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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 scenarios ks2

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.

problem solving scenarios ks2

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.

problem solving scenarios ks2

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.

problem solving scenarios ks2

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.

problem solving scenarios ks2

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 scenarios ks2

Problem Solving 2

Reasoning about numbers, with challenges and simplifications.

Quality Assured Category: Mathematics Publisher: Department for Education

Cambridge University Faculty of Mathematics

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Mathematical mindsets
  • Cross-curricular contexts
  • Physical and digital manipulatives

For younger learners

  • Early Years Foundation Stage

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics

Developing Mathematical Thinking - Primary Teachers

Successful mathematicians  understand curriculum concepts, are fluent in mathematical procedures, can solve problems, explain and justify their thinking, and have a positive attitude towards learning mathematics. 

Exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, convincing, proving... are all at the heart of mathematical thinking. The activities below are designed to give learners the opportunity to think and work as mathematicians.

For problems arranged by curriculum topic, see our  Primary Curriculum  page For problems arranged by mathematical mindsets, see our  Mathematical Mindsets  page

problem solving scenarios ks2

Conjecturing and Generalising at KS2

These tasks will encourage children to conjecture and generalise.

problem solving scenarios ks2

Reasoning and Convincing at KS2

The tasks in this collection can be used to encourage children to convince others of their reasoning, by first convincing themselves, then a friend, then a 'sceptic'.

problem solving scenarios ks2

Conjecturing and Generalising at KS1

problem solving scenarios ks2

Reasoning and Convincing at KS1

The tasks in this collection can be used to encourage children to convince others of their reasoning, using 'because' statements.

problem solving scenarios ks2

Working Systematically at KS1

These problems will challenge your learners to work systematically.

problem solving scenarios ks2

Working Systematically at KS2

problem solving scenarios ks2

Trial and Improvement at KS1

These lower primary tasks could all be tackled using a trial and improvement approach.

problem solving scenarios ks2

Trial and Improvement at KS2

These upper primary tasks could all be tackled using a trial and improvement approach.

problem solving scenarios ks2

Working Backwards at KS1

The lower primary tasks in this collection could each be solved by working backwards.

problem solving scenarios ks2

Working Backwards at KS2

The upper primary tasks in this collection could each be solved by working backwards.

problem solving scenarios ks2

Visualising at KS1

These lower primary tasks all specifically draw on the use of visualising.

problem solving scenarios ks2

Visualising at KS2

These upper primary tasks all specifically draw on the use of visualising.

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Developing Critical Thinking Skills At KS2 Using Same Surface Different Depth Problems: How I Wish I’d Taught Maths (5)

Clare sealy.

Clare Sealy looks at the struggles primary school pupils can have when implementing critical thinking skills when subject knowledge is lacking, and the effect this can have on their attempts at problem solving activities in KS2.

This article is part of a series published to help primary school teachers and leaders implement some of the insights and teaching techniques derived from Craig Barton’s bestselling book How I Wish I’d Taught Maths . Links to the other 5 articles appear at the end.

In the introduction to this series, I outlined how Craig Barton, in his book How I wish I’d taught maths,  described how he had changed his teaching as the result of reading research around learning and memory , in particular cognitive load theory in the classroom . In the latter part of his book, the focus turns to helping pupils use what they know.

Whatever the age of the children we teach, many find it hard to transfer what they know how to do in one context to another. This is most evident when it comes to maths problem solving , or in the SATs reasoning papers. They know the maths, they just can’t work out which bit of maths they need in this specific circumstance.

What are critical thinking skills?

At the basic level, critical thinking is the ability to analyse facts presented to us to form a judgement about a topic. It is an incredibly important skill to have at higher education and beyond, and is one of the key factors in astute decision making. 

Most of us explicitly encounter critical thinking and other higher order thinking skills such as metacognition in the classroom at either GCSE or A-Level, but laying their foundations at primary school is becoming more and more common and valued. 

However, “critical thinking and the ability to solve problems is not a generic skill that can be taught and that children can transfer from one problem to another. While there are some metacognitive strategies that can help a bit, what is really crucial is having a very secure understanding of the actual maths – the domain specific knowledge – that lies at the heart of the problem.” Daniel Willingham (2006)

Critical thinking (as well as scientific thinking and other domain-based types of thinking) is not a skill. There is not a set of critical thinking skills that can be acquired and deployed regardless of context. There are, however, metacognitive strategies that (once learned) make the critical thinking process more likely, and make up a key part of many quality first teaching methods .

The ability to think critically (to actually do what the metacognitive strategies call for) depends on domain knowledge and practice. For teachers, the situation is not hopeless, but no one should underestimate the difficulty of teaching pupils to think critically.

This said, metacognition is an incredibly valuable skill for pupils to have for any number of reasons, from helping low-ability students catch up to their peers to helping the whole class minimise the impact of the summer slide .

The metacognitive strategies mentioned involve reflecting on what you are doing during problem solving activities in KS2, asking yourself questions such as:

‘What am I doing?’

‘Why am I doing this?’

‘How does it help me?’

