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KS2 Design and Technology Hub

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Art & Design

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Building Bridges

Design & Technology, Geography, History, Maths, Science

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Design & Technology, History, Maths

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Topics with aspects of: ks2 dt.

Forest School Games: KS2

Physical Education, Design & Technology

My Skeleton

Design & Technology, English, Geography, History, Maths, Science

Physical Education, Design & Technology, English, Geography, History, Maths, Science

Stone, Bronze and Iron Ages

Design & Technology, Art, History, Maths, Science

How does Design and Technology prepare students for the technological world and wider society?

Design and Technology is a subject that plays a crucial role in preparing students for the technological world and wider society. Through this subject, students are taught how to take risks, be creative, and be resourceful, which are essential skills needed in the ever-changing technological landscape.

One of the key aims of the Design and Technology curriculum is to ensure that students develop the necessary expertise to confidently perform everyday tasks and thrive in our increasingly technological society. By creating in lesson plans that integrate various subjects such as maths, art, science, engineering, and computing, students acquire a wide range of knowledge and skills.

Notably, Design and Technology focuses on building students' abilities to design and create high-quality prototypes and products that cater to the needs of diverse users. By doing so, students gain practical experience in problem-solving, critical thinking, and evaluating their ideas and creations. This empowers them to analyze and develop effective solutions to real-world challenges, contributing to the innovative advancements of the technological world.

Furthermore, Design and Technology education emphasizes the importance of understanding the principles and impact of design and technology in different contexts. This equips students with the skills and knowledge to navigate the complex technological landscape and make informed decisions. Such understanding is crucial as it enables students to actively participate in shaping the technological world rather than being solely passive consumers.

Moreover, Design and Technology also places emphasis on educating students about the principles of nutrition and the ability to cook, preparing them for personal well-being and healthy living. They learn how to critically evaluate their own choices and make informed decisions regarding their nutrition and lifestyle.

In summary, Design and Technology education is a comprehensive approach that prepares students for the technological world and wider society. By fostering creativity, resourcefulness, and critical thinking skills, students are empowered to confidently engage with technology, contribute to society, and shape the future. This subject provides the necessary knowledge and expertise needed to thrive in a constantly evolving technological landscape, ultimately equipping students to make a meaningful impact in the world around them.

How does Design and Technology intersect with other subjects like math, art, science, engineering, and computing?

Design and Technology intersects with other subjects such as math, art, science, engineering, and computing by providing opportunities for students to incorporate these disciplines into their lesson plans. For example, in Design and Technology classes, students can draw from mathematical concepts to understand and apply measurements, proportions, and calculations in their designs. They can also explore artistic principles, using elements such as color, shape, and form, to enhance the aesthetics of their creations.

Incorporating science into Design and Technology allows students to understand the properties of materials, their strengths and weaknesses, and how they can be manipulated or combined to serve specific purposes. Engineering principles are essential in designing and constructing functional and efficient products, understanding how structures work, and solving problems related to mechanics and forces.

Additionally, Design and Technology can integrate computing by encouraging students to use digital tools for design, modeling, and prototyping. They can employ computer-aided design (CAD) software, programming languages, and simulation tools to visualize and test their ideas before actual implementation.

By bringing together these different subjects, Design and Technology not only enhances students' problem-solving and critical thinking skills but also provides a holistic and interdisciplinary approach to learning. It enables students to see the connections and applications of concepts across various disciplines, preparing them for the complexities of the modern world.

What are the key skills and knowledge that students should develop in Design and Technology?

Design and Technology is a school subject offered at both primary and secondary level in schools in England. It aims to help students develop a variety of creative and practical skills through the use of their imagination and creativity. The subject focuses on designing products that address real-life problems while considering the needs, wants, and values of both themselves and others.

In Design and Technology, students learn about various aspects, including design, development, application, implementation, support, and management of computer and non-computer based technologies. These types of lesson plans encourage students to take risks, exhibit creativity and resourcefulness, and gain an understanding of how design and technology impact their daily lives and the larger society. Moreover, Design and Technology often integrates with other subjects such as mathematics, art, science, engineering, and computing, allowing students to draw connections and cross-pollinate their knowledge.

