year 6 problem solving tasks

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Year 6 Maths Worksheets UK Hub Page

Welcome to our Year 6 Maths Worksheets area.

Here you will find a wide range of free printable Year 6 Maths Worksheets for your child to enjoy.

Come and take a look at our rounding decimal pages, or maybe some of our adding and subtracting fractions worksheets. Perhaps you are looking for some worksheets about finding angles in a triangle, or need some ratio problem worksheets to help your child learn about ratio?

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• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 6 Maths Learning

Here are some of the key learning objectives for the end of Year 6:

• know and use Place value up to 10 million
• Counting on and back in steps of powers of 10 from any number up to 10 million
• Round numbers to any given degree of accuracy.
• Count forwards and backwards through zero with positive and negative numbers.
• Read Roman numerals to 1000 and recognise years written in Roman numerals
• solve multi-step problems using addition and subtraction in a range of contexts
• identify multiples and factors including common factors
• multiply and divide up to 4-digit numbers by up to 2 digits
• Use their knowledge of the order of operations to carry out calculations involving the four operations.
• Identify common factors, common multiples and prime numbers.
• solve problems involving addition, subtraction, multiplication and division
• simplify fractions
• compare and order fractions including mixed numbers
• add and subtract fractions with different denominators including mixed numbers
• multiply simple fractions together and simplify the answer
• divide proper fractions by whole numbers
• recall and use equivalence between simple fractions, decimals and percentages.
• Multiply and divide whole numbers and decimals up to 3dp by 10, 100 or 1000
• read, write, order and compare numbers up to 3dp
• round decimals with up to 3dp to the nearest whole
• solve problems with numbers up to 3dp
• work out percentages of different amounts
• solve problems using percentages
• use simple formulae
• express missing number problems using algebra
• find pairs of numbers that satisfy equations with two variables
• solve problems involving simple ratios
• solve problems involving similar shapes where the scale factor is known
• use, read, write and convert between standard units of measure
• measure, compare and calculate using different measures
• know that shapes with the same area can have different perimeters
• find the area of parallelograms and right triangles
• find the volume of cubes and cuboids
• convert between miles and km
• name and understand the parts of circles - radius, diameter and circumference
• draw 2D shapes accurately using dimensions and angles
• compate and classify 2D shapes by a range of properties
• find missing angles in triangles, quadrilaterals and regular shapes
• use coordinates in all 4 quadrants
• draw and translate simple shapes in all 4 quadrants
• interpret and construct pie charts and line graphs
• calculate the mean as an average

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 6 is generally equivalent to 5th Grade in the US.

On this page you will find link to our range of math worksheets for Year 6.

Quicklinks to Year 6 ...

• Place Value Zone
• Mental Math Zone

Word Problems Zone

Fractions percents ratio zone.

• Percentages Zone
• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 6 number worksheets.

Here you will find a range of Free Printable Year 6 Number Worksheets.

Using these Year 6 maths worksheets will help your child to:

• use place value with numbers up to 10 million;
• use place value with up to 3 decimal places;
• understand how to use exponents (powers) of a number;
• understand and use parentheses (brackets);
• understand and use multiples and factors;
• extend their knowledge of prime and composite (non-prime) numbers up to 100;
• know and be able to use the PEMDAS (or PEDMAS) rule.
• Place Value Worksheets to 10 million
• Place Value to 3dp
• Ordering Decimals Worksheets
• PEMDAS Rule Support Page
• PEMDAS Problems Worksheets
• Balancing Math Equations
• Roman Numerals worksheets

Ordering Large Numbers and Decimals to 3dp

The sheets in this section involve ordering lists of decimals to 3 decimal places and also large numbers up to 100 million.

There are sheets with decimals up to 10, and also sheets with numbers from -10 to 10.

