year 6 maths problem solving investigations

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How Do You Do Math Percentage Problems?

year 6 maths problem solving investigations

To calculate percentages, convert the percentage to a decimal and multiply it by the number in the problem. For example, to find 40 percent of 50, change it to 0.40 times 50, which gives you the result of 20.

There are several methods for solving a percentage problem. For example, 100 percent of a number is the same number. So 100 percent of 50 is 50. When you double the percentage to 200, you can just double the number as well, which means that 200 percent of 50 is 100.

Do the same when reducing a number. To find 50 percent of 50, solve the problem by simply cutting the number in half. Therefore 50 percent of 50 is 25.

When you have an uncommon percentage, such as finding 4 percent of 200, you can rearrange the numbers to find the same result. This means that instead of finding 4 percent of 200, you can find 200 percent of four, which would be four times two, or eight. This method serves as a faster way to solve a seemingly complex percentage problem without having to do difficult multiplication.

For the inverse, or finding what percentage one number is of another, divide the first number by the second. If you’ve scored 20 out of 25 on a quiz and want to know your score as a percentage, divide 20 by 25. This calculation has a result of 0.80, or 80 percent. A score of 20 out of 25 is the same as 80 percent.

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 Problem Solving Investigations In Context

Benefits of maths problem solving 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:

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.

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

Spring Term maths investigations year 6 and year 5

Summer term maths investigations year 6 and year 5

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

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

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 plug gaps and boost progress. Since 2013 we’ve helped over 130,000 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.

FREE KS2 maths SATs practice papers

Get ready for SATs with this set of 6 maths SATs practice papers designed to help your Year 6 pupils improve test skills and build confidence.

Includes: - 2 arithmetic and 4 reasoning papers that follow the National Curriculum Assessments. - Mark schemes to diagnose and assess where your pupils need extra support.

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Resources tagged with: Investigations

Filter by: Content type: ALL Problems Articles Games Age range: All 5 to 11 7 to 14 11 to 16 14 to 18 Challenge level:

There are 141 results

Division Rules

Age 7 to 11 challenge level.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

The Domesday Project

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

Age 5 to 11 Challenge Level

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

So It's Times!

Age 7 to 14 challenge level.

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

Count the Digits

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

The Car That Passes

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

In the Playground

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Triple Cubes

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Follow the Numbers

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

The Numbers Give the Design

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

It Was 2010!

If the answer's 2010, what could the question be?

Brush Loads

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

More Transformations on a Pegboard

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Abundant Numbers

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Egyptian Rope

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Buying a Balloon

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Ben has five coins in his pocket. How much money might he have?

Making Cuboids

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Sticky Triangles

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Roll These Dice

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

How many faces can you see when you arrange these three cubes in different ways?

Age 5 to 14 Challenge Level

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Making Squares

Age 7 to 11.

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Street Party

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

My New Patio

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Number Squares

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

Little Boxes

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

How many triangles can you make on the 3 by 3 pegboard?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Go Deeper with Hamilton's Problem-solving Investigations

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

The skills of mathematical problem solving and investigation are fundamental to the maths curriculum for England and for developing sophisticated and modern mathematicians everywhere. However, these skills do not fall naturally out of the teaching of the maths curriculum itself. They require dedicated time, content and pedagogy. Most challengingly, they require teachers to present children with graded activities and problems that are relevant to the curriculum while at the same time develop skills in mathematical reasoning and logical thinking, and give children sufficient practice to feel confident in these.

Hamilton's Problem-Solving Investigations provide materials and advice for teaching these skills well, in a variety of ways and contexts, and with confidence.

Explore our Problem-Solving Investigations

Individually, investigations are incorporated into every unit in our maths blocks . Y1 | Y1/2 | Y2 | Y3 | Y3/4 | Y4 | Y5 | Y5/6 | Y6

Reception and EYFS Investigations

These open-ended investigations for Reception or Early Years settings are designed to take advantage of outdoor learning environments, but many of them can be adapted to run inside. Reception Maths: Open-ended Investigations

Mrs Multiple's cakes : In this video, Nick Barwick discusses using the investigation "Mrs Multiple's Cakes" with a Year 2 class.

The impact of an investigative approach: In this video, Nick Barwick describes the impact of an investigative approach on a Year 5 class.

Do Hamilton provide answers to investigations? Get guidance on assessing problem-solving and reasoning skills.

Investigation Examples

See examples of worked investigations, with explanatory notes about the process.

Contextualised Maths in Topics

Topics present abundant opportunities for contextual maths. Have fun with meaningful maths and explore a cross-curricular topic at the same time. Find hidden maths treasures.

Additional Maths Challenges

For further maths problems and puzzles for your class, try these National Numeracy publications from 2000. They come with answers too!

Download Maths Challenges

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

Use our short maths blocks to follow Hamilton's recommended order of teaching.

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Problem-Solving Investigation: Multiples, factors & prime numbers (Year 6 Multiplication & Division)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

4 October 2019

Year 6 Multiplication and Division: Multiples, factors and prime numbers.

This in-depth Maths Investigation will develop maths meta-skills, and enable children to learn to think mathematically and articulate mathematical ideas.

In-depth Investigation: Magic Multiplication Squares Children complete a magic multiplication square using their knowledge of number properties and relationships. They then explore factors and multiples to create a new multiplication magic square.

This problem-solving investigation is part of our Year 6 Multiplication and Division block. Each Hamilton maths block contains a complete set of planning and resources to teach a terms worth of objectives for one of the National Curriculum for England’s maths areas.

