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KS2 Maths Investigations Based On Real Life In Primary School

Sophie Bessemer

It’s been a long week and it is time to hand out your latest ‘exciting’ KS2 maths investigations, carefully crafted problem solving investigations focused specifically on the work you’ve been doing this week.

But then you hear the the immortal words from your Year 6: ” What Does This Have To Do With The Real World?”

Any good teacher knows, of course, exactly how relevant maths is in the real world and how, without maths, modern society as we know it would never have existed.

The problem is, not all 11 year olds know it too – and you’re going to have a hard time convincing some of them.

In defence of 11 year olds, the curriculum – maths in particular – can sometimes feel all too distant from what’s ‘real’.

So the question then becomes, how do we show young learners how Maths intersects and dominates our day to day life?

How do we give our KS2 pupils maths investigations that inspire them, change their perceptions and help them to move beyond a fixed mindset to see maths problem solving as entirely relevant to what may come next in life?

If you’re just interested in maths investigations for Year 5 and Year 6 we’ve created jump to the end of the blog where they’re all listed by term.

KS2 Maths Investigations: Problem solving in context

Benefits of maths investigations at ks2, 5 top tips for creating your own ks2 maths investigations, year 5 and year 6 maths investigations.

We believe that one of the answers is putting your maths problem solving activities into a context that your pupils can relate to.

We call this Topical Maths, and we’ve used this idea as the source for several of our most popular Year 5 and Year 6 maths problem solving resources, all offering the kind of KS2 maths investigations we know your pupils will love!

KS2 Topical Maths Problems

25 real world maths investigations to practise reasoning and problem solving based on primary school calendar events

There are lots of benefits of course, but the most important as far as we’re concerned are these:

• Pupils are required to talk and reason about their maths
• The maths problem solving investigations cement higher order reasoning skills and problem solving
• Starting early with Year 5 maths investigations you can support familiarity with the sorts of questions that come up in Year 6 SATs.

To encourage you to give these KS2 maths investigations a go, we’ll first look at the benefits and principles of introducing them for your reasoning and problem solving at Year 5 and Year 6, we’ll then give you some ideas for how you can create these problem solving activities for the rest of KS2 yourself.

We guarantee you’ll see your pupils’ reasoning and problems solving skills improve!

1. KS2 Maths Investigations Involve Pupils Talking and Reasoning

Getting pupils to verbalise their numerical reasoning has a knock-on effect on pupils’ overall reasoning skills, which is why the core element of our  KS2 maths intervention  is mathematical reasoning; asking pupils to explain not just what they’re doing, but why they’re doing it.

As a teacher of a large class, it can be difficult to provide the teacher time necessary for each pupil to verbalise to you their reasoning.

The inherently collaborative nature of year 5 and year 6 maths investigations gives pupils the opportunities to to reason out loud and work on their maths problem solving skills.

2. KS2 Maths Investigations Cement Higher Order Reasoning Skills

Our experience teaching thousands of primary school pupils maths every week has shown us that at KS2, even by Year 5 or Year 6, pupils often have good procedural understanding, but struggle with higher order problem solving questions.

The problem solving element to these topical maths investigations naturally improves reasoning skills in Year 5 and Year 6 pupils, as they are more likely on reaching an answer to have to think about not just how but why that answer is correct.

By setting topical maths investigations at KS2 as group-work or a whole class activity, you can ensure that all pupils get to experience this deep level of reasoning.

Many of our topical maths investigations are open ended, but if you’re teaching a fully mixed ability class, we’ve also created some  low threshold high ceiling open ended maths investigations  specifically for mixed ability classes.

3. KS2 Maths Investigations Give Early Exposure To SATs Style, Reasoning Questions

Most, if not all, schools will provide their pupils with exposure to reasoning via SATs-style questions, but this often comes hand in hand with exams and assessment.

Yet, it is equally important to get pupils reasoning and problem solving in a low stakes classroom setting or as a group.

