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Mathematics
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Repeated graphical patterns
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
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Speedometer calibration
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
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Bake a Yule log
Give making a Yule log a STEM twist by using key maths skills to work on the weighing and timing for this delicious Christmas dessert.
This is a great activity that brings together baking skills, mathematics and creativity, and tastes delicious!
The Yule Log is a traditional cake eaten at Christmas. It is thought that this cake originated in France to represent the wooden log that was burned to bring good luck through the winter months. It was hoped that by burning the log and keeping the ashes until the following year, it would ward off evil spirits during the long winter months.
Download the recipe and teaching notes for free.
Oh ho ho, and please do share your experiment highlights with us @IETeducation #SantaLovesSTEM
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Create stained glass you can eat!
Learn how to create colourful, edible stained glass and discover the science of light in this fun experiment for kids.
What ingredients will you need?
• 790g white, granulated sugar
• 475ml water
• 240ml light corn syrup
• ¼ teaspoon cream of tartar
• Food colouring (red or green)
Download the free Edible stained glass activity sheet to learn the science behind this experiment!
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.
Don’t forget to take photos of your edible stained glass and share them with us @IETeducation
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KS2 times table cake challenge
Get children thinking about combinations and KS2 times tables with this visual and hands-on activity for primary aged children.
With a row of 24 cupcakes, what happens when every second cake has white icing and every third cake has a red smartie?
Our lesson plan is mapped to the UK curricula and has all the notes to hand to guide you through the 45 minute resource as a classroom activity or at home.
This activity in partnership with MEI could be used in Key Stage 2 as a stand-alone activity, as a focused task to develop problem solving skills, or as a consolidation task related to 3x,4x,8x multiplication facts.
Pupils develop both their problem-solving and reasoning skills. They will also practice their mental recall of the 3x, 4x and 8x multiplication tables without the standard ‘fill out the multiplication table’.
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 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.
You can download our step-by-step instructions below as either a classroom lesson plan or PowerPoint presentation.
Please do share your highlights with us @IETeducation.
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Measure distance
Make a measuring wheel that measures distances
This activity for primary school kids involves making a measuring wheel for accurately measuring in metres and centimetres.
This activity combines maths and history and is inspired by the achievements of ancient Greece. It is thought that the inventor of the odometer may have been Archimedes, between 2200 and 2300 years ago. Resources are provided to support teachers in furthering their students’ maths abilities.
And please do share your classroom learning highlights with us @IETeducation
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Using time to record
Measure the time taken to complete a task and plot results in a graph
In this activity, students will take part in their own Olympics, an event invented by the Greeks, whilst applying history, maths, and PE.
Students will record distances using a tape measure or an odometer to record the time taken to run different lengths. This activity will enable students to measure using different tools, record results and plot graphs. Resources for teachers are provided.
And please do share your classroom learning highlights with us @IETeducation
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Learn to count: Balloon rocket activity
Learn how to count forwards and backwards by releasing balloon ‘rockets’
During this exercise, participants will practice counting backwards using different steps i.e., 1s, 2s, 3s, 5s, and 10s. This will equip them with the necessary skills to count to and from 100, both forwards and backwards, starting from zero or any given number. To increase engagement, students will release balloon ‘rockets’ at the conclusion of each countdown.
This activity can be used as a main lesson activity, to teach learners how to count backwards using the prompts in the teacher presentation.
This is an engaging and practical exercise that can be carried out as a whole class or in small groups.
When using the presentation, you are prompted with which step to use for the countdown and with a starting number. As you click through the steps each number, in sequence, will be revealed and at zero the balloon will be launched.
If some younger learners struggle with blowing up balloons, some could be inflated prior to the lesson and ‘tied-off’ using clips. As the balloons are released when the count reaches zero, the balloons should not be tied.
If re-inflation is not possible within the time, a proportion of the balloons could be released each time – e.g., a certain colour or all the balloons from one table group.
As an optional extension activity, the count downs could be started from 100 or another integer of the teacher’s choice.
How long will this activity take? It is a quick and simple activity that will take approximately 25-35 minutes to complete.
Tools/resources required
Whiteboards
Whiteboard markers and erasers
Pack of balloons
Balloon pump
The engineering context
An understanding of number combinations and number operations is vital for engineers who need to solve lots of interesting problems. For example, electronic engineers use countdown timers to let motorists know when a traffic light will go from red to green and allow the motorist to drive off safely.
Suggested learning outcomes
By the end of this activity students will be able to count backwards from numbers up to 50 and they will be able to count backwards in steps of 1s, 2s, 3s, 5s, and 10s.
