In today's blog post, we take a look at everyday **Contextual graphs** and how to interpret the data within them. We take a look at Distance-time graphs initially where the gradient of the graph is calculated to be the speed. If your graph is non-linear then you ay have to use a tangent to work out the speed of an object at a specific point. You will also need to use the Speed/Distance/Time formula triangle to help with calculations. We then move onto Velocity-time graphs where the same principles occur except the gradient of the line is now acceleration and the area under the graph can be calculated to give the distance traveled. Finally, we finish off on financial graphs where we can do cost comparison or currency conversions by reading off the graph.

In today's blog, we take a look at** Midpoints, Parallel lines and Perpendicular lines. **We take a look at finding the midpoint between two coordinate points by taking the average of the x values and an average of the y values. We then take a look at parallel lines (two or more lines that always remain the same distance apart) and establish that parallel lines share the same gradient but will have a different y-intercept.

Finally, we finish off with perpendicular lines (two lines intersect to create a right angle) and establish that the gradients of perpendicular lines are negative reciprocals of each other (their products = -1)

Today we are looking the **Equation of a straight line.** Before we move onto the more complex straight line graphs, we must understand the equations of horizontal and vertical lines.

A horizontal line has the equation y =? where ? is the point the line crosses the y-axis. A vertical line has the equation x =? where ? is the point where the line crosses the x-axis.

All straight line graphs follow the general rule **y = mx+c** where m is the gradient (steepness) of the line and c is the y-intercept. You will need to be able to calculate gradients effectively and substitute into the general rule to find the y-intecept if you are given some coordinate points.

Here we take at look at the first 'Graph' section. We start off fairly simply looking at **coordinates.** A set of coordinates provides us with a set of instructions that indicate the position of a point or object. They normally occur in pairs (x,y) where the first number is your direction along and the second value is your direction up/down.

You will need to be able to plot coordinate points accurately for many types of question as well as being able to read the points off a graph as well.

Today we delve a little deeper into the topic of trigonometry, focusing on **SohCahToa **(mnemonic for the trig functions). You will use this when finding missing angles or side lengths in right angled triangles. The first step will be to accurately label the triangle with Opposite, Adjacent and Hypotenuse. We then have to decide which trig ratio to use to solve the problem.

You could use the formula triangles to instruct you or you could substitute values into the function and rearrange to solve.

Today, we are looking at the **Trigonometry Ratios. **Trigonometry is usually used to calculate missing side lengths and angles in right-angled triangles. There are three functions you need to aware of; the Sine, Cosine and Tangent Functions and these are related to the lengths of the key terms of the right-angled triangle (Opposite, Adjacent and Hypotenuse). They are simply one side of a right-angled triangle divided by another and will have a specific value dependent upon the angle marked theta (or x).

You are required to know the specific values for each function when given an angle. It will be important to remember the three tables provided in this snapshot.

Today, we are looking at **Pythagoras' Theorem. **When you have a right angled triangle and you know two of the lengths, you can use Pythagoras' theorem to work out the third and final side. Important to note that it ONLY works for a right angled triangle.

Solving questions using Pythagoras' theorem is a three stage process that may alter slightly depending if you need to find the hypotenuse or a shorter side. There will some questions where Pythagoras' theorem will be required as well as trigonometry in more complex questions.

Every single specification topic is covered by both lecture videos and formative assessments within the EzyMaths A Level course. Lecture Videos are created in our purpose-built green-screen filming studios. The technology provides the basis for an engaging and immersive watching and learning experience for students.

For day 42, we are focusing on **angles in parallel lines.** It is fairly straight forward to calculate the angles on a straight line as we can use the vertically opposite angles reasoning or angles in a straight line reasoning.