The National Curriculum sets out specific aims for Design and Technology, aiming to ensure that students across KS1 and KS2 develop the necessary expertise, confidence, and practical skills to perform everyday tasks in an increasingly technological world. Students are encouraged to build and apply a repertoire of knowledge, understanding, and skills to design and create high-quality prototypes and products that cater to a wide range of users. Additionally, students learn to critique, evaluate, and test their own ideas and products, as well as the work of others. Furthermore, the subject introduces students to principles of nutrition and enhances their culinary skills.

In summary, Design and Technology equips students with the key skills and knowledge required to confidently engage in everyday tasks, participate effectively in a technologically advanced society, develop products for various users, critically evaluate ideas and products, and understand the principles of nutrition and cooking.

How does Hands-On Education's Design and Technology activities help children develop skills?

Design and Technology plays a crucial role in fostering the development of a wide array of creative and practical skills in children. By encouraging them to engage their imagination and creativity, this subject empowers children to design innovative solutions to real-world challenges while considering their own and others' needs, wants, and values. Through the process of designing a product, children learn to take risks, think outside the box, and demonstrate resourcefulness. Moreover, Design and Technology provides children with a comprehensive understanding of how design and technology impact their daily lives and society at large. This interdisciplinary subject allows children to draw upon diverse fields such as mathematics, art, science, engineering, and computing, thereby broadening their knowledge and skill set. Overall, Design and Technology provides children with a platform to develop and refine crucial skills that will benefit them throughout their lives.

What is Design and Technology for key stage two?

Design and Technology, commonly referred to as D&T or D.T., is an academic subject offered in schools across England at both primary and secondary levels. It provides students with opportunities to enhance their creative and practical skills through the utilization of their imagination and ingenuity. The main objective of Design and Technology is to equip students with the ability to conceive and develop solutions to real-world problems while considering their own and others' needs, desires, and principles.

Design and Technology encompasses various aspects such as design, development, application, implementation, support, and management of technologies, both computer-based and non-computer-based. It involves teaching students how to take calculated risks, think innovatively, and demonstrate resourcefulness. Moreover, it emphasizes the significance of design and technology in shaping the daily lives of individuals and the broader society.

Within the Design and Technology curriculum, students have the opportunity to draw upon other subjects such as mathematics, art, science, engineering, and computing. By integrating these subject areas, students can develop a holistic understanding of design processes, problem-solving techniques, and technological advancements.

Overall, Design and Technology nurtures students' abilities to think critically, find creative solutions, and evaluate the impact of design and technology on their own lives and the world around them. It encourages them to explore their own potential, instils confidence, and prepares them for a future where innovation and technological literacy are increasingly important.

How does the National Curriculum allow schools to adapt their own curriculum for Design and Technology?

The National Curriculum for Design and Technology in England empowers schools to customize their own curriculum by providing a framework that serves as a foundation. This framework outlines the essential requirements for the subject, such as the purpose of study, aims, and attainment targets. However, it acknowledges that individual schools have the freedom to interpret and adapt these guidelines to best suit the unique needs of their students and the school itself.

Recognizing the inherent creativity of Design and Technology, the curriculum encourages schools to follow their own visions and ideas. It promotes a dynamic approach to learning, where teachers, students, employers, and industry professionals collaborate to shape the curriculum. By actively involving stakeholders both inside and outside the school community, schools can ensure that the curriculum aligns with local characteristics, employment opportunities, and specific areas of focus.

This flexibility allows schools to provide distinctive learning experiences that are relevant and meaningful to their students. Schools can tailor the curriculum to reflect the diversity of their local area, incorporating elements that resonate with regional industries and interests. Moreover, schools can engage with employers and industry partners to provide real-world experiences, ensuring that students are well-prepared for future career pathways.

In essence, the National Curriculum serves as a starting point, offering a set of minimum requirements and objectives. However, it seeks to empower schools to exercise their autonomy and adapt the curriculum to best serve their unique context, fostering a rich and dynamic learning experience for students in Design and Technology.

What are the aims of the National Curriculum for Design and Technology?

The aims of the National Curriculum for Design and Technology are multifaceted and comprehensive. One of the primary objectives is to equip pupils in Key Stage 1 (KS1) and Key Stage 2 (KS2) with the necessary skills and knowledge to confidently engage in everyday tasks and effectively participate in a technologically advancing world. This includes developing their creative, technical, and practical expertise, enabling them to navigate and utilize various tools and technologies.

