# EdPlace's GCSE Home Learning Maths Lesson: Calculate and Interpret Gradients

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**Get them started on the lesson below **and then jump **into our teacher-created activities** to practice what they've learnt. We've recommended five to ensure they feel secure in their knowledge - 5-a-day helps keeps the learning loss at bay (or so we think!). Are they keen to start practising straight away?** Head to the bottom of the page to find the activities. **

**Now...onto the lesson!**

**Key Stage 3 Statutory Requirements for Maths**

**Year 9**

*students must be able to calculate and interpret gradients.*

# Why Does Your Child Need to Master Gradients?

Gradients are a common topic in Key Stage 3 and having a solid understanding is useful for both maths and science. Students will have been exposed to line graphs already, but now they need to understand the logic behind a gradient on a graph. This knowledge will allow them to calculate gradients using either coordinates or measurements.

We're confident that by following this step-by-step guide your child will be able to:

1) **Recognise **a gradient as positive or negative

2) **Calculate **a gradient by making the correct measurements on a graph

3) **Calculate **a gradient using two sets of coordinates

## Step 1 - What is a Gradient?

Before we learn how to calculate a gradient your child needs to understand what a gradient is. A gradient is just **a number that tells us the steepness of a line**. It can be positive, negative, or zero. Some simple illustrations will demonstrate this:

Shallow line = low gradient Steep line = high gradient

Downwards line = negative gradient Horizontal line = no gradient

## Step 2 - How To Calculate a Gradient From a Graph

Now, we will start to look at how to **calculate **a gradient from a graph. The first thing to do is draw two straight lines to turn your line into a **right-angled triangle**. For example, to find the gradient of this line, we draw the two red lines as shown:

An important point is that it does not matter how big you make the triangle. It will not affect the final answer. However, it is a good idea to make the triangle as large as possible and to make life easier, use a whole number of squares.

## Step 3 - Draw a Triangle then Apply the Equation

The thing to do now is to measure the height and base of this triangle. A common mistake that students make is just measuring the lines in centimetres with a ruler, this will give incorrect numbers if the scale of the axes is not in cm.** Always use the numbers on the axes to work out the lengths. It really is as simple as counting squares.**

In this case:

It is time to introduce the equation.

The equation of gradient is:

It looks complicated, but it just means “change in y co-ordinates divided by change in x co-ordinates”.

In other words, it's just the **height of the triangle ÷ base of the triangle**.

So, the gradient of this line is 1/2.

So, finding a gradient is as simple as drawing a right-angled triangle and dividing the height by the base. One last handy shortcut is knowing that **you don’t even need to have the graph in front of you** to find the gradient.

As gradient is “change in y co-ordinates divided by change in x co-ordinates”, we just need two pairs of coordinates. For example, an exam question may just say:

Find the gradient of a line that passes through (1,3) and (3,15)

**Look at the y co-ordinates: 3 to 15 is a change of 12.
Look at the x co-ordinates: 1 to 3 is a change of 2.**

Gradient = change in y ÷ change in x = 12 ÷ 2 = 6.

So, this gradient is 6. Simple!

## Step 4 - Practice Questions

Using steps 1-3, see if your child can now work out these gradients:

a)

b)

c)

d)

## Step 5 - Give it a Go...

Now that you’ve learnt to simplify algebraic fractions, see if your child can apply their knowledge to the following 5 activities. Have them complete them in the order listed below. All activities are **created by teachers and automatically marked**.

Plus, with an EdPlace subscription, we can **automatically progress your child** at a level that's right for them. Sending you progress reports along the way so you can **track and measure progress, together** - brilliant!

Activity 1 - Calculate the Gradient of a Line

Activity 2 - Calculate the Gradient of a Line Given Two Points

Activity 3 - Find the Gradient Between Two Points

Activity 4 - Find the Coordinates of the Midpoint of a Line Segment

Activity 5 - Find the Equation of a Line

**Answers**

a)

b)

c)

d)

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