When you want to compare one angle on one parallel line to another angle on a different parallel line there are three types of angle reasoning you will need to state. (Alternate, Corresponding, Co-Interior)

On day 41, we start by taking a look at calculating the missing **angle in triangles** (add up to 180 degrees). It is important to aware of the Isosceles and Equilateral triangles as they have very specific angle properties. We then move onto **angles in polygons** which can be found by using a special formula. If in doubt, use the fact that the number of triangles in a shape is always two less than the number of sides.

If in doubt, use the fact that the number of triangles in a shape is always two less than the number of sides.

You will have to be able to calculate the exterior angle of a shape as well (all exterior angles make 360 degrees, Interior + Exterior = 180 degrees)

On day 40, we turn our attention to Angle facts. An angle is a measure of turn and is measured in degrees. You should be able to classify the different types of angles based on their size and use that information to be able to calculate missing angles in straight lines and around a point. Calculating missing angles is achieved by subtracting angles you already know.

**What Is This New Craze?**

The flipped classroom is a teaching model that inverts the traditional method of teaching delivery. Students watch instructional video content online, outside of the classroom, sometimes followed up by a digital assignment that gauges their level of understanding. In-class time is focused on developing that base layer of knowledge and focusing on student misconceptions. A nice infographic on flipped learning can be seen here.

We are taking a look at **3D - Shapes** today and how they are classified. We will take a look at Prisms, Pyramids and Spheres. Being able to identify the 3D - Shape will help with more complex problems involving calculating the the volume of the shape as well as the surface area. We can also classify these shapes according to the number of faces, edges and vertices (corners) it has.

**Polygons** is today's focus on Day 38 in our countdown to exams. You will need to be able to give the names of many sided shapes and use this information to calculate the angles inside these more complex shapes. You may also have to state whether the shape is concave or convex as well as regular and irregular.

Today we are taking a look at the properties of **Triangles.** You will have to be able to name all of the triangles according to properties that they have. The key properties you will have to look out for are Side lengths, and angles.

It is important that you can correctly identify the types of triangle you are working with as it will help with finding missing angles in more complex problems (circle theorems, bearing problems)

Class sizes are one of the educational fundamentals which really attract the attention of parents. Reports recently of one Year 9 Maths class of 46 students, add to the anecdotal evidence that Key Stage 4 class sizes are steadily increasing.

**Funding Unlikely to Allow Any Reverse**

With the well-publicised funding squeeze, and most secondaries funding it difficult to recruit for maths department vacancies, there is little chance of class sizes falling in the near future. The questions we should be asking are, then:

1. What are the implications of larger class sizes for teachers?

2. What can be done to help teachers manage larger classes?

Today we are moving to the Geometry section and taking a look at the properties of **Quadrilaterals.** You will have to be able to name all of the quadrilaterals according to properties that they have. The key properties you will have to look out for are Side lengths, Parallel sides, Angles, Diagonals.

On Day 35, we are focusing on **Proportion**. Remember that there are two types of proportion; Direct and Inverse. As one value increases, the other increases at the same rate is an example of direct proportion (buying cups of coffee). As one value increases, the other decreases at the same rate is an example of inverse proportion (adding more people to paint a wall). When you are asked more challenging questions you will have to work out what the rate of change is (written with a * k*).

One of the clear themes I have encountered when talking to teachers this year is that under the enhanced content of the reformed specifications, teaching time is spread very thinly. The necessity of covering every topic prevents the in-depth exploration required. Whilst a lot of schools have transitioned to viewing the preparation for GCSEs as a 3-year journey, in many cases this does not seem to solve the problem. One solution that has been picking up steam is implementing Parallel Schemes of Work.

Today we are focusing on **Ratio**. We start off with an introduction to ratio and how to write ratios (paying attention to sentence structure) and simplify them (much like fractions). We then look at sharing quantities in a given ratio (almost like sharing out profits to shareholders). Make sure you follow the three step process here. A key thing to note here is when you have your answer, do not simplify it as it will take you back to your original ratio. Only simplify ratios when asked.

Ratio is commonly used in map and bearing questions and we cover this element as well using a scale factor multiplier.