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Problem Solving

Problem Solving and the New Curriculum   Age 5 to 11

Developing a Classroom Culture That Supports a Problem-solving Approach to Mathematics   Age 5 to 11

Developing Excellence in Problem Solving with Young Learners   Age 5 to 11

Using NRICH Tasks to Develop Key Problem-solving Skills   Age 5 to 11

Trial and Improvement at KS1   Age 5 to 7

Trial and Improvement at KS2   Age 7 to 11

Working Systematically - Primary Teachers   Age 5 to 11

Number Patterns   Age 5 to 11

Working Backwards at KS1   Age 5 to 7

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Reasoning   Age 5 to 11

Visualising at KS1 - Primary Teachers   Age 5 to 7

Visualising at KS2 - Primary Teachers   Age 7 to 11

Conjecturing and Generalising at KS1 - Primary Teachers   Age 5 to 7

Conjecturing and Generalising at KS2 - Primary Teachers   Age 7 to 11

• Mathematical Problem Solving in the Early Years
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Statistics and Data Handling

Build confidence working with statistics and data handling from an early age with these lesson plans packs for KS1 and KS2. The colourful slides bring data to life, and the varied activities include opportunities for children to develop their reasoning and problem-solving skills as they tackle gathering, presenting and understanding data.

Let’s Make A Pictogram

Teach your class what pictograms are, how to construct them and how to interpret them through a variety of fun themes with these engaging lessons. ...

Let’s explore charts and tables

Explore tally charts, tables, pictograms and block diagrams in this scheme of work for Year 2. Your class will input given data into tables and cha...

Let’s Make Charts

Introduce your class to drawing and interpreting many-to-one pictograms and block diagrams in this complete set of statistics lessons designed for ...

Organising Data

Explore how to capture, present and interpret data using tally charts and bar charts in this series of five lessons for Year 3 children. Teaching 7...

Collecting and Sorting Data

Challenge children to work collaboratively to plan and carry out a survey using tally charts or questionnaires. These five lessons clearly explain ...

Data Handling

This 'Data Handling' scheme of work for Year 4 is a great way to teach your class how to collect, present and organise various types of data throug...

Presenting Data

In these complete lessons for Year 4, children will read and interpret data presented in a variety of ways, and generate their own questions which ...

Handling Data

Move beyond the mechanics of making bar charts and line graphs, and focus on how they can be used to make meaning from sets of data, how they can s...

Graphs and Diagrams

Teach children to read, interpret and create line graphs – and use the information presented in line graphs to solve a variety of comparison, sum a...

Calendars, Timetables and Calculators

This 'Calendars, Timetables and Calculators' Year 5 scheme of work is perfect for reinforcing their knowledge and understanding of time, how differ...

Describing Data

This Year 5 data handling scheme of work focuses on the use of graphs to describe the data they present. The children will look in detail at how in...

Solving Data Problems

Get technical with your class as they learn how to read, interpret and construct a variety of charts and graphs. This ‘Solving Data Problems’ schem...

Mean, Mode and Median

Teach your class to be dynamic data handlers! These lessons build on your children’s growing knowledge of charts, graphs and interpreting data by r...

Charts and Graphs

Revisit, and build upon, the skills required to read and interpret line graphs and pie charts. Building on those skills, teach children to produce ...

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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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Reasoning and Problem Solving Questions Collection - KS1 and KS2

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

10 March 2023

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These booklets each contain over 40 reasoning and problem solving questions suitable for KS1, KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS.

The answers are provided with some simple notes at the back of the booklet and for some problems supplementary questions and variation has been provided.

As always we welcome any feedback on the work we are doing and the materials that we are releasing. Thank you for taking an interest in our work. The White Rose Maths Hub Team

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A very good and engaging way to teach mastery of maths. Thank you for sharing

thank you for sharing, this is really good

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Problem Solving

 A selection of resources containing a wide range of open-ended tasks, practical tasks, investigations and real life problems, to support investigative work and problem solving in primary mathematics.

Problem Solving in Primary Maths - the Session

Quality Assured Category: Mathematics Publisher: Teachers TV

In this programme shows a group of four upper Key Stage Two children working on a challenging problem; looking at the interior and exterior angles of polygons and how they relate to the number of sides. The problem requires the children to listen to each other and to work together co-operatively. The two boys and two girls are closely observed as they consider how to tackle the problem, make mistakes, get stuck and arrive at the "eureka" moment. They organise the data they collect and are then able to spot patterns and relate them to the original problem to find a formula to work out the exterior angle of any polygon. At the end of the session the children report back to Mark, explaining how they arrived at the solution, an important part of the problem solving process.

In a  second video  two maths experts discuss some of the challenges of teaching problem solving. This includes how and at what stage to introduce problem solving strategies and the appropriate moment to intervene when children find tasks difficult. They also discuss how problem solving in the curriculum also helps to develop life skills.