Another crucial aim is to cultivate a repertoire of knowledge, understanding, and skills that pupils can employ in designing and producing prototypes and products of high quality. This not only fosters their ability to innovate and problem-solve but also prepares them to cater to diverse user needs and preferences.

Furthermore, the National Curriculum seeks to foster critical thinking and evaluation skills among students. Pupils are encouraged to critique and assess their own ideas and products, as well as analyze and appraise the work of others. By engaging in this process, students can better understand the iterative nature of design and technology, refine their own work, and recognize areas for improvement or innovation.

Lastly, a key aim of the National Curriculum is for students to gain a foundational understanding of nutrition and learn essential principles of cooking. This empowers them to make informed decisions about their own well-being, promotes healthy lifestyles, and instills valuable life skills that they can apply throughout their lives.

Overall, the National Curriculum for Design and Technology aims to provide students with a comprehensive set of skills, knowledge, and understanding to confidently engage with technological advancements, design and produce high-quality products, think critically, and make informed choices in relation to nutrition and cooking.

What does the National Curriculum for Design and Technology entail?

The National Curriculum for Design and Technology provides a framework for teaching and learning in this subject in schools across England. It sets out the goals, objectives, and content that students should be taught during their time in Key Stage 1 (KS1) and Key Stage 2 (KS2).

The primary aim of the National Curriculum for Design and Technology is to equip students with the necessary knowledge, skills, and confidence to tackle everyday tasks and actively engage in an increasingly technologically-driven society. This includes fostering creativity, technical expertise, and practical abilities that will enable students to design and produce high-quality prototypes and products to meet the needs of various users.

Additionally, the curriculum places importance on the development of critical thinking and evaluation skills. Students are encouraged to thoroughly analyze and assess their own ideas and creations, as well as those of others. This not only enhances their ability to improve their designs but also fosters an understanding of the iterative nature of the design process.

Furthermore, the curriculum acknowledges the significance of nutrition and cooking skills. Students are expected to learn and apply principles of nutrition, as well as gain practical experience in cooking. This aspect of the curriculum seeks to promote healthy eating habits and empower students to make informed choices regarding their diet.

In terms of content, the National Curriculum outlines the skills and knowledge that students should acquire throughout their Design and Technology lessons, but does not prescribe specific methods for teaching these skills. Whether through activities such as cooking, woodworking, or product design, students are encouraged to develop a repertoire of practical skills that can be applied in various real-life contexts beyond the classroom.

Overall, the National Curriculum for Design and Technology serves as a foundation for schools to develop their own tailored curriculum that meets the specific needs and interests of their students while ensuring a consistent focus on creative problem-solving, practical expertise, evaluation, and the application of design skills across different domains.

How does Design and Technology encourage creativity and problem-solving?

Design & Technology is a subject that encourages creativity and problem-solving skills in students. Through engaging activities like building bridges and seasonal cooking, students are given the opportunity to explore their creativity by designing and constructing their own projects. This hands-on approach nurtures their imagination and allows them to think outside the box when it comes to problem-solving.

In addition to fostering creativity, Design & Technology presents students with real-life problems that require them to think critically and come up with innovative solutions. By tackling these challenges, students develop essential problem-solving abilities that will benefit them in various aspects of their lives.

Furthermore, Design & Technology goes beyond its own boundaries and integrates with other subjects such as Geography, History, Maths, and Science. This interdisciplinary integration allows students to apply their knowledge and skills across different disciplines, enhancing their understanding and providing them with a well-rounded education. For example, when designing a sustainable product, they may need to consider geographical factors, historical context, mathematical calculations, and scientific principles.

By encouraging creativity and problem-solving, Design & Technology provides a platform for students to unleash their imagination, explore new ideas, and develop essential skills that will benefit them in their future endeavours. It not only equips them with the ability to think critically and come up with innovative solutions but also teaches them the importance of considering different perspectives and the impact of their designs on their daily lives and wider society.

skills by providing hands-on experiences, presenting real-life challenges, integrating with other subjects, and promoting critical thinking. It empowers students to think creatively, solve problems effectively, and make a positive impact in the world around them.