This is all very well if you have secure domain knowledge and can answer these questions. However, if you lack this knowledge, the questions are just frustrating.

Crib Sheet for How I Wish I'd Taught Primary Maths

Download the key findings from research; share with your staff, your SLT, and at your next job interview!

How to help your pupils develop critical thinking skills for problem solving activities throughout KS2

There are of course  problem solving strategies  we can give pupils to help them become better critical thinkers. For example, underlining the important words. However, this relies on pupils understanding what the important word are in the first place.

Often, irrelevant surface features seem important to pupils whereas we experts can see they are completely irrelevant, because our domain knowledge and experience of answering many, many questions means we can spot the deep underlying structure a mile off.

It’s the same with other strategies such as setting work out systematically (you have to know what system is likely to be helpful), working backwards (you have to know whether this is likely to be useful in this situation) or even using a bar model. Bar models can be so helpful, but you have to know whether or not this kind of question is suitable for the bar model treatment.

‘Same surface, different deep’ or SSDD Problems

Problem solving maths questions usually have an arbitrary surface structure and a deep structure. The surface structure involves the context in which the problem is set and has nothing to do with the actual maths; for example, in a question about buying tickets to a funfair, the funfair and ticket are part of the surface structure.

They are but the wrapper in which the real maths is wrapped. Pupils can get fixated on this ‘wrapper’, rather than the underlying deep mathematical structure held within it.

I recall a SATs question about paving inside a greenhouse. The child thought that they couldn’t do it because they didn’t know what a greenhouse was! Whereas I immediately knew that this was going to be an area question. The surface structure was transparent to me whereas, it was thoroughly opaque to the pupil.

All the underlining, systematic working or bar modelling in the world wouldn’t get past this erroneous latching onto surface features.

How to get past the surface features 

To overcome this hurdle, Craig recommends teaching children to recognise the deep structure of maths problems and how to identify and then disregard surface features.

It should go without saying that children need to be thoroughly secure in the underlying maths before attempting problem solving.

Problem Solving Activities KS2 Quote

It is a mistake to think that maths problem solving is a good way of consolidating learning, let alone using it in the initial knowledge acquisition phase. Problem solving is about transferring learning from one context to another.

SATs problem solving question from Third Space Learning

Problem solving at KS2 is about using your critical thinking skills to generalise

It therefore comes at the end of learning to do something, not mid- way and definitely not at the beginning.

But what is more, if at the end of a unit on, say division, we give children a load of division problems, this will not help them work out what the deep structure is. They already know; it’s division! This is fine, but it won’t help children learn to decide whether or not a particular problem requires division or not.

As well as problem solving activities at the end of units, teachers also need to allocate separate times where children have to work out what the deep structure of a problem actually is, regardless of surface features.  

This means setting a range of SSDD problems sharing the same surface features – for example a shopping problem involving apples and pears – but which each have a different deep structure .

Read more: KS2 Problem Solving and KS3 Maths Problem Solving

Translating this to a primary school context.

Let’s return to the question about stickers from the 2017 KS2 SATs paper we considered when considering goal free problems:

thinking skills problem solving activities ks2

The surface feature here is stickers.

As experts, we know straightaway that we could substitute packs of stickers with boxes of apples or packets of balloons or even a family ticket to the cinema.

In fact, in a variation of Craig’s SSDD technique for a primary context, I’d suggest also doing DSSD problems (different surface, same deep) problems too, asking children to cross out the words ‘pack of stickers’ and replace with suitable alternative, and then repeat the problem to understand that the surface features do not change the underlying maths at all.

KS2 Problem Solving Activities in Maths

Then I’d suggest moving on to SSDD problems, with appropriate differentiation in the classroom . Let’s stick with stickers as our ‘same surface’.  

The deep structure of our original question involved knowing that you had to multiply to find the price of 12 separate stickers and then subtracting to find the difference. But we could ask mathematically different questions while keeping the context and visual look of the problem the same.

For example:

Example of a problem solving activity for KS2 using thinking skills

  • How much does one sticker cost? (though I’d adapt the price so the division came out as a whole number of pence)
  • Stickers are 8cm wide and 6cm high. Ally sticks 3 stickers in a row, without any gaps. What is the perimeter of the shape she has now made?
  • Ally buys 7 packs of stickers a month, Jack buys 3 packs of stickers a month and Chen buys 5 packets a month. What is the average number of packets bought by the 3 children in one month?
  • Ally buys a pack of 12 stickers. She has spent 15% of her birthday money. How much birthday money has Ally got left? (again, I would adjust the price into something more workable)

Another great way to translate problem solving into a primary context is through topical maths investigations.

Extension ideas for problem solving activities in KS2

Extending both ideas, we could make a grid where the rows contained questions with a different surface structure and the columns contained questions with the same deep structure. This grid could be cut into individual boxes with pupils having to sort each box accordingly, to reconstruct the grid.

KS2 Problem Solving Activities Grid

Tigers, Cake or Money? A unique approach to critical thinking

One questioning in the classroom strategy for helping children understand the deep structure of division problems, is to ask children if this is a tiger, cake or money sort of division question.

