How to draw an exploded view This is one of a set of resources developed to support the teaching of the primary national curriculum. They are designed to support the delivery of key topics within design and technology and maths. This resource focusses on drawing exploded views of products. Different types of drawing are used to communicate different types of information. Exploded views show how the component parts of a product relate to each other. These are widely used to support the assembly of products, for maintenance activities and when building flat pack furniture at home. Producing an exploded view develops drawing skills, whilst simultaneously allowing concepts such as dimensions, proportion and scale to be introduced in a practical context. In this activity learners will produce an exploded view drawing of a pen, working in proportion and ideally to scale. This could be used as a one-off activity, an extension to maths learning on scale, or linked to D&T activities such as product analysis or section drawing. It could also be used in conjunction with the IET primary poster – Exploded Views. Download the activity sheets for free! All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Please share your classroom learning highlights with us @IETeducation.

In this lesson, learners will apply the lift equation to carry out a real-world aircraft design activity. This will support their understanding of: manipulating the subject of equations; using equations; interpreting data presented in tables and graphs. The resource is designed to support teaching of key engineering concepts at both key stage 3 and key stage 4, including the GCSE in Engineering. This resource focuses on the application of maths in engineering. This could be used as a one-off main lesson activity, as an introductory lesson to a wider unit of work focussing on aerodynamics or as part of a scheme on aircraft design using all of the resources developed in association with Arconic. Activity: Writing flowchart programs to meet a given design brief Students will firstly view our Flying by Numbers presentation to make sure that they understand the concept of lift and the lift equation. Using the information from within this presentation, they will change the subject of the formula to make wing area and velocity the focus, and then interpreting data using the tables and graphs that have been provided. Download our activity overview and presentation for a detailed lesson plan on how to write a flowchart program to meet a given design brief. What is the lift equation? The lift formula is as follows: L = d x v2 x s x CL / 2 Where: L = lift; for level flight this equals the weight of the aircraft d = density of the air. This changes with altitude – the higher you get, the ‘thinner’ (less dense) the air is v = velocity of the aircraft s = wing area of the aircraft CL = coefficient of lift. This is read from a graph Wing area: s = 2 L / (d x v2 x CL) Velocity: v = √(2L / (d x s x CL )) The engineering context This lift equation is used by aerospace designers to determine the necessary characteristics of an aircraft so that it can fly. Suggested learning outcomes This lesson will teach students how to manipulate the subject of a formula. They’ll be able to use a formula and interpret data in tables and graphs. Download our activity sheet and related teaching resources The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. Please do share your highlights with us @IETeducation.

In this pulleys A Level maths resource, you examine forces in equilibrium in a hands-on activity and explore A Level maths. Can you use your knowledge of mechanics to predict the mass of the unknown object? Do the ks5 calculations and then check your predictions. This practical is designed to be easily set up and carried out in an A Level maths classroom using simple equipment. It will help students to understand the mechanics topics of forces and Newton’s laws in A level Mathematics. It is covered in KS5 AQA A Level maths and Edexcel A Level maths curricula. The pulleys video features the equipment needed and the practical procedure. The teacher notes contain additional guidance on carrying out the activity, sample calculations and suggested points for discussion, as well as an indication of some relevant real-life applications. Download the activity sheets for free! And please do share your classroom learning highlights with us @IETeducation as you find more A Level maths resources and A Level maths lesson plans from the IET.

Calculate tension force using pulleys In this practical activity two objects are connected via a string that passes over a pulley; then they are released from rest. Participants are tasked to use their knowledge of mechanics to predict the time taken for the heavier object to fall to the ground and the greatest height reached by the lighter object? Once each participant has made their calculations, complete the experiments, and compare to the predictions. This practical is designed to be easily set up and carried out in a maths classroom using simple equipment. It will help students to understand the mechanics topic of kinematics and constant acceleration equations in AS and A level Mathematics. The video features the equipment needed and the practical procedure. The teacher notes contain additional guidance on carrying out the activity, sample calculations and suggested points for discussion, as well as an indication of some relevant real-life applications. The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland, and Wales. All activity sheets and supporting resources are free to download and are fully editable, so you can tailor them to your students’ and your schools’ needs. Links to stream and download the videos can be found resources section below. Tools/resources required: Board 2 cup hooks 2 washing line pulleys Long piece of string with 3 loops in it 3 different masses, e.g. different coloured plasticine Pencil Ruler Tape measure/plumb line Protractor Kitchen scales Sticky tape And please do share your classroom learning highlights with us @IETeducation To watch a video about pulleys, please visit the IET Education website.