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Design & Technology: Upper Key Stage 2

UKS2 Design and technology scheme of work and lesson plans. Including teacher and pupil videos. Teach your class with confidence!

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Useful resources

Choose your unit - year 5 and year 6.

Design an eco-bike with gears and pulleys to harness the energy from an exercise bike or create a functional pop-up book using levers, sliders, layers and spacers to create paper-based mechanisms.

Choose one:

Apply Computing knowledge and understanding to program a Micro: bit animal monitoring device. Develop 3D CAD skills by learning how to navigate the Tinkercad interface and essential tools to combine multiple objects.

Our refreshed Y5 cooking and nutrition unit including opportunities for children to learn a simple bolognese recipe and adapt it to improve nutritional content.

Test and analyse various types of bridge to determine their strength and stability. Explore material properties and sources, before marking, sawing and assembling a wooden truss bridge.

Design a stuffed toy and make decisions on materials, decorations and attachments (appendages), after learning how to sew a blanket stitch.

Alternative theme: Stuffed Easter eggs .

Our Doodlers unit explores series circuits further and introduces motors. Explore how the design cycle can be approached at a different starting point, by investigating an existing product, which uses a motor, to encourage pupils to problem-solve and work out how the product has been constructed, ready to develop their own.

This unit has been archived on safety grounds because the final card contains coin batteries that present a choking hazard, particularly if the cards are taken home. Assess the risks of this unit of lessons if you wish to proceed.

Discover the farm to fork process, understand the key welfare issues for rearing cattle. Compare the nutritional value of existing sauces and develop a healthier recipe.

Design and program a navigation tool to produce a multifunctional device for trekkers using CAD 3D modelling software. Pitch and explain the product to a guest panel.

Our refreshed Y6 cooking and nutrition unit including optional opportunities to supplement the ‘Come dine with me’ project with learning about the basic tastes and complementary flavours.

Research existing playground equipment and their different forms, before designing and developing a range of apparatus to meet a list of specified design criteria.

Using a combination of textiles skills such as attaching fastenings, appliqué and decorative stitches, children design, assemble and decorate a waistcoat for a chosen purpose.

Understand what is meant by fit for purpose design and form follows function. Design and develop a steady hand game using a series circuit, including housing and backboard.

Children discover the problems facing high-street shops and how window displays are important in attracting customers. They develop design criteria to meet a design brief by creating items for an interactive display. Using technical knowledge they build a mechanical system of cams, followers and axles to create an automata toy.

Develop a three-course menu focused on three key ingredients, as part of a paired challenge to develop the best class recipes. Explore each key ingredient’s farm to fork process.

Develop a functional automata window display, to meet the requirements in a design brief. Explore and create cam, follower and axle mechanisms to mimic different movements.

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DT / Science: Design and make a KITE

Subject: Design, engineering and technology

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

24 May 2023

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DT / Science: Design and make a KITE!

• A 4-page activity booklet for designing and making a kite.
• Students can choose the ‘type’ of kite they want to design and the materials required to construct the frame, kite covering, tail and assembly.
• The booklet also allows the children to evaluate their design and construction.
• Fully editable.

Tes paid licence How can I reuse this?

Get this resource as part of a bundle and save up to 74%

A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

DT BUNDLE - 10 PROJECTS!!

**10 DT PROJECTS AND RESOURCES:** 1. DT - Design & make a Healthy Sandwich. 2. DT - Design and Make a BAG. 3. DT - Design and Make a money container. 4. DT - Slippers (PowerPoint & Lesson Plan). 5. DT - Design and make a KITE. 6. DT - Design & Make a Musical Instrument. 7. DT - Romans 'Mosaics' DT Project. 8. DT - Pneumatics Project. 9. DT - Design your own floor plans. 10. DT - Design & Make a Musical Instrument.

Design and Technology - Bundle - 8 PROJECTS!!

**A HUGE selection of DT Projects including:** 1. Healthy sandwich project. 2. Bag project. 3. Slippers project. 4. Kite project. 5. Musical instrument project. 6. Roman mosaic project. 7. Pneumatics project. 8. Money container project.

Design Technology Bundle - 16 PROJECTS!!

