together
When students study linear graphs at AS level, they don't really learn anything new - my GCSE pupils should have the necessary skills and knowledge to answer C1 coordinate geometry questions. I gave my Year 11 pupils questions 5 - 7 from this AS worksheet last year - it took them ages to answer each question, but they were certainly capable. Essentially it's just the wording of the questions that throws them.

Here's some more recommended resources suitable for GCSE students:
Finally, fun for puzzle-lovers in linear relationships sudoku and a nice Key Stage 3 Christmas activity on plotting linear graphs from Teachit Maths - Mistletoe and Lines.

Finally, ever wondered which countries use y = mx + c notation and which countries use something different? Check out this map.

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