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Year 6 Multiplication and Division - Problem-Solving Investigations

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Maths Investigations 1st Edition

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$Random Sampling and Making Inferences ~ Investigation Activity 7th Grade Math$

Random Sampling and Making Inferences ~ Investigation Activity 7th Grade Math

$Math Maker$

Chance and Data Mini Math Investigations | Fun Probability

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Telling the Time - Analog clock word problems | Grade 2

Internet Activities

Also included in: Grade 2 Maths Problem Solving Investigations - Scavenger Hunt

$Grade 4 Time Unit - Ontario Math 2020 Measurement - PDF and Slides$

Grade 4 Time Unit - Ontario Math 2020 Measurement - PDF and Slides

Also included in: Grade 4 Math Units Bundle 2 - Ontario 2020 Curriculum - PDF and Google Slides

Distributive Property Investigation - Bracelets

$Math Giraffe$

Also included in: Expressions & Equations Bundle: Activities, Games, & Notes for Algebra Skills

It's Holiday Time! Maths Investigation

Pumpkin Investigation

Grade 5 Multiplication and Division Unit - Ontario Math 2020 - PDF and Slides

Also included in: Grade 4 & Grade 5 Multiplication and Division Units Bundle - Ontario Math 2020

$Grade 4 Probability Unit - Ontario Math 2020 Data Strand - PDF and Slides$

Grade 4 Probability Unit - Ontario Math 2020 Data Strand - PDF and Slides

Also included in: Grade 4 Math Unit Bundle - Ontario 2020 Curriculum - PDF and Google Slides

Pumpkin Science Activities for Preschool Prek & Kinder - Pumpkins Investigation

Also included in: Preschool Science Center Activities Bundle - Spring PreK Science Units & Lessons

$Grade 4 Patterning Unit - Ontario Math 2020 - PDF and Slides$

Grade 4 Patterning Unit - Ontario Math 2020 - PDF and Slides

$Mini Math Investigations Worksheets | Volume and Capacity Tasks and Activities$

Mini Math Investigations Worksheets | Volume and Capacity Tasks and Activities

Time Zones Investigation

Also included in: Elapsed Time Bundle

$Math Investigation Bundle$

Math Investigation Bundle

Slope Investigation Fun Activity / Experiment Algebra Graphing Linear Equations

Also included in: Bundle of Linear Graphing worksheets, tests, games, activities, investigations

$Mini Math Investigations | Number and Place Value worksheets$

Mini Math Investigations | Number and Place Value worksheets

Time investigation - FLY AROUND AUSTRALIA

Word Document File

Elapsed Time - Stopwatch Investigation

Time Interval Investigation - Series of Lessons (EDITABLE)

1st Grade Bridges Math Smartboards Unit 8, Module 1 Time & Duration

NOTEBOOK (SMARTboard) File

$100th Day Math and Science Investigations, STEM STEAM Activities & Centers$

100th Day Math and Science Investigations, STEM STEAM Activities & Centers

Also included in: 100th Day of School Bundle | Math and Science Activities |

Fall Leaf Investigation and Leaf Activities

Also included in: Fall Activities for Preschool - Math, Literacy & Dramatic Play Activities

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😀 Year 6 problem solving. Year 6 maths problem solving worksheets. 2019-01-11
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Problem Solving Questions

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COMMENTS

What Are the Six Steps of Problem Solving?
The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...
What Is the Answer to Your Math Problem?
The answer to any math problem depends on upon the question being asked. In most math problems, one needs to determine a missing variable. For instance, if a problem reads as 2+3 = , one needs to figure out what the number after the equals ...
How Do You Do Math Percentage Problems?
To calculate percentages, convert the percentage to a decimal and multiply it by the number in the problem. For example, to find 40 percent of 50, change it to 0.40 times 50, which gives you the result of 20.
Open-Ended Year 6 Maths Investigations (Teacher-Made)
Open-ended maths investigations have more than one solution and are designed to provide children with the freedom to come up with their own strategy and
KS2 Maths Investigations
These KS2 maths investigations include lots of problem-solving activities for year 3, 4, 5 and 6 pupils. You can find mystery games, challenge cards and
KS2 Maths Investigations For Real Life Problem Solving
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
NRICH topics: Thinking Mathematically Investigations
This challenge encourages you to explore dividing a three-digit number by a
NRICH topics: Thinking Mathematically Investigations
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen? Shaping It. Age 5 to 11. Challenge Level.
Go Deeper with Hamilton's Problem-solving Investigations
Individually, investigations are incorporated into every unit in our maths blocks. Y1 | Y1/2 | Y2 | Y3 | Y3/4 | Y4 | Y5 | Y5/6 | Y6. Or, you can find
Maths: Solving Problems: Investigations & Puzzles
Clues Suspects Solutions; Murder Mystery Maths 6 (Peter Barnett) Story
Problem-Solving Investigation: Multiples, factors & prime numbers
Year 6 Multiplication and Division: Multiples, factors and prime numbers. This in-depth Maths Investigation will develop maths meta-skills
Maths investigations ks2 & ks3
Year 6). • Allow pupils to apply learning in different contexts.
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Free - Percentage Investigation - A Birthday Interactive Activity Year 4 Maths, ... Year 6 Maths.
Maths Investigation Time Teaching Resources
This is the 1st edition of my Maths Investigations. These activities allow students to apply their knowledge and understanding of maths