This is a PowerPoint presentation that can be used to introduce normal distributions. The lesson covers what a normal distribution is and then talks through how to convert to a standardised normal distribution (find the z-score). The idea is to encourage the students to understand exactly what they are finding, rather than just using a formula and reading from a table. This means that they will be able to interpret questions and adapt to new situations more easily. The presentation discusses what we mean by standard deviation and how it applies to a normal distribution. We then look at how we can find the z-score and how this helps us find the probability. We then look at a couple of examples, where we use a table to find the probability from the z-score and vice-versa. I use a 'tail end' table of z-scores but the lesson can easily be adapted to other forms of tables. I spent quite a lot of time putting the presentation together to use with my Engineering apprentices so hopefully someones else can also find it useful. I must also give credit to www.mathsisfun.com (https://www.mathsisfun.com/data/standard-normal-distribution.html) where I found a lot of the images used in the presentation.

This is a PowerPoint presentation that leads through the process of finding maximum and minimum points using differentiation. It starts off with simple examples, explaining each step of the working. It gradually builds the difficulty until students will be able to find turning points on graphs with more than one turning point and use calculus to determine the nature of the turning points. I have found in the pass that students are able to follow this process when taught but often do not understand each step. As a result, they often use the wrong equation (for example, they use the equation for dy/dx to try to find y or make simple errors. This presentation is designed to lead the students through the process with an understanding of each step. NOTE: I have updated the PowerPoint to now include an example of how this can be used to solve practical problems.

This presentation focuses on what standard deviation really is. We look at some examples of data that all have the same mean, but where the variation in data is different. This enables us to see how the standard deviation can be useful and why we need to square the values before square rooting. A good visual representation to enhance understanding of what the standard deviation of a set of data means.

A PowerPoint that goes through linear regression using the method of least squares. There are three examples to go through, each with editable Excel spreadsheets within the slides. The lesson leads through exactly what the least squares method is trying to achieve and explains where the formulas come from. There are many different formats of the formulas available for linear regression. This PowerPoint uses the sum formulas (that must be solved simultaneously). The second presentation is exactly the same as the first but with the tables filled in. Note: these have been updated to make them a little more user friendly. To open the Excel spreadsheets you now need to click on the spreadsheet within the presentation. They will no longer open automatically on click (in case you don't want them to keep popping up).

This is a table that can be filled in either at the end of transformations or at the beginning to remind students of the different transformations. It gets the students thinking about the effect of transformations rather than a process to be done.

Students can use the scale bar on each image to work out the scale. They can then measure each object, calculate the real-life size and order these real landmarks in terms of size. There are then some bonus questions on each card for extension work.

This analogue clock face is broken into 12 sections to help kids understand how the hour hand moves. You can either use pencils/crayons as clock hands or cut a hole in the middle and make a clock hand using a split pin. If you print it off in colour, the numbers match the following section and this helps children to understand that, while the hour hand is in the red section, it is still 'something past 1' even if it is closer to the two. I like to make the numbers into little doors with the 5 times table behind to help the children get used to the meaning of a minute hand. Because the 5 times table is hidden , they can use it as a checking mechanism, rather than relying on reading the numbers. To see how to make a really useful learning clock with little doors, click here: https://www.youtube.com/watch?v=3VFRTOHO3Qw

Students find logs notoriously difficult to understand. This video provides a simple, easy to follow explanation of what logs are and how to use them. With examples and questions for the viewer to try, this video can really enhance the understanding of the learner. I create my videos and upload them to YouTube for my students to watch at home if they miss a lesson or need extra help. However, I have received feedback from other learners who have come across my videos that they have been very useful to them. I therefore thought I would share them on TES in case anyone else finds them useful. Whether you are a teacher or a student, if you need help with understanding or explaining logarithms, this video can really help. Please let me know what you think :) Link to video: https://youtu.be/p1r2W7WU3A4 Previous Knowledge Required: A basic understanding of indices: https://youtu.be/WApdBOaAoec Where to go next: How to use Logarithm Laws: https://youtu.be/eBpVXPKK100

A presentation leading through the Euler method, improved Euler method and Taylor series method for solving first order differential equations. The presentation goes through one example using each of the three methods. The first steps are explained in detail with animations to help understanding. There is then a blank Excel table to enable you to demonstrate to the class how you could do it using a computer. Simply click the spreadsheet during slideshow view and the excel document will open up ready to be edited. The second presentation is exactly the same but with the formula filled in.