What this means is, could we swap the surface features of the problem we are given to one involving tigers, or cake or money?

Why these three I hear you ask?

This is because, where division problems do not divide exactly, it is really useful to:

  • Be able to decide if you need to round up or down (These are the tiger questions. If you haven’t got enough cages for your tigers you might get eaten)
  • Have a remainder that’s a fraction (These are the cake questions as we can each have 1 and a half cakes)
  • Or have a remainder expressed as a decimal (These are the money questions as we can have £2.47 each)

An example of a Tiger question

thinking skills Tiger Question as a problem solving activity for KS2

This is a great example of a tiger question. With 4 spare tigers, you need to have an extra box! Having 2/3 of a box wouldn’t work, neither would having 0.666 of a box. Rewriting this as a tiger question helps understand the deep structure.

A cage holds 6 tigers

How many cages are needed to hold 52 tigers?

How to make a trickier Tiger question

Here is a slightly harder ‘tiger’ problem:

thinking skills Tiger Problem for KS2 Problem Solving Activities

Let’s rewrite this:

A zookeeper has 7,600 tigers (!)

Cages can contain 500 tigers.

How many cages does the zookeeper need?

The answer:

15.2 cages is obviously not enough to stop the keeper from being eaten.

Answers requiring a decimal answer are usually money questions already, or calculations rather than word problems. Hence they are easy to categorise.

Some children find ‘tiger’ type questions particularly hard, and give answers that don’t make sense because they haven’t rounded up or down. So in the brick example above, they give the answer as 15.2 because they haven’t recognised that doesn’t make sense.

By naming certain deep structures, children are more able to identify them when they arise, and this is a fantastic way to help children with problem solving activities throughout KS2.

Sources of Inspiration

  • Willingham, D.T. (2006) ‘How knowledge helps: it speeds and strengthens reading comprehension, learning and thinking’. American Educator 30 (1) p.30

This is the fifth blog in a series of 6 adapting the book How I Wish I’d Taught Maths for a primary audience. Some have already been mentioned in this post, but if you wish to read the remaining blogs in the series, check them out below:

  • Direct Instruction: How I Wish I’d Taught Maths (2)
  • Deliberate Practice In Education: How I Wish I’d Taught Maths (4)
  • How Retrieval Practice Helps Long-Term Maths Skills: How I Wish I’d Taught Maths (6)

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to address learning gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more 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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All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

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Play of the Wild

Education is an admirable thing, but it is well to remember from time to time that nothing that is worth knowing can be taught. -Oscar Wilde

problem solving scenarios ks2

Outdoor Problem Solving Activities KS2- Learning Maths

aerial view of farmland

Outdoor Problem Solving Activities KS2 – Learning Maths Outdoors

These are some ideas for outdoor problem solving activities for KS2 to help children with learning maths outdoors. One of the most critical aspects of teaching and learning maths is to be able to solve problems. While teaching maths in school, I found that it can become easy to get overly focused on teaching the rules and procedures for doing maths. These are essential tools that everyone needs, but the actual point is to be able to apply those skills in real life. Therefore, children must be given opportunities to practice problem-solving and make it purposeful.

I hope you find these outdoor problem solving activities for KS2 useful, and perhaps they will also inspire you to try other ideas. If you would like some other ways to take learning maths outdoors, you may also want to see my post, Outdoor Maths Activities KS2 .

Nim is a mathematical strategy game where two players take turns removing objects from a pile. Each player must take at least one object per turn. The goal is to either take or avoid taking the last item from the stack. Children can play nim with a pile of sticks or rocks.

Ordering natural objects by different features

Children can place in order objects such as rocks or pinecones based on the characteristic(s) they decide upon. It might be longest to shortest, least to the greatest circumference or smallest to greatest volume.

Outdoor Maths Activities KS2 – Teaching Maths Outside. Measure and displacement. Finding the difference.

Observing the sun & moon

Children can explore and investigate the sun and moon, including changes that take place over time. They can try to figure out some of the following questions, and ask some of their own questions as well.

  • What time does the sun set and rise? Does this ever change? How do you know?
  • Where on the horizon do you first/last see the sun or the moon? Does this change? How do you know?
  • Can you observe the phases of the moon- how does it change? Are there any patterns that you notice?

photography of body of water and mountains

Measuring circles

Children can measure circles (such as flower pots, tree stumps or other circular objects found outside). They can measure the circumference, radius and diameter and then investigate the relationship between radius/diameter and circumference. What do children notice? Is there a pattern? They may even be able to ‘discover’ pi.

How tall is a tree?

Measure / calculate the height of a tree with the shadow & calculation method, triangle method and/or clinometer method.  If children try more than one method, do they get the same results?  Which method might be more accurate?

green leafed tree

(ex. Estimating by height, clinometer method, looking through legs method, pencil method, meter stick method)

Different ways children can help with planning in a garden

Children can figure out how much space is available in the garden and how many different types of plants can be planted. Can they figure out how many of one kind of plant will fit into one planter box? Can they figure out how many different sized plants fit into the same planter box? Children would need to use their measuring skills to calculate the surface area of the garden. Then they would need to find out how much space each plant requires (e.g. from seed packets) and then determine how many and which of the plants can be used.

growing broccoli with children. How to make a vegetable garden for kids.