Cards for Cubes: Problem Solving Activities for Young Children

Quality Assured Category: Mathematics Publisher: Claire Publications

This book provides a series of problem solving activities involving cubes. The tasks start simply and progress to more complicated activities so could be used for different ages within Key Stages One and Two depending on ability. The first task is a challenge to create a camel with 50 cubes that doesn't fall over. Different characters are introduced throughout the book and challenges set to create various animals, monsters and structures using different numbers of cubes. Problems are set to incorporate different areas of mathematical problem solving they are: using maths, number, algebra and measure.

Problem solving with EYFS, Key Stage One and Key Stage Two children

Quality Assured Category: Computing Publisher: Department for Education

These three resources, from the National Strategies, focus on solving problems.

  Logic problems and puzzles  identifies the strategies children may use and the learning approaches teachers can plan to teach problem solving. There are two lessons for each age group.

Finding all possibilities focuses on one particular strategy, finding all possibilities. Other resources that would enhance the problem solving process are listed, these include practical apparatus, the use of ICT and in particular Interactive Teaching Programs .

Finding rules and describing patterns focuses on problems that fall into the category 'patterns and relationships'. There are seven activities across the year groups. Each activity includes objectives, learning outcomes, resources, vocabulary and prior knowledge required. Each lesson is structured with a main teaching activity, drawing together and a plenary, including probing questions.

Primary mathematics classroom resources

Quality Assured Collection Category: Mathematics Publisher: Association of Teachers of Mathematics

This selection of 5 resources is a mixture of problem-solving tasks, open-ended tasks, games and puzzles designed to develop students' understanding and application of mathematics.

Thinking for Ourselves: These activities, from the Association of Teachers of Mathematics (ATM) publication 'Thinking for Ourselves’, provide a variety of contexts in which students are encouraged to think for themselves. Activity 1: In the bag – More or less requires students to record how many more or less cubes in total...

8 Days a Week: The resource consists of eight questions, one for each day of the week and one extra. The questions explore odd numbers, sequences, prime numbers, fractions, multiplication and division.

Number Picnic: The problems make ideal starter activities

Matchstick Problems: Contains two activities concentrating upon the process of counting and spotting patterns. Uses id eas about the properties of number and the use of knowledge and reasoning to work out the rules.

Colours: Use logic, thinking skills and organisational skills to decide which information is useful and which is irrelevant in order to find the solution.

GAIM Activities: Practical Problems

Quality Assured Category: Mathematics Publisher: Nelson Thornes

Designed for secondary learners, but could also be used to enrich the learning of upper primary children, looking for a challenge. These are open-ended tasks encourage children to apply and develop mathematical knowledge, skills and understanding and to integrate these in order to make decisions and draw conclusions.

Examples include:

*Every Second Counts - Using transport timetables, maps and knowledge of speeds to plan a route leading as far away from school as possible in one hour.

*Beach Guest House - Booking guests into appropriate rooms in a hotel.

*Cemetery Maths - Collecting relevant data from a visit to a local graveyard or a cemetery for testing a hypothesis.

*Design a Table - Involving diagrams, measurements, scale.

Go Further with Investigations

Quality Assured Category: Mathematics Publisher: Collins Educational

A collection of 40 investigations designed for use with the whole class or smaller groups. It is aimed at upper KS2 but some activities may be adapted for use with more able children in lower KS2. It covers different curriculum areas of mathematics.

Starting Investigations

The forty student investigations in this book are non-sequential and focus mainly on the mathematical topics of addition, subtraction, number, shape and colour patterns, and money.

The apparatus required for each investigation is given on the student sheets and generally include items such as dice, counters, number cards and rods. The sheets are written using as few words as possible in order to enable students to begin working with the minimum of reading.

NRICH Primary Activities

Explore the NRICH primary tasks which aim to enrich the mathematical experiences of all learners. Lots of whole class open ended investigations and problem solving tasks. These tasks really get children thinking!

Mathematical reasoning: activities for developing thinking skills

Quality Assured Category: Mathematics Publisher: SMILE

Problem Solving 2

Reasoning about numbers, with challenges and simplifications.

Quality Assured Category: Mathematics Publisher: Department for Education

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SevenRooms CEO Joel Montaniel Is Solving the Hospitality Industry’s Data Problem

Sevenrooms ceo joel montaniel speaks about how his crm company helps restaurants redefine their relationship with customers..

Joel Montaniel ’s SevenRooms is more than just another restaurant reservation system. “If you ask a restaurant, ‘What are your top 10, your top 25, and your top 50 customers?’ There are 15 million restaurants on the planet and 14.95 million of them can’t answer that question today,” Montaniel tells Observer. So, SevenRooms set out to solve that problem—by offering a suite of tools that empower restaurants and other types of hospitality operators to take full control and make the best use of their customer data. 

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“Basically what Shopify has been doing for retail is what we’re doing for restaurants,” Montaniel explained. “We help restaurants do three things: make money, build relationships with their customers, and then streamline their operations.” Montaniel, a former investment banker and real estate investor, founded SevenRooms in 2011 with his childhood friend Kinesh Patel and former Credit Suisse (CS) colleague Allison Page . Inspired by the   former Vanity Fair editor Graydon Carter ‘s “seven rooms theory,” the company aspires to create spaces where patrons feel at home, regardless of the venue’s exclusivity. From high-end establishments to smaller independent eateries, SevenRooms caters to a diverse range of hospitality operators, boasting an impressive clientele of more than 11,000 hospitality operators around the world.