**10 Design and Technology Projects!** DT - BOXTASTIC Homework Project! DT - Bridge Building + Problem Solving Challenge. DT - Design & make a Healthy Sandwich. DT - Design and Make a BAG. DT - Design and Make a Board Game (Problem Solving Activity). DT - Design and Make a MONEY CONTAINER. DT - DESIGN YOUR OWN FLOOR PLANS. DT - Dominoes Challenge (Problem Solving). DT - Make a Megastructure - Problem Solving. DT - Pneumatics Project. DT - Slippers (PowerPoint & Lesson Plan). DT - Tracking Pupil Progress (14 pages). DT - Science: Design and make a KITE. DT - Design & Make a Musical Instrument. DT - IRON MAN PROJECT. DT - Roman 'Mosaics' Project. DT - CANDLE HOLDERS.

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DT structures lesson planning packs from PlanBee include detailed teacher's notes, slides, resources and practical activities for building structures and exploring ways of strengthening, stiffening and reinforcing them. 

Homes DT Lessons

Turn your children into budding architects with these KS1 'Homes' lessons for Year 1. Full of practical activities and inspirational ideas, these D...

Wacky Windmills

Visit a variety of windmills around the world and encourage them to get their builder hats on with this 'Wacky Windmills' scheme of work for Year 1...

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Light-Up Signs

Use woodworking DT tools and materials, card and paper or even scrap materials to make an decorative light box with illuminated words or letters. T...

British Inventors

Teach children all about famous British inventors and their revolutionary inventions, and challenge them to design and evaluate problem-solving pro...

Building Bridges

Building Bridges is a six-lesson KS2 Design and Technology scheme of work for Year 5 or Year 6, all about different types of bridges and the struct...

Chinese Inventions

Use this KS2, six-lesson scheme to explore the innovative culture of ancient China and discover the inventions that have helped shape the world, in...

Making African Instruments

Inspire your class to design and create a range of African instruments in this six-lesson DT scheme for Years 5 and 6. Explore the rich and energet...

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Year 4 Round to the Nearest 10 Reasoning and Problem Solving

Give children the opportunity to use and apply their rounding skills with this Year 4 Round to the Nearest 10 Reasoning and Problem Solving worksheet. It includes a range of engaging questions such as identifying which child's statement is correct and which place value counters are hidden by a splat. As always, we've got the answers covered too to save you valuable marking time!

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National Curriculum Objective

Round any number to the nearest 10, 100 or 1,000

This resource is available to download with a Premium subscription.

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FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)

Fun maths problems are one of the things mathematicians love about the subject; they provide an opportunity to apply mathematical knowledge, logic and problem solving skills all at once.  In this article, we’ve compiled 25 fun maths problems, each covering various topics and question types. They’re aimed at students in KS2 & KS3. We’ve categorised them as:

Maths word problems

Maths puzzles, fraction problems, multiplication and division problems, geometry problems, problem solving questions, maths puzzles are everywhere, how should teachers use these maths problems.

Teachers could make use of these maths problem solving questions in a number of ways, such as:

• embed into a relevant maths topic’s teaching.
• settling tasks at the beginning of lessons.
• break up or extend a maths worksheet.
• keep students thinking mathematically after the main lesson has finished.

Some are based on real life or historical maths problems, and some include ‘bonus’ maths questions to help to extend the problem solving fun! As you read through these problems, think about how you could adjust them to be relevant to your students or to practise different skills. 

These maths problems can also be used as introductory puzzles for maths games such as those introduced at the following links:

• KS2 maths games
• KS3 maths games

Need more support teaching reasoning, problem solving and planning for depth ? Read here for free CPD for you and your team of teachers.

1. Home on time – easy

Type: Time, Number, Addition

A cinema screening starts at 14:35. The movie lasts for 2 hours, 32 minutes after 23 minutes of adverts. It took 20 minutes to get to the cinema. What time should you tell your family that you’ll be home?

Answer: 17:50

2. A nugget of truth – mixed

Type: Times Tables, Multiplication, Multiples, Factors, Problem Solving 

Chicken nuggets come in boxes of 6, 9 or 20, so you can’t order 7 chicken nuggets. How many other impossible quantities can you find (not including fractions or decimals)?

