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Mathematics
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
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
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
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
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.
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
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
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
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
Mathematics behind revolving door design
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.
Power station event tree analysis
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.
Water aqueduct shapes
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!
How to make a zip line
Designing and making a zip line for a toy
This is a project to build a model of a zip Line. It could be carried out in pairs but will work for individuals. It requires some space to complete successfully but can be executed both indoors and outdoors.
This activity could be used as a main lesson activity to teach learners about the effect of gravity on a body falling in a controlled manner, friction or the practical application of trigonometry.
Resources required:
String or thin rope, 10m should be enough
A ‘passenger’ for the zip line
Paper clips or stiff wire
Sticky tape
A stopwatch or a stopwatch App on a phone
A ruler or tape measure
A protractor
Some paper and a pen to take notes
Download the activity sheets for free!
And please do share your classroom learning highlights with us @IETeducation
Select a Golden Ball recipient maths activity
Use fractions, percentages and averages to decide the best footballer
In this engaging activity students will explore statistics and use them to decide on a ranking of football players. Football players are ranked in different ways and there are a variety of awards that they can be rewarded with. Each year the Ballon D’Or is awarded to the player judged to be the ‘best’. The Golden Ball is given to the best player in the World Cup tournament. In this activity, pupils are presented with data and can use it to decide who they consider to be the best footballer.
The purpose of this activity is to explore statistics and to use them to decide on a ranking of football players. Pupils will compare data and use average scores to find ways of comparing data and making decisions.
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 as a classroom lesson plan and PowerPoint presentation
And please do share your learning highlights and final creations with us on social media @IETeducation
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
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
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.