Creating a learning environment where the types of problem solving questions found in SATs just become part of  your lessons will help pupils feel comfortable with exam terminology, and ensures they are more at ease with being asked the same kind of question (say, multiplying and dividing fractions) in lots of different ways.

These maths problem solving investigations and downloadable resources enable you to include these type of SATs style questions in a way which is fun and confidence boosting.

More problem solving and reasoning articles

• Ultimate Guide to Maths Problem Solving Techniques
• Maths Investigations: How To Develop Mathematical Reasoning
• 35 Year 6 Maths Reasoning Questions .

You don’t need to create your own problem solving investigations – the links at the end of this article should provide you with everything you need. However if you do want to have a go these were our principles and, judging by the number of visits. to the date related articles and downloads of these resources we get every year, they’re still very popular.

1. Date-based themes for maths problem solving activities

Nothing solidifies maths in the real world quite like the real world. Nearly, if not everyday of the year holds some significance to someone.

February? Pancake day, Valentines Day, and Fairtrade Fortnight.

March? Red Nose Day, World Book Day, and Holi.

Why not spice your lesson up and throw in some Pancake Day Maths for ratios, or Bonfire Night Maths for measurements. Capitalise on special celebrations throughout the world to excite and enthuse young learners.

For example these  Christmas activities always prove popular with KS1 and KS2  or at a different time of year you could try these summer  holiday maths investigations  or any of these  maths activities .

2. Trends and pop-culture KS2 maths investigations

Peers and pop culture hold huge sway over most pupils, and the reason for this is that as growing persons we want to fit in and find friends.

Nothing achieves this more effectively than mutual interest. As a teacher, utilise it – whether this is measuring the speed of explosions in the latest Transformer film, or totalling the high notes in Disney’s Moana – you’ll have pupils hooked in no time.

For the exceptionally savvy teacher, you might want to capitalise on the latest fads and trends within your school. How about measuring amounts via the infamous bottle trick, or examining angles through the lens of the dab?

3. Simple stuff engages pupils with maths problem solving and reasoning

Sometimes when teachers link maths back to real world issues, politics, and the universe at large, it can still feel a little dissonant for the younger pupils.

Don’t be afraid to stick with the simple stuff and the smaller aspects of the world.

Everybody needs to know how much change they’ll have left over after a bus ride home, everyone wants to know exactly how many chocolate bars they can gorge themselves on with two pounds, and everyone wants to know how many times they can go on the log-flume with five tickets.

Keeping it simple can be one of the most effective ways to engage pupils by showing them the mathematics they will employ in every-day life.

4. Cool factor for primary teachers – even in maths

Generally – note this is a generalisation – as a secondary teacher, one can spend eternity being uncool. Luckily primary school teachers get an easier rap, and KS2 pupils are willing to be ‘wowed’. All students can be ‘wowed’ under the right circumstances, but with younger, more malleable minds it can be somewhat easier.

Astronauts, magicians, superheroes, cute animals, cartoons, all carry the power of enthusiasm. They can be your secret weapon for making percentages fun – you’re not halving a number, you’re a magician halving a 167cm person in a special box, etc.

5. Make your maths investigations REALLY relevant

Relevance can be highly underrated when it comes to linking seemingly abstract topics to the real world.

One trick is to instead of distributing your problem solving activity sheets with strangers’ names and unrelatable allegories in the questions, why not make those names and allegories about your class.

Instead of a stranger gathering four apples and eating three, make your pupil.

Instead of apples, why not their favourite snack?

Letting students pick names in questions gives them greater agency in their learning and can be highly engaging.

Better still, putting their names/hobbies/likes/dislikes will not only show them that you know them, and that you care, but it will establish clear links between the work they are doing and the world proper.

Here’s our complete list of topical maths investigations for year 5 and year 6.