If a new planter box is purchased, children can help work out how many bags of compost would be needed to fill it. (They would need to measure, calculate the size, etc.) Will there be any leftover soil from one of the bags? How do you know?

If children grow crops such as pumpkins, they can do things like ordering them from heaviest to lightest. This way they might see which is the ‘prize-winning pumpkin’ in a harvest festival.

Outdoor Problem Solving Activities KS2 – Learning Maths Outdoors. pumpkins by size

They might also consider how much each pumpkin could be sold for.  This would involve calculating each pumpkin’s cost, based on a price of £1.00 per kilo, £2.00 per kilo (or whatever reasonable price is determined). They might also try to figure out if larger pumpkins (or other crops like corn) always weigh more than smaller ones? *The children will have to define what is the larger, longer, or wider circumference.

Children could get involved with selling the crops they grow.  This will give them plenty of opportunities to use mathematical skills and handle money in real-life contexts. They will also need to plan the pricing of different vegetables based on weight, the number of vegetables, or selling them in combinations. Children could even try to figure out the appropriate amount to charge for each crop based on the cost of the seeds, the growing time, grocery store costs or any other factors.

vegetable stand. Outdoor Problem Solving Activities KS2 – Learning Maths Outdoors

If they do sell some of what they grow after school or possibly at a market, then the children can apply their maths skills to figure out how much each customer will need to pay when buying any particular fruit or vegetable.  

Monitoring Plant Growth

See if children can figure out how quickly different plants grow. Can they determine the rate of growth (e.g. mm per week)? Which seedlings / plants grow fastest? Is it a steady rate of growth, or does it change?

*To take this further, children might also conduct an experiment to compare different groups. They might compare the growth or the growth rate of plants whose seeds have been frozen vs those that have not, or something else.  

Making Shapes

How many shapes can you make (including shapes within shapes) using a set number of sticks (ex. 6 large sticks and 6 small sticks)? Is there a way to make more or fewer shapes using the same number of sticks?

Outdoor Problem Solving Activities KS2 – Learning Maths Outdoors

Planning and holding a bake sale

(Some parts of this activity take place inside and some outside. This activity can be linked further to learning maths outdoors if children use some ingredients grown from a school garden).

Baking for a bake sale is a great way to give children hands-on practice solving problems in real contexts. For a baking project they will need to follow recipes and accurately use measuring cups and weighing scales. They might also want to make larger quantities and scale up recipes by doubling, tripling, or quadrupling them. The children will need to plan ahead and calculate how much of each ingredient they need to buy to make a set number of cookies, cupcakes, etc. They must also determine how many batches would be needed to make 200 cupcakes if the recipe makes 2 dozen.

Then when they hold an actual sale they will be using their maths skills to calculate how much to charge people.  They must also learn how to give people the proper change (just like selling vegetables above). They can setup a stall outside of school and sell them after school one day. 

cute black girl showing homemade gingerbread man

Organizing and running a track & field event

Children can get involved in organizing a sports day or track and field event. They can first decide which events to include and then figure out how much space is needed for each activity (e.g. measuring the appropriate length and width required). The children can then help measure and set up the activities.

Once races are held, that data can be used to make calculations. For example – for a jumping event, children can measure how far people jump, and after several tries, figure out if there is improvement and how much (finding the difference). Children can time how far it takes them to run certain distances, e.g. 500 meters versus ½ a mile. They can figure out how fast they are running. They might then calculate how fast they ran different races (e.g. miles per hour) and then figure out when they ran faster or slower.  

fit athlete during training on running track

Finding ways to approximate measurements

See if children can find different ways to measure the approximate distance between two far points with a meter stick and string. This might be the length of the playground or the distance between two trees, etc. Children might compare different ways of measuring the approximate distance such as measuring the length it takes them to take one step and then counting the number of steps between two points. They might also use the string to go between the two points and measure the string’s length. See if they can find any other ways to find the approximate distances.

I hope that you find these outdoor problem solving activities for KS2 helpful and it helps you take teaching and learning maths outdoors!

Arithmetic , Gardening , Geometry , Maths , Measurement , Number & Place Value , School Age , Sticks

hands-on learning , Learning Outdoors , learning outside , outdoor learning , Sticks

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Maths Problem Solving Booklets

Maths Problem Solving Booklets

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Paul Tyler

Last updated

23 August 2022

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pdf, 424.8 KB

Maths problem solving booklets covering a wide range of mathematical problems designed to improve problem solving strategies as well as numeracy and mathematical ability.

Designed to be printed as A5 booklets.

Disclaimer: These are free because the problems are from a wide variety of sources, most of which I have forgotten. I am a maths problem magpie and collect maths problems wherever I find them. All I have done is bundled these ones up to make it convienent.

If you find a problem that is yours and you don’t want it used please comment and I’ll remove it - cheers.

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Very impresses. Ta.

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Excellent resource

Great resource to use at KS3

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Just what I have been looking for. Thanks so much!

Good resources. Thanks you!