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
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Solving maths problems (KS1)
Use a number balance see-saw
This engaging activity is designed for KS1 to enhance students’ addition and subtraction skills through a practical and engaging approach! Learners will use a model of a see-saw to balance a range of numbers. They will then decide how many items need to be added or subtracted to bring the see-saw into balance.
By actively participating in this hands-on exercise, learners will gain a deeper understanding of addition and subtraction as they work to achieve equilibrium on the see-saw by carefully selecting and arranging various numbers.
This activity could be used as a main lesson to teach learners how to make a model see-saw and solve number problems using the prompts in the presentation and carried out in pairs or small groups.
To get started, download the activity sheet containing a comprehensive, step-by-step guide on building the see-saw. Additionally, we have included printable box templates for your convenience. Students can easily position these box templates onto the see-saw and then experiment by placing coins or marbles into the boxes, effectively achieving balance on the see-saw.
The engineering context
Engineers rely on problem-solving daily to find solutions to a wide array of issues. For instance, when an aerospace systems engineer is tasked with determining the amount of cargo that can be loaded onto a rocket bound for a space station, they will skilfully adjust the contents, either adding or removing items, to ensure that the cargo meets the precise weight requirement.
Suggested learning outcomes
By the end of this activity, students will be able to solve one-step problems that involve addition and subtraction, and they will be able to make a see-saw model and solve practical balance number problems.
Download for free!
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
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Tree trunk circumference
Measuring the circumference of tree trunks and working out their age. They will then repeat this process with other trees and share their findings as a group.
This exercise could serve as a main lesson activity to teach learners how to gather data through measurement and apply their numerical skills in a practical context. It could also be incorporated into a larger curriculum that emphasises the use of maths and science to comprehend the natural world.
This is one of a set of free STEM resources developed to support the teaching of the primary national curriculum. They are designed to support the delivery of key topics within maths and science. This resource focuses on measuring the circumference of a tree trunk and using this information to calculate its age.
Trees can be identified and measured in and around the school grounds as available. Appropriate safeguarding checks and risk assessments will need to be put in place by the teacher depending on where the measuring of the trees takes place.
Taking the measurements may need two learners working as a pair or a group of three, one holding the end of the tape in place, the other wrapping around and taking the reading, optionally with a third recording the measurement. The measuring tape must be kept straight and level to give an accurate reading.
This is a fun and practical exercise that will challenge learners’ maths and science skills and encourage them to think about the ways in which environmental engineers interact with the natural world.
This activity will take approximately 40-60 minutes to complete.
Tools/resources required
Access to an outside area with trees
Measuring tape
Clipboards
Calculators
The engineering context
As part of their daily job, engineers are obligated to frequently apply their mathematical knowledge and skills. Hence, it is imperative that they possess a thorough understanding of fundamental concepts, including measurement taking and interpretation.
Environmental engineers are responsible for enhancing the quality of the surrounding natural environment. Their job performance improves as they expand their comprehension of it.
Suggested learning outcomes
By the end of this activity students will be able to measure the circumference of a tree, they will be able to calculate the age of a tree using its circumference and they will be able to communicate measurements using appropriate SI units.
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
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Network Rail maths challenge
A maths-based challenge to find stations on the rail network based on their journey times
Can you use a rail network map to find stations based on journey times? Use your math skills to complete our station hunt activity sheet in this fun STEM challenge for kids!
This is one of a series of free resources developed in conjunction with Network Rail to develop understanding and skills in key maths, science, and engineering concepts.
Activity:
In this fun maths challenge, learners will use a known starting position (station) and a journey time to identify a destination. It will involve adding different combinations of journey times to identify the answer.
This activity could be carried out as individuals or in pairs and could be used as a one-off main lesson activity to develop basic maths skills in context.
Learners will complete the questions on the activity sheet using the station hunt map as a guide. They should find the starting point station and move along the rail lines, adding up the time as they go along, until they reach their destination station.
The transport speeds are estimates based on typical values, found using the most common search engine. Any statistics or data on transport speeds used in this activity are solely for the purpose of this activity and may not be an accurate reflection of actual current times, which may vary due to seasonal, environmental or legal limitations, for example.
Additional complexity could be added by adding a set time (for example, 15 minutes) when train changes are needed.
As an extension activity, students could work out their own journey time questions and try them on their friends.
How long will this activity take?
This activity will take approximately 30-50 minutes to complete.
Tools/resources required
Pencils
Calculators
The engineering context
Calculating times is a vital skill that engineers use – it helps them make decisions about the best way to complete a task. For example, it helps aerospace engineers plan how much fuel to carry on a plane to allow it to fly for a long time.