Throughout this engaging activity designed for GCSE students, learners will face intriguing challenges that revolve around wind turbines, where their problem-solving skills will be tested using equations and systematic listing techniques. By applying mathematical principles and systematic approaches, learners will uncover the secrets behind these sustainable energy marvels and gain a deeper appreciation for their significance in today’s world. It is recommended to utilise a table format for displaying the values learners substitute into the equation, along with the corresponding outcomes, indicating whether they are too large or too small. Problem Solving Students will likely employ trial and improvement or a graphical method to tackle the first question. Some may also opt to utilise a spreadsheet for their calculations. To ensure the accuracy of their solutions up to two decimal places, they are encouraged to consider using a number line, which can aid in the verification process. As for the final problem, students will need to adopt a systematic listing approach or explore other methodologies to ensure that every possible combination of gears has been thoroughly explored and tested. This activity aims to empower students to approach challenges creatively and thoughtfully by providing various problem-solving techniques and strategies. This process will sharpen their mathematical abilities and cultivate critical thinking skills, enabling them to tackle complex problems with confidence and precision. Discussion points Promote active discussion among the students regarding the diverse approaches they have employed and how they can ensure the accuracy of their answers up to two decimal places. If students have not chosen the graphical approach to solve the problem, consider demonstrating it to the class. Encourage a comparative analysis of the various methods used to address the subsequent problems and enquire about the students’ strategies to ensure they have explored all potential combinations of gears. Potential GCSE content This activity will cover using trial and improvement to solve an equation, calculations with fractions, ratios and systematic listing. Download the free activity sheet! All activity sheets and supporting resources are free to download, and all the documents are fully editable so that you can tailor them to your students and your schools’ needs. The activity sheet includes teacher notes, guidance, helpful web links, and links (where appropriate) to the national curriculum in the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Please share your classroom learning highlights with us @IETeducation

Calculate the distance from a village to a potential well position In a large semi-desert area, three small villages are to share a new well. Engineers will create the well by drilling down to the water table. But where should the well be placed? Activity info, teachers’ notes and curriculum links An engaging activity in which students will determine the best location for a well between 3 villages. The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Download the activity sheets for free! All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. The related GeoGebra file for this activity can be view on the geoGebra website And please do share your classroom learning highlights with us @IETeducation

Calculating the angles and lengths of components in a water wheel In this starter activity students will use a water wheel model to determine various angles and lengths. This is one of a set of resources developed to aid the class teaching of the secondary national curriculum, particularly KS3. It has been designed to support the delivery of key topics within mathematics and engineering. Activity: Calculating the angles and lengths of components in a water wheel Students will review our presentation, which explains the structure of a water wheel. Students are tasked with calculating the central angle of the water wheeling by diving 360 degrees by the number of equally spaced spokes. Learners must then find the size of a specified angle and two sides of a shape by identifying familiar shapes within our water wheel diagram (e.g., a type of triangle). Students can approach this in more than one way, using either trigonometry or by sketching a scale drawing. After the lesson is complete, there can be a class discussion on the accuracy and usefulness of both methods. Download our activity overview for an introductory lesson plan on calculating angles and lengths in a water wheel for free. The engineering context Mathematical modelling is often used in manufacturing, construction, and civil engineering, where mathematical shapes and principles are used by engineers to inform design specifications, architectural drawings, and design schematics. Suggested learning outcomes In this activity students will learn about the angle properties of a regular polygon and an isosceles triangle. Learners will use the knowledge of trigonometry to find the length of a side and also be able to draw a scale diagram of a triangle for the purposes of construction. Download our activity sheet and other teaching resources The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your class’s and your schools’ needs. You can download our classroom lesson plan for free! Please do share your highlights with us @IETeducation