Answer: 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, or 43

There is actually a theorem which can be used to prove that every integer quantity greater than 43 can be ordered.

3. A pet problem – mixed

Type: Number, Problem Solving, Forming and Solving Equations, Simultaneous Equations, Algebra

Eight of my pets aren’t dogs, five aren’t rabbits, and seven aren’t cats. How many pets do I have?

Answer: 10 pets (5 rabbits, 3 cats, 2 dogs)

4. The price of things – mixed

Type: lateral thinking problem

A mouse costs £10, a bee costs £15, and a spider costs £20. How much does a duck cost? Answer: £5 (£2.50 per leg)

Looking for more word problems, solutions and explanations? Read our article on word problems for primary school.

25 Fun Maths Problems - Printable

Download a printable version of these fun maths problems together with answers and mark scheme.

5. A dicey maths challenge – easy

Type: Place value, number, addition, problem solving

Roll three dice to generate three place value digits. What’s the biggest number you can make out of these digits? What’s the smallest number you can make?

Add these two numbers together. What do you get?

Answer: In most cases, 1,089.

Bonus: Who got a different result? Why?

6. PIN problem solving – mixed

Type: Logic, problem solving, reasoning

I’ve forgotten my PIN. Six incorrect attempts locks my account: I’ve used five! Two digits are displayed after each unsuccessful attempt: “2, 0” means 2 digits from that guess are in the PIN, but 0 are in the right place.

What should my sixth attempt be?

Answer: 6347

7. So many birds – mixed

Type: Triangular Numbers, Sequences, Number, Problem Solving

On the first day of Christmas my true love gave me one gift. On the second day they gave me another pair of gifts plus a copy of what they gave me on day one. On day 3, they gave me three new gifts, plus another copy of everything they’d already given me. If they keep this up, how many gifts will I have after twelve days?

Answer: 364

Bonus: This could be calculated as 1 + (1 + 2) + (1 + 2 + 3) + … but is there an easier way? What percentage of my gifts do I receive on each day?

8. I 8 sum maths questions – mixed

Type: Number, Place Value, Addition, Problem Solving, Reasoning

Using only addition and the digit 8, can you make 1,000? You can put 8s together to make 88, for example.

Answer: 888 + 88 + 8 + 8 + 8 = 1,000 Bonus: Which other digits allow you to get 1,000 in this way?

9. Quizzical – easy

Type: Fractions, Adding Fractions, Equivalent Fractions, Fractions to Percentages

4 friends entered a maths quiz. One answered \frac{1}{5} of the maths questions, one answered \frac{1}{10} , one answered \frac{1}{4} , and the other answered \frac{4}{25} . What percentage of the questions did they answer altogether?

Answer: 71%

10. Ancient problem solving – mixed

Type: Fractions, Reasoning, Problem Solving

Ancient Egyptians only used unit fractions (like \frac{1}{2} , \frac{1}{3} or \frac{1}{4} ). For \frac{2}{3} , they’d write \frac{1}{3} + \frac{1}{3} . How might they write \frac{5}{8} ?

Answer: \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} is correct. So is \frac{1}{2} + \frac{1}{8} .

Bonus: Which solution is better? Why? Can you find any more? What if subtractions are allowed?

Learn more about unit fractions here

11. everybody wants a pizza the action – hard.

An infinite number of mathematicians buy pizza. The first wants \frac{1}{2} pizza. The second wants \frac{1}{4} pizza. The third & fourth want \frac{1}{8} and \frac{1}{16} each, and so on. How many pizzas should they order?

Answer: 1 Each successive mathematician wants a slice that is exactly half of what is left:

12. Shade it black – hard

Type: Fractions, Reasoning, Problem Solving What fraction of this image is shaded black?

Answer: \frac{1}{3}

Look at the L-shaped part made up of two white and one black squares: \frac{1}{3} of this part is shaded. Zoom in on the top-right quarter of the image, which looks exactly the same as the whole image, and use the same reasoning to find what fraction of its L-shaped portion is shaded. Imagine zooming in to do the same thing again and again…

13. Giving is receiving – easy

Type: Number, Reasoning, Problem Solving

5 people give each other a present. How many presents are given altogether?