Suggested learning outcomes
By the end of this activity students will be able to solve a contextual problem using a time calculation and they will understand how to calculate different journey times between rail stations.
Download the free Network Rail maths challenge activity sheet!
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
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Data logging - difference calculations
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.
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IET Faraday® DIY Challenge Day - IHEEM (Institute of Healthcare Engineering and Estate Management)
A set of printable resources and guidance notes giving teachers and technicians the basic ingredients to run their very own Faraday Challenge Day. This cross-curricular activity day brings science, design and technology, engineering and maths together in an engaging way.
The IHEEM challenge is based on the IET Faraday® Challenge of the same name from our 2021/22 season of IET Faraday® Challenge Days.
Students are given an engineering brief (found in the student booklet) to help IHEEM to design a prototype which could be used in a children’s hospital to make a stay in hospital more comfortable and relaxing for young patients and their families, carers and friends. They will need to demonstrate that they have the engineering skills required to engineer and construct a working prototype of their design and pitch their products to the judges.
Designed for six teams of six students (36 students in total) aged 12-13 years (year 8 England, and equivalent), the challenge encourages the development of students’ problem solving, team working and communication skills.
This activity day can be tailored to the needs of your school and your students by adapting the PowerPoint presentation and the editable student booklet.
What’s included?
The complete set of downloadable materials includes:
Teachers’ pack
A list of the practical materials needed, presenters’ notes highlighting key areas and reinforcing key themes throughout the day, some handy hints on how to deliver the day . . . plus printable Faradays currency and student certificates.
Student booklet
Available as an editable MSWord document to allow the booklet to be adapted to meets the needs of your students and your school.
PowerPoint presentation
A step-by-step guide for your students throughout the day, with supporting notes for the delivery of the presentation.
Film clip
Full briefing video introducing the challenge to your students.
All online resources are free to download, and the student booklet and PowerPoint presentation are fully editable, so you can tailor them to your students’ and your schools’ needs.
And please do remember to share your activity highlights with us @IETeducation
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Well placement between villages
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
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Eggnog for the family
Make a non-alcoholic family friendly eggnog this Christmas, and learn about science and mixtures in this quick and easy festive recipe.
Learn some amazing scientific facts while making this delicious, creamy Christmas treat - the magic of science is real-life fun!
More recently, non-acholic eggnog has become a staple of Christmas celebrations, with Americans drinking over 58 million kilograms each year and Christmas Eve now being named National Eggnog Day.
Ingredients needed:
500ml whole milk (swap for unsweetened almond milk if dairy-free or vegan)
200g caster sugar
100ml double cream (swap for full-fat coconut milk if dairy-free or vegan)
100ml water
4 egg yolks (swap for vegan vanilla pudding mix if vegan)
1 teaspoon vanilla paste (remove this ingredient if you are following the vegan recipe)
Ice
The engineering context
Baking is engineering. It is using science, maths and technology skills to engineer and create solutions and new tasty products. Engineers need all these skills – precision in weighing out ingredients, the safety required in the kitchen and product design and quality engineering to test, taste and improve with each delicious creation!
Download the free recipe and template!
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.
Oh ho ho, and please do share your experiment highlights with us @IETeducation #SantaLovesSTEM
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How to make a crown activity
Use card to craft your very own crown - fit for royalty…
In this practical STEM activity for kids, students will learn about 3D structures within a graphics context. Learners will have the opportunity to use a template to help them cut out the parts for a crown.
This exercise is aimed at primary school students and could be used as a main lesson activity to teach learners about simple structures made from separate parts.
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 maths and science. This resource is a structure-making activity which involves using graphics media to make and assemble a crown. Parts of this activity may be challenging to some learners as it requires good manual dexterity.
Download the activity sheet below for a step-by-step guide on how to construct your own crown using card strips from a template.
Once students have made their crown, the teacher will discuss the results of the activity with learners and explain how nets are used to make objects and how separate parts are used to make a larger structure.
This activity will take approximately 50 – 80 minutes.
Tools/resources required
Glue sticks
Coloured card
Coloured crepe paper
Scissors
Paper fasteners
Decoration materials
Suggested learning outcomes
By the end of this activity students will be know what a 3D shape is, they will understand how structures are made using separate parts and they will be able to make and assemble a crown structure from card strips.
The engineering context
Engineers use nets to allow them to make scale models of their design ideas. Nets are also used to make almost all the card-based packaging we use.
Download the free How to make a crown 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.
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
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Fault detectors using circles
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.