Calculate the cross-sectional areas of different aqueducts to determine which is most effective In this STEM activity students will investigate different aqueduct shapes to determine which is the most efficient design. This is one of a set of resources developed to aid the class teaching of the secondary national curriculum, particularly KS3. It has been designed to support the delivery of key topics within mathematics and engineering. Activity: Calculating the cross-sectional areas of different aqueducts In this lesson, students must calculate the cross-sectional area of various aqueducts to determine which one is most effective in terms of least water lost via evaporation. Using our Aqueduct presentation, learners will be introduced to the engineering behind aqueducts by estimating the volume of water follow through the aqueduct in one second. Students will then calculate the cross-sectional areas of various aqueduct shapes, including rectangles and trapezoids. To do this, learners must apply their understanding trigonometry to find the missing side lengths. Alternatively, students can use this GeoGebra file to calculate the area of the trapezium. Download our activity overview for an introductory lesson plan on trigonometry for free! The engineering context Aqueducts are constructed to carry water across gaps such as valleys or ravines. In modern engineering, the term aqueduct is used for any system of pipes, ditches, canals, tunnels, and other structures used for this purpose. Aqueducts can be used to enable water to be transported to areas where it is in short supply. Suggested learning outcomes In this activity students will apply their knowledge of mathematics such as calculating the area of a rectangle and trapezium or the volume of a cuboid. They will also be able to specifically apply their knowledge of trigonometry. Finally, they’ll learn how to plot graphs using a table of values. Download our activity sheet and other teaching resources The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your class’s and your schools’ needs. You can download our classroom lesson plan for free!

In this fun GCSE maths activity, students will delve into the exciting world of bicycle speedometers and put their accuracy to the test. By conducting this experiment, learners will better understand how speedometers work and sharpen their mathematical and analytical skills. Download the presentation below and allow the students to read the problem and contemplate how to model the situation mathematically. Some students may need assistance comprehending terms such as “front fork.” Encourage them to ponder the meaning of “ms-1,” such as the number of meters the wheel covers in one second. Furthermore, ask them to consider how they can determine the distance the wheel covers in a single rotation, two, or even 100 rotations. Problem Solving To solve this problem, the students will need to engage in logical thinking to determine the necessary information. One possible approach is to work backwards from the information required to answer the question (as shown below). We need the distance travelled (m) and the time taken (s) to calculate the speed. Given that the time is 1 minute, equal to 60 seconds, the question becomes: How can we find the distance? The wheel covers 0.5π meters per rotation, so for n rotations, the distance will be 0.5π x n. Consequently, the speed in ms-1 can be expressed as (0.5π x n)/60. The students can determine the percentage errors using this information and the speedometer readings. These errors vary slightly for each reading. Discussion points Examine how the students approached the problem, specifically analysing their thought processes. How did they determine the necessary information and identify ways to obtain it? You can review concepts such as calculating the circumference of a circle, working with percentages, rounding numbers, and ensuring precision. Potential GCSE content This activity will cover calculating the circumference of a circle from a radius, using compound measures (speed) and converting from minutes to seconds. Download the activity sheets below! All activity sheets and supporting resources are free to download, and all the documents are fully editable so that you can tailor them to your students and your schools’ needs. The activity sheet includes teacher notes, guidance, helpful web links, and links (where appropriate) to the national curriculum in the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Please share your classroom learning highlights with us @IETeducation