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problem solving scenarios ks2

Connect 4 Factors

Playing solo: The player must fill the grid with the counters from both boxes. They must avoid lining up four numbers with a common factor (other than one).

Playing duo: Each player has a box of counters to choose from. Take it in turns to drop a counter into the game board. The winner is the first to line up four numbers with a common factor (other than one).

problem solving scenarios ks2

There are nine squares shown. The squares have side lengths of   1 ,  4 ,  7 ,  8 ,  9 ,  10 ,  14 ,  15  and  18  cm. They can be fitted together with no gaps and no overlaps to form a rectangle. How?

problem solving scenarios ks2

Factors and Multiples

The aim of the game is to try and make the longest chain possible by connecting factors and multiples.

problem solving scenarios ks2

Thinking Skills

In this activity your children will be working on capacity. They must create a given amount in one of the containers in the least amount of moves. Sounds simple eh?

The game has different levels to complete and will really get your children thinking.

Super for outside the box thinking.

problem solving scenarios ks2

Puppies Puzzle

The puppies need to go to sleep. There needs to be an even amount of puppies in each basket to make this happen. How many ways can they be sorted?

problem solving scenarios ks2

Broken Calculator

This is a great activity that encourage the children to use limited numbers and functions to make totals.

The children can progress through the levels to challenge themselves even further.

problem solving scenarios ks2

Pets Puzzle

Can you solve the Pet shop Puzzle? Mr Jones sells two kinds of animals and there are 44 animal legs in the shop. Over half of the pets are puppies. How many puppies and budgies are there in the pet shop?

problem solving scenarios ks2

River Puzzle

How can you safely bring the goat, wolf and cabbage  across the river?

problem solving scenarios ks2

The sum of each side of the triangle should equal the number in the centre of the triangular shape.

problem solving scenarios ks2

The first player to make a square on the grid wins. Encourage your children to think about developing winning strategies and movement patterns.

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problem solving scenarios ks2

30 Problem Solving Scenarios for Speech Therapy Practice

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SEE ALSO: Houston We Have a Problem! Activities for Problem Solving

Problem solving scenarios.

  • Your friends came over to your house for a movie night. One of your friends brought another friend so there are more people than you planned for. You want to pass out the drinks but you only have five cans of soda and you need 6 for everyone to have one. What could you do?
  • After basketball practice you go back to the locker room with your team to shower and change. When you are done dressing, you can't find your shoes. What could you do?
  • You have been waiting all day for lunch to come because you are starving. Finally class gets over and you get to go to lunch. Except when you go to get to your lunch, it's not there. You probably left it at home. What could you do?
  • There is a guy in your class who is always mean to you. He always bumps you when he walks by and he calls you names. He knocks stuff out of your hands and makes you feel stupid. You don't think you can take it anymore. What could you do?
  • You really want to invite this new girl/guy to come to your birthday party, but you have never talked to them before. You are worried they will say no. What could you do?
  • You rode the bus to school today and on the way in people are pointing and laughing at you. You go in the bathroom and see that you have pink gum all over the back of your pants. What could you do?
  • You wake up and see that your alarm never went off. So you are starting your morning 15 minutes later than you planned. It is a really important day at school and you cannot be late. What could you do?
  • You are giving a group presentation in front of class and it's your turn to talk. All of the sudden you sneeze. You cover it with your hand, but now your hand is full of stuff you sneezed out. What could you do?
  • You are eating dinner at a fancy restaurant with your parents and their friends. You have a really messy dinner and accidentally flip a noodle into the lady's lap. They are busy talking and don't notice it. What could you do?
  • You are taking a test and there is no talking allowed. You are writing your answers on the paper and your pencil breaks. What could you do?
  • You are taking a test and the guy behind you asks you for help. He wants to know what you put for question number two. What could you do?
  • You are at a birthday party and you have waited in line for a long time for your turn to hit the pinata. It is finally going to be your turn and it looks like the next hit will break the pinata. But you suddenly have to go to the bathroom. What could you do?
  • You are hanging outside with your friend and she decides to pick your neighbor's flowers. She gives you the pretty handful of flowers and right then your neighbor opens the door. She asks you why you picked her flowers. What could you do?
  • You borrowed your sister's skates one day without asking and they broke while you were using them. What could you do?
  • You are eating at a friend's house and the mom piles your plate full of food. It looks really good and you want to eat it all but you can't because you just ate a snack. What could you do so you don't hurt her feelings?

SEE ALSO:   The Best Free App for Speech Therapy

problem solving scenarios ks2

  • Your teacher was working at her desk.  You wanted to ask her a question, but she didn't see your hand raised. What should you do?
  • You started to do your work, but you weren't sure if you were doing it right. What should you do?
  • You were playing tether-ball and were the champion so far.  In the next game, you slightly touched the rope.  Only one student saw you touch the rope. What will you do?
  • The teacher is giving directions, but your friend sitting next to you keeps talking.  You can't hear the directions. What should you do?
  • You didn't do your homework.  Your teacher was upset with you. What should you do?
  • You finished eating and felt a burp coming. What are you going to do?
  • You were waiting to swing.  When it was your turn, another boy jumped in front of you and took the swing. What would you do?
  • You waited a long time, but your mom didn't come to pick you up after school. What should you do?
  • A bully threatened to beat you up after school. What should you do?
  • A boy on the playground keeps pushing you and making you mad. What would you do?
  • You were sitting in class doing your work and you hear the fire alarm. What should you do?
  • An adult you didn't know came on to the playground and asked if you would help look for his lost dog. What would you do?
  • You forgot your lunch at home. What would you do?
  • The person sitting behind you keeps tapping your chair with his foot. What should you do?
  • You finished your work early. What should you do?

