I See Problem-Solving - UKS2
The ebook i see problem-solving - uks2 helps all children to learn how to solve multi-step maths questions. questions are broken down step-by-step and represented visually to build understanding, whilst extension tasks and reasoning prompts allow children to explore ideas at greater depth. the ultimate resource for teaching problem-solving in y5/6.
I See Problem-Solving - UKS2 Sample provides 5 free sample tasks. For each task there is a main question , a support prompt and explain and extend features to deepen the challenge. The worked examples model the solutions to the main tasks step-by-step - download below for free. The 58 tasks span all areas of the UKS2 maths curriculum. The purchase price is £30 (£25 + £5 VAT) for the PDF digital download.
I See Problem-Solving - UKS2: Worked Examples (PowerPoint)
I See Problem-Solving - UKS2: Worked Examples (PDF)
In these blogs I explain how the task prompts provide extra scaffold to give children additional help , and how extra layers of challenge can be added. Each task starts with a main question, like the examples below:
Children can use the support prompt if they need some extra help to answer the main question. The support prompt may give a suggested starting point, represent the question visually or address a possible misconception. It helps children to understand and access the task. Here are the support prompts for the above examples:
The explain features then provide an opportunity for children to reason based on the initial task. Prompts may ask children to explain a mistake, spot a pattern or make a link with a similar question. Children have to explain their opinion, deepening their understanding of the main question.
The extend feature gives a more challenging, related question for the children to solve. The mathematical structure of these tasks are similar to the initial prompt, usually with one added layer of complexity. Extend tasks may require children to make a generalisation, think laterally or find all possible answers to a question.
The 58 tasks of I See Problem-Solving - UKS2 cover all areas of the UKS2 curriculum. It corresponds to US grade 4&5 and Australian school years 5&6. The sale price is £30. When ordered, the PDF file is emailed direct to your inbox for your use.
To purchase, click on the link below. If you need assistance ordering, please read the Frequently Asked Questions below or email [email protected].
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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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Problem solving
Subject: Mathematics
Age range: 11-14
Resource type: Game/puzzle/quiz
Last updated
29 April 2018
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So many questions...on a variety of strands... amazing resource.
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a lot of différents questions ! Thanks !!
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This beautifully-illustrated PowerPoint is a wonderful introduction to teaching about problem-solving. It guides learners through different problem-solving strategies involving all four mathematical operations in a helpful and engaging way. It's a great revision tool, too, particularly when it comes to revising strategies for SATs or other assessments that children will need to complete. By ...
A powerpoint outlining the universally accepted strategies to solve a problem - * look for a pattern * draw a sketch * make an organised list * simplify the problem * guess and check * make a table * write a number sentence * act out a problem Each strategy is accompanied by an example and a problem for student to try, plus solutions. Thanks ...
Created as an emergency supply teaching maths lesson. Activities taken from https://nrich.maths.org/trial-and-improvement-ks2 and made into a PowerPoint format. Ther
ppt, 145.5 KB. Maths lesson resource pack focusing on breaking down the problem solving process. Suitable for years 4-6. Incudes detailed lesson plan with suggestions how to use the powerpoint and the activity sheets. The word problems are grouped by operation with a separate set of multi step problems. They are also grouped by difficulty with ...
You can use this lovely PowerPoint presentation to introduce or revise different strategies that can support solving mathematical calculations involving all four operations. Perfect for helping children to have a range of techniques to use independently in their work.To practise the techniques listed in this PowerPoint, you may be interested in our blether stations on solving maths problems ...
Find out how we encourage children to approach problem solving independently in our blog: 20 Maths Strategies KS2 That Guarantee Progress for All Pupils. The most commonly used model is that of George Polya (1973), who proposed 4 stages in problem solving, namely: Understand the problem. Devise a strategy for solving it.
Tackle challenging questions using a variety of mathematical skills with our range of problem-solving maths resources, designed for KS2 students. Problem-solving in KS2 is a key skill that will form the foundation of future learning. That's why we've designed some brilliant PowerPoints, worksheets, games, and lots of maths mastery resources to ...