Montaniel was named on Observer’s 2023 Nightlife + Dining Power List. We interviewed him earlier this month about SevenRooms’ founding story, his journey of finding the right business model, and the broader landscape of the hospitality industry amid high inflation and shifting consumer behavior. The following conversation has been edited for length and clarity.

Observer: How did you meet your co-founders and how did the idea of SevenRooms come about? 

Joel Montaniel: There are three of us. One of them, our CTO, Kinesh, I grew up with in Texas, so we’ve known each other since we were 10 years old. My other co-founder, Alison, and I met at our first jobs out of school—we were investment banking analysts and shared a cubicle wall.

At first, our idea was to solve a consumer problem and try to make it easier for consumers to go to these exclusive places. We launched a website in 2009 and it failed miserably. W hat we learned was that there actually was a bigger problem to solve. When we looked at the systems that hospitality operators were using, they didn’t have any customer data. So, we switched over from thinking about the consumer to thinking about the restaurant or the operator. We found that by solving that problem and giving them the technology that can help them understand their customers, that could then translate into an amazing customer experience, which is what we were trying to solve in the first place.

Before diving into the SevenRooms we know today, in retrospect, why do you think your original idea “failed miserably?”

I think we weren’t solving a real problem at that point in time, and I don’t think the world was ready for something like that. I remember talking to a restaurant and they told us point blank, “We sell dinner here, we don’t sell the right to have dinner.” 

We learned that we shouldn’t be solving things that we think are cool. We should work on things that actually create real value based on problems that we’ve experienced ourselves or problems that the industry talked to us about.

How would you describe SevenRooms’s core products and services? 

The way we think about ourselves is basically what Shopify is doing for retail is what we’re doing for restaurants. At the center is CRM—that is guest data. Then, there’s operations marketing, and commerce that sit on top of it. We work with restaurants, hotels and entertainment venues. We help them do three things: make money, build relationships with their customers, and streamline their operations.

What was the traditional approach to achieving those three objectives and what innovation and value does SevenRooms provide?

The traditional approach would have been to use a reservation system. In the U.S., that means using an OpenTable or a Resy system, for example. Those systems are really good at bringing customers in. But what hospitality operators haven’t really made as much investment in is the guest database and marketing tools. All of the guest information would be stored in their heads. 

If you ask a restaurant, “What are your top 10, your top 25, and your top 50 customers?” There are 15 million restaurants on the planet and 14.95 million of them can’t answer that question today, because restaurants don’t have the customer data, they’re not really doing retention marketing. 

On your website, it says the company’s name was inspired by the “seven rooms theory.” Can you explain what that is and why it’s a fitting name for your company?

We believe technology is more than just transactional, and so we wanted to find a name that is about helping companies build relationships with people. W e stumbled across this theory by the former Vanity Fair editor Graydon Carter called “the seven rooms theory.” It says that, in New York, there are seven interconnected rooms, each one more exclusive than the one before it. It suggests that when you think you’re at the top spot and the best place, there’s always another room that you don’t have access to that you haven’t discovered yet.

It hit the nail on the head for us where, you know, the seventh room is not about exclusivity; it’s about the place you go to where you feel most at home. For one of us, it might be a coffee shop, and for another one of us, it might be a bar. That captures the essence of what we want to do, which is we’re in business to help restaurants and hospitality operators make their guests feel at home. 

What types of hospitality operators does SevenRooms work with?

At the very beginning, we were working with more higher-end restaurants and nightclubs. These were places that want to make people feel special. One of the very first customers we had was Tao Group Hospitality in New York. Another really early customer was LDV Hospitality, which owns Scarpetta and other places. They were super helpful in helping us understand the technology and what customer information mattered.

But today, we are in every size and dollar amount. We have over 11,000 restaurants using the platform.  We power 80 percent of Las Vegas today, so all of MGM, Wynn, Cosmo and Venetian. We have everything from big hotel groups like Marriott to small, independent restaurants. And we have everything from inexpensive to $200-plus per person. As an example, 40 percent of our customers are under $50 per person and 9 percent are under $25. 

Covid-19 and high inflation for the past two years have changed consumer behavior in many ways. What are some of the emerging trends you’ve observed in hospitality?

Hospitality has been resilient overall. Sales are roughly flat, but they’re not going down. People are going out a little bit more, but they’re spending a little bit less.

We will continue to see that trend, which I think is largely driven by an older demographic that has a lot of disposable income. They’re spending money on travel and they’re going out to eat. Then you have a younger generation that is all about the experiences, all about Instagram and TikTok. The reason I think restaurants are really taking off is that they’re the new kind of social currency, and people are posting about food, restaurants and even dinner reservations on social media. I’m finding that food and experiences are central to both the younger generation and the older generation. 

• SEE ALSO : FCC Chair Jessica Rosenworcel Supports TikTok Ban, Calls Lack of Oversight ‘Stunning’

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