This list of functional words was professionally selected to be the most useful for a child or adult who has difficulty with problem solving scenarios.

We encourage you to use this list when practicing at home.

Home practice will make progress toward meeting individual language goals much faster.

Speech-Language Pathologists (SLPs) are only able to see students/clients 30-60 mins (or less) per week. This is not enough time or practice for someone to handle Problem solving scenarios.

Every day that your loved one goes without practice it becomes more difficult to help them. 

SEE ALSO:   The Best Books for Speech Therapy Practice

Speech therapy books for targeting multiple goals

We know life is busy , but if you're reading this you're probably someone who cares about helping their loved one as much as you can.

Practice 5-10 minutes whenever you can, but try to do it on a consistent basis (daily).

Please, please, please use this list to practice.

It will be a great benefit to you and your loved one's progress.

problem solving scenarios ks2

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Read our research on: Immigration & Migration | Podcasts | Election 2024

Regions & Countries

How americans view the situation at the u.s.-mexico border, its causes and consequences, 80% say the u.s. government is doing a bad job handling the migrant influx.

problem solving scenarios ks2

Pew Research Center conducted this study to understand the public’s views about the large number of migrants seeking to enter the U.S. at the border with Mexico. For this analysis, we surveyed 5,140 adults from Jan. 16-21, 2024. Everyone who took part in this survey is a member of the Center’s American Trends Panel (ATP), an online survey panel that is recruited through national, random sampling of residential addresses. This way nearly all U.S. adults have a chance of selection. The survey is weighted to be representative of the U.S. adult population by gender, race, ethnicity, partisan affiliation, education and other categories. Read more about the ATP’s methodology .

Here are the questions used for the report and its methodology .

The growing number of migrants seeking entry into the United States at its border with Mexico has strained government resources, divided Congress and emerged as a contentious issue in the 2024 presidential campaign .

Chart shows Why do Americans think there is an influx of migrants to the United States?

Americans overwhelmingly fault the government for how it has handled the migrant situation. Beyond that, however, there are deep differences – over why the migrants are coming to the U.S., proposals for addressing the situation, and even whether it should be described as a “crisis.”

Factors behind the migrant influx

Economic factors – either poor conditions in migrants’ home countries or better economic opportunities in the United States – are widely viewed as major reasons for the migrant influx.

About seven-in-ten Americans (71%), including majorities in both parties, cite better economic opportunities in the U.S. as a major reason.

There are wider partisan differences over other factors.

About two-thirds of Americans (65%) say violence in migrants’ home countries is a major reason for why a large number of immigrants have come to the border.

Democrats and Democratic-leaning independents are 30 percentage points more likely than Republicans and Republican leaners to cite this as a major reason (79% vs. 49%).

By contrast, 76% of Republicans say the belief that U.S. immigration policies will make it easy to stay in the country once they arrive is a major factor. About half as many Democrats (39%) say the same.

For more on Americans’ views of these and other reasons, visit Chapter 2.

How serious is the situation at the border?

A sizable majority of Americans (78%) say the large number of migrants seeking to enter this country at the U.S.-Mexico border is eithera crisis (45%) or a major problem (32%), according to the Pew Research Center survey, conducted Jan. 16-21, 2024, among 5,140 adults.

Related: Migrant encounters at the U.S.-Mexico border hit a record high at the end of 2023 .

Chart shows Border situation viewed as a ‘crisis’ by most Republicans; Democrats are more likely to call it a ‘problem’

  • Republicans are much more likely than Democrats to describe the situation as a “crisis”: 70% of Republicans say this, compared with just 22% of Democrats.
  • Democrats mostly view the situation as a major problem (44%) or minor problem (26%) for the U.S. Very few Democrats (7%) say it is not a problem.

In an open-ended question , respondents voice their concerns about the migrant influx. They point to numerous issues, including worries about how the migrants are cared for and general problems with the immigration system.

Yet two concerns come up most frequently:

  • 22% point to the economic burdens associated with the migrant influx, including the strains migrants place on social services and other government resources.
  • 22% also cite security concerns. Many of these responses focus on crime (10%), terrorism (10%) and drugs (3%).

When asked specifically about the impact of the migrant influx on crime in the United States, a majority of Americans (57%) say the large number of migrants seeking to enter the country leads to more crime. Fewer (39%) say this does not have much of an impact on crime in this country.

Republicans (85%) overwhelmingly say the migrant surge leads to increased crime in the U.S. A far smaller share of Democrats (31%) say the same; 63% of Democrats instead say it does not have much of an impact.