Reading and interpreting wave patterns in a graph Engineers sometimes have to analyse data which shows a repeating pattern. Plotting a graph of the data is often helpful as it shows a picture of the pattern. This pattern may sometimes go on and on in a sequence. In this activity, students will learn about the concept of repeated graphical patterns. Inspired by wave patterns, this lesson plan will offer a practical way for students to learn about reading, interpreting graphs as well as sequences. It will explore the periodic nature of these wave patterns, identifying maximum and minimum values, and looking for symmetrical properties. This is one of a set of resources developed to aid the teaching of the secondary national curriculum, particularly KS3. It has been designed to support the delivery of key topics within mathematics. Activity: Interpreting wave patterns in a graph Students will start by reading the slides and answering questions on the first slide in pairs or small groups. They’ll delve into the world of wave patterns, discussing points like maximum and minimum values, the frequency of the pattern repetition, and the location of symmetry. The second slide will challenge them further by asking them to predict the shape of the pattern at various points based on its period. Download our activity overview and presentation for a detailed lesson plan for teaching students about how to interpreted wave patterns in a graph. The engineering context Many fields of engineering, such as signal processing, acoustics, and telecommunications, heavily rely on understanding wave patterns and their properties. By exploring these concepts in a fun and engaging way, students will see how engineers use mathematical concepts like these to create innovative solutions and products. Suggested learning outcomes Upon completion of this activity, students are expected to have a deeper understanding of reading and interpreting graphs, particularly wave patterns. They will learn how to identify maximum and minimum values, understand the concept of the period of a function, and recognise lines of symmetry. Furthermore, they’ll develop problem-solving skills as they use these concepts to predict sequences and future points in the pattern. Download our activity sheet and other teaching resources for free The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. Download our classroom lesson plan, presentation and handout. Please do share your highlights with us @IETeducation

Queuing theory is a mathematical discipline that helps us understand the behaviour of queues and make predictions about their performance. It considers various factors such as arrival rates, service times, and queue lengths to analyse and optimise queuing systems. By applying queuing theory principles, students will learn how to evaluate different queues and determine which will likely offer a shorter waiting time. Through this activity, you will develop your analytical and problem-solving skills and gain a deeper understanding of queuing theory concepts. You will also learn how to apply these principles in real-life situations, making you a proficient queue navigator in the future! Activity In this activity, students will be presented with two different systems of queues. They should think about the benefits and problems with each system. Encourage the students to think about how they can compare the two systems. What figures could they calculate? What diagrams would help to provide a picture of the advantages and disadvantages of each system? Give the students time to find/calculate their figures and then ask them to present their case. This task provides an opportunity to discuss the most appropriate average. The mean time for the first system is affected by longer wait times for a few customers. Would the mode time be a better average, as this is the most frequent experience, or is the median better? The engineering context Queuing theory is an area of maths which has many applications. When you log onto the internet, you join a queue for a server. Computer engineers and systems designers study queues to help them make systems work more efficiently. Civil engineers use it for traffic lights, and retailers use queuing theory to reduce wait time. Potential GCSE content In this activity, students will learn how to determine the mean and calculate the median from a frequency table, compare two data sets using an average and measure of spread and find the quartiles and the interquartile range (IQR). This exercise will also cover statistical diagrams, reasoning, problem-solving, estimation, and modelling. Download the free activity sheet! All activity sheets and supporting resources are free to download, and all the documents are fully editable so that you can tailor them to your students and your schools’ needs. The activity sheet includes teacher notes, guidance, helpful web links, and links (where appropriate) to the national curriculum in the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Please share your classroom learning highlights with us @IETeducation

Use proportional reasoning to estimate the radius of a circle of light produced by shining a torch at various distances from the wall This is an engaging activity for GCSE students in which learners will estimate the radius of a circle of light produced by shining a torch at various distances from the wall. In order to estimate the radius, students will need to use proportional reasoning or Pythagoras theorem. Students are encouraged to use GeoGebra to gather data. Problem Solving To solve the problem presented on the first slide, students will have to employ proportional reasoning. This can be utilised to reinforce concepts of enlargement, and potentially Pythagoras if the follow-up question is used. For the second problem, students will need to collect data, consider how to manipulate the control variable (distance) and organise the data to aid in identifying any connections between distance and area. Some students may choose to create a graph and extrapolate to determine the distance, while others may seek out a function. The related GeoGebra file for this activity can be viewed at the GeoGebra website. What is GeoGebra? GeoGebra is a free and open-source dynamic mathematics software that allows users to create and manipulate mathematical figures and interact with them in real-time. It can be used to plot graphs, create 3D models, solve equations, and perform complex mathematical operations. It is widely used in education, particularly in the teaching and learning of STEM subjects. GeoGebra is available for use on desktops, tablets, and mobile devices. Potential GCSE content covered By the end of this activity students will have an understanding of Pythagoras’ Theorem, the area of a circle, and enlargement. Download the free Estimate the Radius of a Circle of Light activity sheet below! All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Please share your classroom learning highlights with us @IETeducation