Autumn Term maths investigations year 6 and year 5

• Autumn maths activities
• Halloween maths activities
• Bonfire Night maths activities
• Christmas maths activities

Spring Term maths investigations year 6 and year 5

• Heart Month Months activities
• Shrove Tuesday Maths activities
• Pancake Day Maths activities
• World Book Day Maths activities
• International Women’s Day Maths activities
• British Science Week Maths activities
• Holi Maths activities
• Easter/Lent Maths activities

Summer term maths investigations year 6 and year 5

• Share-a-Story Month activities
• FA Cup Maths activities
• Walk to School Week activities
• Ramadan Maths activities
• Child Safety Week activities

And if that’s not enough we’ve even got maths activities for Year 5 and Year 6 for events you’re likely to celebrate in primary school but don’t come round every year… 

• Red Nose Day Maths activities
• World Cup Maths activities
• Election Maths
• Jubilee Maths activities

We update these blog posts every year so keep an eye on your calendar, and let us know how you get on @thirdspacetweet.

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Problem-solving maths investigations for year 6.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 6 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 6 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 6:

• Individually, they are incorporated into every unit in our Year 6 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 6 .

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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Lesson 6 Problem-Solving Investigation: Make a Table

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McGraw Hill My Math Grade 3 Chapter 1 Lesson 6 Answer Key Problem-Solving Investigation: Use the Four-Step Plan

All the solutions provided in McGraw Hill Math Grade 3 Answer Key PDF Chapter 1 Lesson 6 Problem-Solving Investigation: Use the Four-Step Plan  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 3 Answer Key Chapter 1 Lesson 6 Problem-Solving Investigation: Use the Four-Step Plan

Practice the Strategy

4. Check _________________

Answer: Given that, A one-way ticket costs $43. A round-trip ticket costs $79. Two one way tickets = $43 + $43 = $86. Therefore less expensive to buy the one round- trip ticket.

Apply the Strategy

Solve each problem by using the four-step plan.

Question 2. Cameron and Mara walked 2 blocks. Then they turned a corner and walked 4 blocks. If they turned around now and returned home the way they came, how many blocks will they have walked altogether? Answer: Given that, Cameron and Mara walked 2 blocks. Then they turned a corner and walked 4 blocks. If they turned around now and returned home the way they came. Therefore they will 8 blocks to returned home the way they came.

Question 4. In 1,000 years from now, what year will it be? What year will it be 100 years from now? 10 years from now? Answer: This year is 2022. This year from 1000 years = 2022 + 1000 = 3022. This year from 100 years = 2022 + 100 = 2122. This year from 10 years = 2022 + 10 = 2032.

Review the Strategies

Use any strategy to solve each problem.

• Use the four-step plan.
• Guess, check, and revise.
• Act it out.

Question 6. Mathematical PRACTICE 1 Plan Your Solution Two students traveled during their summer vacation. Tina traveled 395 miles. Carl traveled 29 more miles than Tina. How many miles did Carl travel? Answer: Given that, Two students traveled during their summer vacation. Tina traveled 395 miles. Carl traveled 29 more miles than Tina = 395 + 29 = 424 Therefore carl traveled 424 miles.

McGraw Hill My Math Grade 3 Chapter 1 Lesson 6 My Homework Answer Key

Problem Solving

Question 1. Victoria buys two pairs of sunglasses for $8 each. About how much did she pay for both pairs of glasses? Round to the nearest ten. Solve the problem using the four-step plan. Answer: Given that, The total cost of sunglasses = $8. The total cost of two sunglasses = $8 x 2 = $16. 16 rounded to the nearest ten is 20. In 16 the ones place is greater than 5. So, replace the ones place by 0 and add 1 to the tens place.

Solve each problem using the four-step plan.

Question 2. Ridgeway Elementary School collected eight thousand, five hundred thirty-one cans of food. Park Elementary School collected eight thousand, six hundred forty-two cans. Which school collected more cans of food? Write the greater number of cans in expanded form. Answer: Given that, Ridgeway Elementary School collected eight thousand, five hundred thirty-one cans of food = 8531. Park Elementary School collected eight thousand, six hundred forty-two cans = 8641. Park Elementary School is greater than Ridgeway Elementary School The expanded form of 8641 is 8000 + 600 + 40 + 1.