Government widely criticized for its handling of migrant influx

For the past several years, the federal government has gotten low ratings for its handling of the situation at the U.S.-Mexico border. (Note: The wording of this question has been modified modestly to reflect circumstances at the time).

Chart shows Only about a quarter of Democrats and even fewer Republicans say the government has done a good job dealing with large number of migrants at the border

However, the current ratings are extraordinarily low.

Just 18% say the U.S. government is doing a good job dealing with the large number of migrants at the border, while 80% say it is doing a bad job, including 45% who say it is doing a very bad job.

  • Republicans’ views are overwhelmingly negative (89% say it’s doing a bad job), as they have been since Joe Biden became president.
  • 73% of Democrats also give the government negative ratings, the highest share recorded during Biden’s presidency.

For more on Americans’ evaluations of the situation, visit Chapter 1 .

Which policies could improve the border situation?

There is no single policy proposal, among the nine included on the survey, that majorities of both Republicans and Democrats say would improve the situation at the U.S.-Mexico border. There are areas of relative agreement, however.

A 60% majority of Americans say that increasing the number of immigration judges and staff in order to make decisions on asylum more quickly would make the situation better. Only 11% say it would make things worse, while 14% think it would not make much difference.

Nearly as many (56%) say creating more opportunities for people to legally immigrate to the U.S. would make the situation better.

Chart shows Most Democrats and nearly half of Republicans say boosting resources for quicker decisions on asylum cases would improve situation at Mexico border

Majorities of Democrats say each of these proposals would make the border situation better.

Republicans are less positive than are Democrats; still, about 40% or more of Republicans say each would improve the situation, while far fewer say they would make things worse.

Opinions on other proposals are more polarized. For example, a 56% majority of Democrats say that adding resources to provide safe and sanitary conditions for migrants arriving in the U.S. would be a positive step forward.

Republicans not only are far less likely than Democrats to view this proposal positively, but far more say it would make the situation worse (43%) than better (17%).

Chart shows Wide partisan gaps in views of expanding border wall, providing ‘safe and sanitary conditions’ for migrants

Building or expanding a wall along the U.S.-Mexico border was among the most divisive policies of Donald Trump’s presidency. In 2019, 82% of Republicans favored expanding the border wall , compared with just 6% of Democrats.

Today, 72% of Republicans say substantially expanding the wall along the U.S. border with Mexico would make the situation better. Just 15% of Democrats concur, with most saying either it would not make much of a difference (47%) or it would make things worse (24%).

For more on Americans’ reactions to policy proposals, visit Chapter 3 .

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Say “Alexa, enable the Pew Research Center flash briefing”

Report Materials

Table of contents, fast facts on how greeks see migrants as greece-turkey border crisis deepens, americans’ immigration policy priorities: divisions between – and within – the two parties, from the archives: in ’60s, americans gave thumbs-up to immigration law that changed the nation, around the world, more say immigrants are a strength than a burden, latinos have become less likely to say there are too many immigrants in u.s., most popular.

About Pew Research Center Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of The Pew Charitable Trusts .

IMAGES

  1. Problem Solving Maths Activities KS2

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  2. How I Wish I'd Taught (Primary) Maths: Problem Solving at KS2

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  3. KS2 problem solving: book 1

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  4. KS2 Problem Solving Worksheets Pack (33 sets of differentiated

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  5. Problem Solving Scenarios (School) by MsJocelyn

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  6. Problem Solving Fun for KS2 by

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VIDEO

  1. PROBLEM (solving) CHILD

  2. Problem-Solving With My Elementary Students

  3. Problem solving 🔥🌋🏝️ #learning #shorts

  4. problem Solving Skills

  5. Mastering the Art of Risk Mitigation: Strategies for Success

  6. PMRF- NPTEL LIVE SESSION-1 (FUNDAMENTALS OF POWER ELECTRONICS)

COMMENTS

  1. Problem Solving

    Working Systematically at KS2 Age 7 to 11 Tasks for KS2 children which focus on working systematically. Number Patterns Age 5 to 11 The tasks in this collection encourage children to create, recognise, extend and explain number patterns. Working Backwards at KS1 Age 5 to 7

  2. KS2 Maths Investigations For Real Life Problem Solving

    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.

  3. Problem Solving

    ALL Teacher guidance 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.

  4. Problem Solving Games for Key Stage 2 children

    Free problem solving maths games for KS2 children.

  5. Maths Problem Solving KS2: Strategies & Resources

    Maths problem solving KS2 is crucial to succeeding in national assessments. If your Key Stage 2 pupils are still struggling with reasoning and problem solving in Maths, here are some problem solving strategies to try with your classes; all aligned to Ofsted's suggested primary school teaching strategies.

  6. Maths Problem-Solving for kids. KS2 Primary Resources

    Problem-solving key stage 2 primary resources for children. We have tons of maths problem-solving activities for kids, and resources available to help your key stage 2 students practice their problem-solving skills. There are lots of themed resources too. This includes things like sports-themed investigate puzzles, or code cracking problems.