Assessing the probability of a particular situation occurring in a power station In this lesson students will use event tree analysis to roleplay an exercise where they quantify the risk of safety systems failing in a power station. This is one of a set of resources developed to aid the class teaching of the secondary national curriculum, particularly KS3. It has been designed to support the delivery of key topics within mathematics. In this activity, students will roleplay the following scenario: ‘A power station experiences a loss of coolant to its reactor about once per year. To prevent a dangerous explosion, a set of controls are in place. Firstly, an alarm which alerts the operator, this works on 99% of occasions. If this does fail various other systems will become operational to monitor the issue and prevent disaster.’ Using the examples in our Power station event analysis handout and Event analysis presentation, students will learn how event tree analysis can be used to model the probability of the risk of safety systems failing. Students can also use our Event analysis simulator tree spreadsheet to run simulations to check their workings. Download our activity overview for a detailed lesson plan (including answers) for teaching students about event tree analysis. The engineering context Event trees allow engineers to visualise the chain of events that could lead to system failures. Analysing the probabilities of these events helps them understand the likelihood of various outcomes as part of their efforts to design measures that can help to mitigate risks. Suggested learning outcomes In this lesson, students will learn about frequency trees, probability, and relative frequency. Download our activity sheet and other teaching resources The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download (including the video), and all the documents are fully editable, so you can tailor them to your class’s and your schools’ needs. You can download our classroom lesson plan for free! Please do share your highlights with us @IETeducation.

Calculate the distance a model boat will travel across water Two friends are on opposite banks of a river which is 30m wide. One of them has a model boat and plans to send it across the river to the other. The boat has a small motor which moves it forward. Once the boat is in the water, it cannot be steered. Can your students calculate the distance that the model boat will need to travel across the water? This fun maths challenge will teach students about forces and motion and is perfect for GCSE students! Activity: Model boat maths challenge for GCSE The students can work individually or in pairs. Download the teacher presentation below and allow the students some time to read the task on the first slide, then show them slide 2. Students will need to find the distance downstream from the starting point. A generalised approach to such problems should be introduced along with slide 2. Leave the students to work on the task and then compare approaches and answers. A GeoGebra file has been supplied to help with the discussion. Problem Solving The students can tackle the problem in a number of ways. Some may choose to look at the path of the boat at 1 second intervals, possibly plotting the path on a graph. This is the way the GeoGebra file works. Others may use trigonometry to find the angle the boat travels and then use this with the 30m width of the river to find the distance downstream. Another approach would be to use a scale drawing. Pythagoras theorem or trigonometry can be used to find the displacement of the boat from its original position. The GeoGebra file may be useful to students who wish to gather some results for the general approach or to check their answers. Discussion Points This activity could provide an opportunity to introduce vectors and possible resultant force, making a connection with Physics. Comparing the advantages and disadvantages of various approaches would provide students with the opportunity to consolidate their learning. Extending the problem It could also be possible, with some students, to consider how to point the boat upstream, so that it ends up at the point directly opposite the start. Potential GCSE content covered In this activity students will cover graphs, Pythagoras theorem and vectors. All activity sheets, worksheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Please share your classroom learning highlights with us @IETeducation