14. Sharing is caring – mixed

I have 20 sweets. If I share them equally with my friends, there are 2 left over. If one more person joins us, there are 6 sweets left. How many friends am I with?

Answer: 6 people altogether (so 5 friends!)

15. Times tables secrets – mixed

Type: Area, 2D Shape, Rectangles

Here are 77 letters:

BYHRCGNGNEOEAAHGHGCURPUTSTSASHHSBOBOREOPEEMEMEELATPEPEFADPHLTLTUT IEEOHOHLENRYTITIIAGBMTNTNFCGEIIGIG

How many different rectangular grids could you arrange all 77 letters into?

Answer: Four: 1⨉77, 77⨉1, 11⨉7 & 7⨉11. If the letters are arranged into one of these, a message appears, reading down each column starting from the top left.

Bonus: Can you find any more integers with the same number of factors as 77? What do you notice about these factors (think about prime numbers)? Can you use this system to hide your own messages?

16. Laugh it up – hard

Type: Multiples, Lowest Common Multiple, Times Tables, Division, Time

One friend jumps every \frac{1}{3} of a minute. Another jumps every 31 seconds. When will they jump together? Answer: After 620 seconds

17. Pictures of matchstick triangles – easy

Type: 2D Shapes, Equilateral Triangles, Problem Solving, Reasoning

Look at the matchsticks arranged below. How many equilateral triangles are there?

Answer: 13 (9 small, 3 medium, 1 large)

Bonus: What if the biggest triangle only had two matchsticks on each side? What if it had four?

18. Dissecting squares – mixed

Type: Reasoning, Problem Solving

What’s the smallest number of straight lines you could draw on this grid such that each square has a line going through it?

19. Make it right – mixed

Type: Pythagoras’ theorem

This triangle does not agree with Pythagoras’ theorem. 

Adding, subtracting, multiplying or dividing each of the side lengths by the same integer can fix it. What is the integer?

Answer: 3 

8 – 3 = 5

The new side lengths are 3, 4 and 5 and  32 + 42 = 52.

20. A most regular maths question – hard

Type: Polygons, 2D Shapes, tessellation, reasoning, problem-solving, patterns

What is the regular polygon with the largest number of sides that will self-tessellate?

Answer: Hexagon.

Regular polygons tessellate if one interior angle is a factor of 360°. The interior angle of a hexagon is 120°. This is the largest factor less than 180°.

21. Pleased to meet you – easy

Type: Number Problem, Reasoning, Problem-Solving

5 people meet; each shakes everyone else’s hand once. How many handshakes take place?

Person A shakes 4 people’s hands. Person B has already shaken Person A’s hand, so only needs to shake 3 more, and so on.

Bonus: How many handshakes would there be if you did this with your class?

22. All relative – easy

Type: Number, Reasoning, Problem-Solving

When I was twelve my brother was half my age. I’m 40 now, so how old is he?

23. It’s about time – mixed

Type: Time, Reasoning, Problem-Solving

When is “8 + 10 = 6” true?

Answer: When you’re telling the time (8am + 10 hours = 6pm)

24. More than a match – mixed

Type: Reasoning, Problem-Solving, Roman Numerals, Numerical Notation

Here are three matches:

How can you add two more matches, but get eight? Answer: Put the extra two matches in a V shape to make 8 in Roman Numerals:

25. Leonhard’s graph – hard

Type: Reasoning, Problem-Solving, Logic

Leonhard’s town has seven bridges as shown below. Can you find a route around the town that crosses every bridge exactly once?

Answer: No!

This is a classic real life historical maths problem solved by mathematician Leonhard Euler (rhymes with “boiler”). The city was Konigsberg in Prussia (now Kaliningrad, Russia). Not being able to find a solution is different to proving that there aren’t any! Euler managed to do this in 1736, practically inventing graph theory in the process.

Many of these 25 maths problems are rooted in real life, from everyday occurrences to historical events. Others are just questions that might arise if you say “what if…?”. The point is that although there are many lists of such problem solving maths questions that you can make use of, with a little bit of experience and inspiration you could create your own on almost any topic – and so could your students. 

For a kick-starter on creating your own maths problems, read our article on KS3 maths problem solving .

Looking for additional support and resources at KS3? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach.

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Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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