  7. KS2 Problem Solving in Maths

    Our exciting KS2 teaching resources will help introduce your year 3, year 4, year 5, and year 6 students to problem-solving and reasoning topics. Be sure to take a look at our fun and engaging maths word problems, maths investigations, and maths games, which can all be used with the accompanying key stage 2 worksheets and activities. Our fun ...

  8. Problem solving

    KS2 Maths Problem solving learning resources for adults, children, parents and teachers.

  9. KS2 Maths Investigations

    Applying maths problems to real scenarios is a great way for KS2 students to develop their maths skills and to engage their learning more effectively. All of our investigation resources feature fun problem-solving activities that your students can get involved with and develop key maths skills! They all feature brilliant illustrations to help ...

  10. Developing Mathematical Thinking

    Working Systematically at KS2 These problems will challenge your learners to work systematically. Age 5 to 7 Working Backwards at KS1 The lower primary tasks in this collection could each be solved by working backwards. Age 7 to 11 Working Backwards at KS2 The upper primary tasks in this collection could each be solved by working backwards.

  11. Developing Thinking Skills At KS2: How I Wish I'd Taught Maths (5)

    Extension ideas for problem solving activities in KS2. Extending both ideas, we could make a grid where the rows contained questions with a different surface structure and the columns contained questions with the same deep structure. This grid could be cut into individual boxes with pupils having to sort each box accordingly, to reconstruct the ...

  12. KS2 Maths Word Problems

    Challenge your children using our KS2 maths word problems resources. Here you can find a wide array of maths word problems from division to fractions and more. All are designed to help your Key Stage 2 pupils develop their problem-solving skills in a fun and engaging way! Choose from differentiated worksheets, challenge cards, fun activities ...

  13. Outdoor Problem Solving Activities KS2- Learning Maths

    These are some ideas for outdoor problem solving activities for KS2 to help children with learning maths outdoors. One of the most critical aspects of teaching and learning maths is to be able to solve problems. While teaching maths in school, I found that it can become easy to get overly focused on teaching the rules and procedures for doing ...

  14. Maths Problem Solving Booklets

    Maths problem solving booklets covering a wide range of mathematical problems designed to improve problem solving strategies as well as numeracy and mathematical ability. Designed to be printed as A5 booklets. Disclaimer: These are free because the problems are from a wide variety of sources, most of which I have forgotten.

  15. Problem Solving Activities and Games for KS2

    Connect 4 Factors Playing solo: The player must fill the grid with the counters from both boxes. They must avoid lining up four numbers with a common factor (other than one). Playing duo: Each player has a box of counters to choose from. Take it in turns to drop a counter into the game board.

  16. PDF Problem-solving activities: ideas for the classroom

    KS1 / KS2 Introduction 33 schools from the Royal Society Schools Network were chosen to take part in a problem-solving club pilot scheme, with the aim to set up a new mathematics or computing focused problem-solving club for their students. Each club developed its own programme of activities, and teachers were encouraged to explore opportunities

  17. Problem-Solving Resilience Activity (teacher made)

    This Problem-Solving Resilience Activity provides a range of everyday problems for children to discuss and suggest solutions to. Twinkl Key Stage 2 - Year 3, 4, 5, 6 Subjects PSHCE/RSHE Relationships Caring Friendships Related Searches

  18. Primary Resources: Maths: Solving Problems: Investigations & Puzzles

    9 Teddies & 3 Boxes Problem (Chris Duffy) Nim (Palmz) PNS Problem Solving (Chris Duffy) The Magic Carpet (from NNS) (Max Smith) Magic Carpet Lesson Plan (Katy Hebblewhite) DOC. 'The Red Express' Investigation (Fiona Venus) DOC. Solving Puzzles (Melanie Braithwaite) DOC. Tricky Word Problems (Hayley Kushner) DOC.

  19. 17 Fun Problem Solving Activities & Games [for Kids ...

    Balloon Tower Problem Solving Activities for Kids Walking the Plank "Laser" Web Group Drawing Animals Alphabet Game There are four basic steps in problem solving: define the problem generate possible solutions evaluate and select possible solutions implement solutions Problem solving activities use one of more of these steps.

  20. 30 Problem Solving Scenarios for Kids & Teens

    Home practice will make progress toward meeting individual language goals much faster. Speech-Language Pathologists (SLPs) are only able to see students/clients 30-60 mins (or less) per week. This is not enough time or practice for someone to handle Problem solving scenarios. Every day that your loved one goes without practice it becomes more ...

  21. What Would You Do? Social Scenario Discussion Cards

    What is this resource useful for? Navigating social scenarios can sometimes be difficult, even for adults. Society is made up of a diverse range of individuals, all with their own ideas, opinions and agendas so sometimes it can be tricky for people to find common ground with others. Show more Related Searches

  22. The U.S.-Mexico Border: How Americans View the Situation, Its Causes

    Democrats mostly view the situation as a major problem (44%) or minor problem (26%) for the U.S. Very few Democrats (7%) say it is not a problem. In an open-ended question, respondents voice their concerns about the migrant influx. They point to numerous issues, including worries about how the migrants are cared for and general problems with ...