Using the circumference formula and estimation to design an efficient revolving door This lesson tasks students with designing a functional and efficient revolving door. It tests practical maths skills such as estimation and calculating the circumference of a circle, while also challenging students with a fun design activity. It’s one of a set of resources developed to aid the teaching of the secondary national curriculum, particularly KS3, supporting the teaching in maths. Activity: Using the circumference formula and estimation to design an efficient revolving door In this activity students will examine the design of revolving doors for maximum efficiency both in terms of reducing space and minimising heat loss. They’ll firstly be tasked with calculating the idea entrance/exit arc length based on the door’s diameter. They’ll then be asked to estimate how many people can fit into each door section and how this will impact getting 200 people in and out of the building as the arrive and leave for work. The GeoGebra file Revolving doors allows teachers to demonstrate the problem and check the solution to the first task. Download our activity overview and Revolving door presentation for a detailed lesson plan on the maths behind designing a revolving door. The engineering context Revolving doors are energy efficient as they prevent drafts (via acting as an airlock), thus preventing increases in the heating or cooling required for the building. At the same time, revolving doors allow large numbers of people to pass in and out. As such, architects and engineers need to apply mathematics to their designs, which can help to determine how they will work in practice and whether or not they’re fit for purpose. Suggested learning outcomes Students will learn how mathematical concepts like circumference and arc length are applied to solving real-world design problems. Download our activity sheet and other teaching resources The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. Download our classroom lesson plan and presentation for free! Please do share your highlights with us @IETeducation.

Programming algorithms for drawing shapes In this programming activity, students will use the programming language Logo to understand and create algorithms for drawing shapes. Through creating their own unique shapes via algorithms, students will see their code come to life on screen. This is one of a set of resources developed to aid the teaching of the secondary national curriculum, particularly KS3. It has been designed to support the delivery of key topics within maths, engineering and computing. Activity: Programming algorithms for drawing shapes The first part of this activity is intended to encourage students to examine a sequence of instructions, look for a pattern, and explain this pattern. The next problem asks the students to continue the pattern, making deductions about how the pattern will continue. Students are then challenged to produce a set of instructions for drawing different shapes before trying some designs of their own. They will be encouraged to use an online logo app like Papert to try out their instructions. Problem-solving questions will stimulate students to identify and extend a sequence, requiring reasoning and proof. The engineering context Algorithms form the backbone of many engineering processes, from automation and improving efficiency to data analysis and problem solving. As such, learning about algorithms prepares students for more advanced engineering studies. Pythagoras’ theorem and trigonometry are fundamental in multiple engineering fields such as civil engineering for structural design, electrical engineering for signal analysis, and mechanical engineering for understanding dynamics and mechanisms. Suggested learning outcomes This lesson plan aims to cover potential GCSE content such as identifying and explaining patterns and sequences, understanding the exterior angles of shapes, and applying Pythagoras and trigonometry. In the process, students will also develop key problem-solving skills as they predict sequences, work out instructions, and discuss their reasoning. This activity will also give students a deeper appreciation for the role of algorithms in our daily lives. Download our activity sheet and other teaching resources The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. Please do share your highlights with us @IETeducation.

Create a flowchart which identifies the properties of different shapes Flowcharts show the order in which a series of events is to be carried out. They are used for lots of purposes including; programming microcontrollers with instructions, mapping processes and sorting. Activity info, teachers’ notes and curriculum links An engaging activity in which students will make a flowchart to sort various shapes and ensure that each shape finishes in a unique place at the end of the flowchart. The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Download the free activity sheet! All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. And please do share your classroom learning highlights with us @IETeducation