Question 3. Mathematical PRACTICE 1 Make a Plan There are 398 students at Rebecca’s school and 462 students at Haley’s school. There are 10 more students at Ronnie’s school than there are at Rebecca’s school. Order the number of students at each school from least to greatest. Answer: Given that, The total students at the Rebecca’s school = 398. The total students at the Haley’s school = 462. There are 10 more students at Ronnie’s school then Rebecca’s school = 398 + 10 = 408. The order of the number in each school from least to greatest is 398; 408; 462.

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These curated links provide MAV members with access to nine authentic tasks from some of our primary consultants’ favourite resources. The 11 criteria provide MAV members with a research-informed context to consider each task’s potential impact on student thinking, ways of working, attitudes towards mathematics, their knowledge and understanding.

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TES Maths Investigations Collection

Engaging investigation ideas to inspire creative thinking in your classroom

Since the abolition of maths coursework, there is no formal requirement to carry out investigations with your students. However, it is only through investigative work that students of all ages and abilities can start to appreciate the true beauty of the subject. They can hypothesise, be creative, challenge themselves, work with other students and potentially discover things that have never been discovered before.

At our school, we do an investigation with each year group every half term. They may last 20 minutes or five lessons. Here is a selection of the best investigations that the TES Maths community has to offer.

I really hope you and your students find them useful, enjoyable and stimulating.

Craig Barton, TES Maths adviser

• Creativity in maths This useful guide is worth reading before embarking upon any maths investigation. What does it mean to be creative and how can you provide opportunities for creativity in your classroom? It comes complete with five puzzles in a ready-to-print format.
• Maths investigations A collection of over 20 maths problems, puzzles, games and investigations that are designed for KS2, but which could easily be used to extend the learning and problem solving skills of younger KS3 students.
• More maths investigations This resource contains lots of ideas for real-life maths investigations, covering number, algebra, shape, space and measure. Again, while they are aimed at KS2 pupils, they could be adapted for use with KS3 students as well.
• Even more maths investigations! These starter sheets introduce a topic for investigation and come with levelled guidance to help students to self- and peer-assess as they progress through it. Although they are targeted at Year 7, these are suitable for year groups at both KS2 and KS3.
• Investigative lesson presentations A collection of classic maths investigations, including chessboards and tetrahedron towers, presented as PowerPoint presentations with learning objectives and level expectations.
• Challenging ideas for KS4 and Post-16 This was one of my TES Maths Resources of 2014 and it’s easy to see why. These investigations are ideal for gifted and talented GCSE and sixth form students and include everything from code-breaking and Goldbach’s conjecture to the Riemann hypothesis and game theory.
• Diagonals of rectangles This may be one of my own resources, but it is one of my all-time favourites as it’s so versatile. It can be accessed by Year 6 students, while still challenging the most able Year 11s. The concept is so simple, but the potential depth is great.
• Investigating circle theorems Some of the best investigations are topic-specific and this activity is no exception. It uses the free dynamic geometry package, GeoGebra, to help students derive, identify and better understand all of the key circle theorems.
• Prison cells investigation The famous investigation about the numbers on prison cell doors is well-presented, has a really clear structure and some fantastic ideas for differentiation.
• Pentominoes Pentominoes are a superb, versatile teaching resource that can be used for investigating many aspects of shape. This resource takes you through lots of ideas for making the most of them.
• Mathemagic These maths magic tricks are engaging way of presenting a problem to your KS3 pupils, before challenging them to investigate how and why they work. Better still, can they go on to design their own?
• Noughts and crosses investigation Who would have thought you could get so much maths goodness from a game of noughts and crosses?  This game will appeal to secondary students of all ages.

