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      This unit of work is on straight line graphs

      It can be difficult to prepare resources to teach straight line graphs and can be a challenge to teach because learners find it hard to understand the connections between a graph and its equation.

      We are going to explore straight line graphs, investigating gradients as a measure of steepness and recognising them as rates of change.

      We will also look at straight line equations and help learners to make connections between straight line graphs and their corresponding equations.

      It is useful for learners to experience a range of graphs and learners will study a variety of scales and contexts.

      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 ability level of your learners as well as your school context.



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      Lesson 1: What is gradient?

      Look at this road sign. It tells road users the gradient of the road ahead.

      25% is the same as one quarter.  So we say this gradient is ‘1 in 4’. This means you go up 1 unit vertically for every 4 units horizontally. Let’s look at this on a diagram.

      This car travels 1 unit up for every 4 units along. The gradient is the change in height divided by the horizontal distance travelled.

      Some people call this rise over run. Here, the gradient is the change in height, which is 1, divided by the horizontal distance, which is 4.That’s 1 divided by 4, or one-quarter.

      We often need to find the gradient of a straight line on a graph.

      The gradient tells us the slope of the line. The larger the gradient, the steeper the slope. When we work with gradients on graphs, instead of saying the change in height divided by the horizontal distance travelled, we usually say the change in y divided by the change in x.

      The gradient is the change in y divided by the change in x.

      For this graph, the change in y is 2 and the change in x is 1 so the gradient is 2 divided by 1 - which is 2. Another way to think of this is that the graph goes up two units for every one unit across so the gradient is 2.

      But what if the graph slopes in the opposite direction? We still work out the change in y divided by the change in x, but this time the answer is – 2. The negative symbol shows us the line is sloping the opposite way.

      Another way to think of this is that the graph goes down two units for every one unit across, so the gradient is −2.

      The key thing to remember is that the gradient tells us the slope of a line. You work out the gradient by calculating the change in y divided by the change in x.