In this activity students will calculate the area of a circle to design a fault detector system. They’ll use a GeoGebra file to measure the size of the defect in hot steel bars produced by the company. They’ll then have to organise the information they receive into an understandable table. This is one of a set of resources developed to aid the teaching of the secondary national curriculum, particularly KS3, supporting the teaching in mathematics. Activity: Organising mathematical information to choose the optimum size for a ‘fault detector’ coil In this lesson students will engage in a roleplay activity that uses mathematical calculations to figure out the ideal size for a fault detection coil. A company has invented a system to find defects in hot steel bars. The hot cylindrical bar must pass through a defect detector which is shaped like a ring. To work properly the bar must fill between 60 to 80% of the area inside the detector ring. The activity starts with a warm-up question related to circles and percentages to introduce the concept of fault detectors used in factories, where students can check their answers with the fault detectors GeoGebra file. Then, students will need to use reasoning to work out a more challenging problem related to fault detector design. Students will use the same GeoGebra file but they’ll need to work out how to organise the given information to answer the question. Download our activity overview and presentation for a detailed lesson plan and worksheet with answers on making fault detectors using the area of a circle. The engineering context Engineers rely on fault detectors as an essential tool in various manufacturing processes to guarantee the quality of their products. To ensure the safety and dependability of products, engineers must carefully design fault detectors capable of precisely identifying any imperfections or defects. Suggested learning outcomes Working with both diameter and radius, students will be able to use a formula to calculate the area of a circle. They’ll also be able to organise data using tables. Download our activity sheet and related teaching resources for free The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. Download our classroom lesson plan and presentation below. Please do share your highlights with us @IETeducation.

Making calculations and applying formulas to a spreadsheet of data In this maths activity students will be asked to estimate the number of visitors within an aquarium. They’ll do this by using a spreadsheet mathematical formula that calculates the difference between the number of people entering and the number of people leaving the building. This is one of a set of resources developed to aid the teaching of the secondary national curriculum, particularly KS3, supporting the teaching in maths. Activity: Making calculations and applying formulas to a spreadsheet of data Students will view a dataset that has monitored the number of visitors entering and leaving a large aquarium. Learners will be asked questions based on this data, including how many visitors were in the building at a specific time. They will also be given a spreadsheet formula for calculating the difference between the number of people entering and exiting the building and be asked to adapt that formula for the different times of the day. Download our activity overview and presentation for a detailed lesson plan for teaching students about data logging. The engineering context Learning how to use maths formulas within spreadsheets saves a significant amount of time and brainpower, allowing engineers to quickly extract information from raw data. Devices that allow public buildings to monitor the number of visitors that are within a building at any one time are an example of data logging in practice. This may be essential for fire safety regulations or to prevent various areas from getting overcrowded. Suggested learning outcomes This data logging activity will give students the opportunity to identify and then attempt to explain numerical patterns and sequences. It also allows students to practice using formulas within spreadsheets such as Excel or Google Sheets. Download our activity sheet and related teaching resources for free! The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. Download our classroom lesson plan and presentation below. Please do share your highlights with us @IETeducation.

Decide on a systematic way to estimate the number of objects in an image In this engaging STEM activity, designed for secondary school students, learners will take images from the Hubble telescope and use them to estimate the number of stars contained in those images. Activity: Counting stars using estimation The first slide in the presentation below introduces students to the context of the challenge and pushes them to think about how mathematics can be used to solve a real-life problem. The second slide asks the students to estimate the number of stars in the image. A Geogebra file “counting stars” which subdivides the enlarged image into smaller grids for sampling has been supplied. Students will need to find a systematic way of estimating the number of objects in the enlarged image. One approach is to subdivide the enlarged image into smaller sections, count some of these and work out the mean. This mean can then be taken as the number of objects per subsection and multiplied by the number of subsections to get an estimate of the number of objects in the enlarged image. To obtain an estimate for the number of stars in the original image, this figure then needs to be multiplied by the number of enlarged images in the original image. Students will need to consider when to round off and what degree of accuracy is appropriate. Discussion points Comparing the different estimates obtained by the students would be interesting. Looking at the differences in their estimates for the number of objects in the enlarged image first and then observing how this transferred to the differences in the original image. Extending the problem This method is used in a wide variety of contexts, from estimating the number of hairs on someone’s head to auditing the number of insects in an enclosure at a zoo. This activity could be extended by looking at capture/recapture as a method of estimating animal populations. Potential GCSE content covered In this activity students will cover mean average, rounding and accuracy and reasoning from calculations. All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs. The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales. Please share your classroom learning highlights with us @IETeducation