A couple of presentations introducing vectors and unit vector notation. There is a strong focus on the dot and cross product and the meaning of these two products. The dot product is multiplication in multidimensional space when you are interested an parallel components. The cross product is multiplication in multidimensional space when you are interested an perpendicular components. By understand exactly what the dot and cross product are all about, students will more easily be able to correctly apply them and adapt to new situations.

This is a fantastic task to help kids learn to count in 5s. It is fun and creative and produces a lovely visual resource to help kids with counting in 5s and the 5 times table. The task is designed to help kids really understand what it means to count in 5s (rather than learning by repetition). See a video of the task in action here https://youtu.be/NLw9sc6wz8E I also write a blog. To see a full description of the task, with ideas questions and other activities click here: http://kidsunderstandmaths.blogspot.co.uk/2016/05/understand-how-to-count-in-2s-and-5s.html The final product can be used to extend kids by linking it to the 5 times table (e.g. if we have 3 hands each with 5 fingers, how many fingers will we have in total).

This is a fantastic task to help kids learn to count in 2s. It is fun and creative and produces a lovely visual resource to help kids with counting in 2s and the 2 times table. The task is designed to help kids really understand what it means to count in 2s (rather than learning by repetition). See a video of the task in action here https://youtu.be/gVNhak-uwoY I also write a blog. To see a full description of the task, with ideas questions and other activities click here: http://kidsunderstandmaths.blogspot.co.uk/2016/05/understand-how-to-count-in-2s-and-5s.html I started by using a wooden Noah's Ark toy and asking the kids to count the animals into the ark (in 2s). We then created a display by making a poster with 12 little pocket boats (I made the one in the picture but there is no reason that the kids can't practise their drawing, cutting and sticking skills and make it themselves). We put 2 animals in each boat and counted them as we went along, writing the relevant number on each boat. The final product can then be used to extend kids by linking it to the 2 times table (e.g. if we have 6 boats each with 2 animals in, how many animals will we have in total).

This activity is a great way to get kids to discover the number bonds for themselves. It leads them towards a true understanding of number bonds, rather than just a pattern of number facts to memorise. It is a very simple task, and you can use a set of any five objects (it doesn't have to be Lego blocks). The first picture is the worksheet (A3), The second picture shows the task in action. By using the same set of five object to make the prints each time, it really reinforces the idea that you are always making the same total. To see a video of the full task in action, as well as links to other areas of maths and possible questioning to develop understanding please click here: https://youtu.be/2oKG0sCTzCY Please see my other resources for an activity for number bonds to 10. To extend the learning of number bonds, see my blog by clicking here: http://kidsunderstandmaths.blogspot.co.uk/2016/05/number-bonds.html

A PowerPoint presentation leading through the process of Gaussian elimination. The first time, all the steps are show. The second example is the more succinct method.

This maths board game is essentially a numberline but kids won't even know they are learning. The game introduces '+' and '-' signs and focuses on going backwards and forwards along the numberline in 1s and 2s. A simple game like this can have so much potential for learning opportunities. Within our game, we also included some number bonds (by putting prize squares and asking what you need to roll to land on the prize) and had some danger squares where you could get stuck (squares 24-26). These squares create the opportunity to discuss the relationship between adding and subtracting and how taking away two "undoes" adding two. You are welcome to download and print our version of the game, but we had great fun making it and even practised counting down from 30 in doing so. See us making the board game here: https://youtu.be/H63zWeDtg7M

This activity is a great way to get kids to discover the number bonds to 10 for themselves. It leads them towards a true understanding of number bonds, rather than just a pattern of number facts to memorise. It is a very simple task, and kids really seem to enjoy it. The first picture is the worksheet (A3 with movable bottles), The second picture shows the task in action and the third is the completed product. By keeping the same set of 10 bottles and just moving one at a time, it really reinforces the idea that you are always making the same total. To see a video of the full task in action, as well as links to other areas of maths and possible questioning to develop understanding, please click here: https://youtu.be/2oKG0sCTzCY Please see my other resources for an activity for number bonds to 5, which can be used to introduce the idea of number bonds before moving on to this activity. To extend the learning of number bonds, see my blog by clicking here: http://kidsunderstandmaths.blogspot.co.uk/2016/05/number-bonds.html

Homemade Dienes blocks are a fantastic resource for many early mathematical topics including place value, zeros as placeholder, column addition and subtraction... I like to use the single digit monsters for extra impact/fun. The idea is that the monsters get angry if they have more than 9 (double digits). To see how this can be used and for fun ideas, see my single digit monsters YouTube playlist at Kiducation UK: https://www.youtube.com/watch?v=LZnNOmNxUgg&list=PLu7pIHvEIsL6R2w3FlAkm09Cf9xIuMWtg