This word problems PowerPoint (Year 2-6) is fantastic for helping your children practise a range of Maths skills. Whether you want to focus on addition, subtraction, multiplication or division, this presentation covers all bases.Our PowerPoints are fully editable and lovingly decorated with beautiful illustrations. Sometimes, it can be tricky to make Maths problems visually exciting for kids ...
Maths starters, like our quick mental maths starters for KS2, can introduce your group to a new topic, help to revise previously learned content or even get your children ready for the day ahead. They're a perfect example of exercises that are short but aim to engage children and test their skills of problem-solving, reasoning, fluency and ...
Here are our top 5 picks of teaching resources that you can use to teach KS2 equations: Expressing Missing Numbers Activity Pack. Simplifying Algebraic Expressions Worksheet. Alphabet Algebra Worksheet. Balancing Equations Worksheet Pack. Balance Equations Using Missing Numbers Worksheet.
Our maths problems of the day provide four problems across KS1, KS2 and Lower KS3 for pupils to solve. View our Maths resources from White Rose Maths. Cookie Consent. We use cookies to help provide a better website experience for you, and help us to understand how people use our website. Our partners will also collect data and use cookies for ...
Reasoning Y6. Reasoning and problem-solving questions (28), all with clue pages and go deeper challenges to support maths mastery over 86 PowerPoint pages, for each KS2 year group. Includes modelled answer for every question to save time marking. Ready to pick up and use!
I See Problem-Solving - LKS2 Sample provides 5 free sample tasks. Most tasks have a build task, main question, a support prompt and explain and extend features to deepen the challenge. There are sometimes practise questions too. The worked examples model the solutions to the main tasks step-by-step - download below for free.The 54 tasks span all areas of the LKS2 maths curriculum.
This is a fantastic collection of resources to teach key stage 2 pupils how to improve their problem-solving skills, and they are just waiting to be downloaded. There are tons of maths display resources that can help teach your year 3, year 4, year 5, and year 6 pupils about fluency, reasoning, and problem-solving.
I See Problem-Solving - UKS2 Sample provides 5 free sample tasks. For each task there is a main question, a support prompt and explain and extend features to deepen the challenge. The worked examples model the solutions to the main tasks step-by-step - download below for free.The 58 tasks span all areas of the UKS2 maths curriculum. The purchase price is £30 (£25 + £5 VAT) for the PDF ...
Twinkl Apps. Use our range of KS2 maths resources to teach addition, multiplication, fractions, money, measurement, 2D & 3D shapes and all the other key for KS2 maths topics. All our primary maths resources are designed to be in line with the national curriculum for maths for KS2. So you can be sure you'll be hitting key standards and ...
Also discusses top questioning strategies to use (e.g. key problem solving maths questions as learning objectives, if this is the answer… what is the question?, just one more question). You might also be interested in: KS2 Problem Solving; KS3 Maths Problem Solving; Why SSDD Problems Are Such An Effective Tool to Teach Problem Solving At KS3 ...
Maths reasoning, fluency and problem-solving skills are incredibly important. Being able to use and apply maths and number skills will enable children to develop their confidence and mastery in maths. This fantastic year 6 autumn-themed morning starter PowerPoint is the perfect way to help children develop their key skills each day with a variety of year 6 problem solving questions that ...
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.
This has also lessened workload time for teachers around adapting maths sessions. We use the White Rose Education schemes and lesson-by-lesson overviews throughout the school, and the printed workbooks add yet another top quality layer of time- and stress-saving benefits on top of those! We no longer spend precious time printing and sorting ...
These fun Maths challenges are great for engaging KS2 maths students in a variety of topics and encouraging both in-class discussion and individual development. Find challenge cards, games and problem-solving tasks that are perfect for taking your lessons to new levels of depth.
Problem solving. Subject: Mathematics. Age range: 11-14. Resource type: Game/puzzle/quiz. I'm a secondary school maths teacher with a passion for creating high quality resources. All of my complete lesson resources come as single powerpoint files, so everything you need is in one place. Slides have a clean, unfussy layout and I'm not big on ...