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TodayTix CEO Brian Fenty took over at 31. Now 38, he warns aspirational young leaders: ‘There’s a fine line between fake it till you make it and learn it and do it well’

There’s much to be said about playing the part for the job you want, not the job you have—especially if you’re young and worried about appearing too youthful for a promotion or senior ranking. Brian Fenty would know. While the average Fortune 500 CEO is over 57 years old , he took TodayTix’s helm in 2017 at just 31.

Under his leadership, the theatre ticketing platform has partnered with Netflix for a live production of Stranger Things: The First Shadow , acquired Secret Cinema and Goldstar, and now reaches over 25 million users on the app.

Although Fenty says he initially struggled with being taken seriously by peers and investors because of his age, the now 38-year-old knew better than to pretend to be wise beyond his years as that had backfired in the past—and his experience offers a valuable leadership lesson for the young and aspirational.

“There’s a fine line between fake it till you make it and learn it and do it well,” he tells Fortune .

Looking back to earlier in his career at the private equity firm Hamilton Investment Partners, where he went on to become its youngest-ever managing director, Fenty recalls a time he was asked to do a task he had never heard of.

“I was asked to create a discounted cash flow, and I was too embarrassed to say, I don’t know what that is,” he says. Instead of getting advice from someone more experienced, Fenty pulled an all-nighter, called in friends at other firms, and attempted to teach himself the task. 

In the end, it left him exhausted and no closer to finishing the task at hand, which he says needed “real world application”. 

“I burned myself out and I let my team down by not asking for help,” he concluded, adding that the experience taught him an early lesson in playing to your strengths—not your weaknesses. 

“My secret weapon is I always bring helium to any situation—and that’s my codeword for optimism,” he adds. “I try always to bring a problem-solving lens: How do we turn this around? Is it worth turning around?”

Instead of getting hung up on what you can’t do, Fenty’s advice to young aspirational workers is simple: Surround yourself with people who fill your skills gaps and ask for help when you need it so that you can focus on excelling in the areas that you’re naturally already good at.

That’s why Fenty recommends that those who want to progress up the ladder quickly put their all into finding their “superpower.” 

“Exploit the hell out of that as early as you can,” he says. “And if you’re doing something that doesn’t exploit it, you’re wasting time.” 

“You can learn in any job,” he doubles down. “If you’re in a job where you’re learning things that don’t allow you to navigate the thing that makes you unique, then you’re going to waste a lot of time.”

Don’t sell yourself short 

Although Fenty doesn’t recommend lying to yourself (or others) about where your skills fall short, he does encourage giving it your best shot.

“Never telling myself I couldn’t do it,” he says, is the secret to why he’s done so well for his age, adding that he had a “vision” for his future himself and just went for it.

His advice for climbing the ladder echoes that of Pret A Manger’s CEO, Pano Christou. Like Fenty, Christou is one of few leaders to gain access to the C-suite over a decade earlier than the average leader (he became CEO at 40).

Now, Christou leads Britain’s biggest sandwich chain—and he echoed that he got to where he is today by saying yes to opportunities that he may not have been quite ready for, but believing in himself anyway. 

“Whenever new, bigger opportunities have been given to me I’ve always taken them— I’ve never said no —even if it really puts me out there,” he told Fortune . “I may have not been ready for a while, but I would always like to take it on and give it my best chance and it has worked out well.”

Likewise, Walmart’s CEO, Doug McMillon, scaled the retail giant’s ranks from unloading trailers for $6.50 an hour to becoming the company’s youngest CEO since its founder—he said he learned the ropes by stepping in for his boss frequently.

“One of the reasons that I got the opportunities that I got was that I would raise my hand when my boss was out of town and he or she was visiting stores or something,” he recently revealed.

The CEO added that he would even offer to step in for his boss in meetings—whether or not he was prepared to answer all the questions that came up. 

Plus, instead of brushing off queries above his pay grade and waiting for his manager’s return, he would proactively respond: “I don’t know, but I’ll find out fast and get back to you.”

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Chapter 6, Lesson 5: Problem-Solving Investigation: Look for a Pattern

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Chapter 9, Lesson 6: Problem-Solving Investigation: Act It Out

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