• Ordering Large Numbers up to 100 million
• Ordering Decimals to 3dp

Rounding Decimals

• Rounding to the nearest tenth
• Rounding Decimal Places Sheets to 2dp
• Rounding Decimals Worksheet Challenges

Year 6 Decimal Counting Worksheets

Using these sheets will support you child to:

• count on and back by multiples of 0.1;
• fill in the missing numbers in sequences;
• count on and back into negative numbers.
• Counting By Decimals

Year 6 Mental Maths Zone

Each worksheet tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math quiz!

• Year 6 Mental Maths Tests

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Year 6 Addition Worksheets

• add decimals including tenths and hundredths mentally;
• add a columns of multi-digit numbers, including decimals.
• Decimal Addition Fact Worksheets
• 5th Grade Addition Worksheets BIG Numbers
• Decimal Column Addition Worksheets
• Money Worksheets (randomly generated)

Year 6 Subtraction Worksheets

Using these sheets will help your child to:

• subtract decimals including tenths and hundredths mentally;
• subtract multi-digit numbers, including decimals using column subtraction.
• Subtracting Decimals Worksheets (mental)
• Subtraction Worksheets up to Billions (columns)
• Column Subtraction with Decimals

Year 6 Multiplication Worksheets

• extend their knowlege of multiplication to decimals;
• use their multiplication tables to answer related facts, including decimals;
• multiply a range of decimals with up to 2 decimal places (2dp) by a whole number;
• multiply different money amounts by a whole number.
• Multiplying Decimals by 10 and 100
• Multiplication Fact Sheet Decimals
• Decimal Multiplication Worksheets to 1dp
• Decimal Multiplication Worksheets to 2dp
• Free Multiplication Worksheets (randomly generated)
• Multiply and Divide by 10 100 (decimals)
• Multiplication & Division Worksheets (randomly generated)
• Multiplication Word Problems

Division Worksheets 5th Grade

Using these Year 6 maths worksheets will help your child learn to:

• divide any whole number up to 10000 by a two digit number;
• express any division with a remainder in the form of a mixed number (a number with a fraction part).
• Long Division Worksheets (whole numbers)
• Long Division of Decimal Numbers
• Decimal Division Facts
• Division Facts Worksheets (randomly generated)

Year 6 Maths Problems

• apply their addition, subtraction, multiplication and division skills;
• apply their knowledge of rounding and place value;
• solve a range of problems including "real life" problems and ratio problems.

These sheets involve solving one or two more challenging longer problems.

• Year 6 Math Problems (5th Grade)

These sheets involve solving many 'real-life' problems involving data.

• Year 6 Math Word Problems (5th Grade)

These sheets involve solving a range of ratio problems.

Year 6 Fraction Worksheets

Year 6 percentage worksheets, year 6 ratio worksheets.

• compare and order fractions;
• add and subtract fractions and mixed numbers;
• understand how to multiply fractions by a whole number;
• understand how to multiply two fractions together, including mixed fractions;
• understand the relationship between fractions and division;
• know how to divide fractions and mixed fractions;
• convert decimals to fractions.
• Comparing Fractions Worksheet page
• Adding Fractions Worksheets
• Adding Improper Fractions
• Subtracting Fractions Worksheets
• Adding Subtracting Fractions Worksheets
• Improper Fraction Worksheets
• Converting Decimals to Fractions Worksheets
• Fractions Decimals Percents Worksheets
• Multiplying Fractions Worksheets
• Dividing Fractions by Whole numbers
• Divide Whole numbers by Fractions
• Simplifying Fractions Worksheets
• Free Printable Fraction Riddles (harder)

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

• Percentage of Numbers Worksheets
• Money Percentage Worksheets
• Percentage Word Problems

These Year 6 Ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

• Ratio Part to Part Worksheets
• Ratio and Proportion Worksheets

Year 6 Geometry Worksheets

• know how to find missing angles in a range of situations;
• learn the number of degrees in a right angle, straight line, around a point and in a triangle;
• know how to calculate the area of a triangle;
• know how to calculate the area of a range of quadrilaterals.
• learn the formulas to calculate the area of triangles and some quadrilaterals;
• write and plot coordinates in all 4 quadrants.
• (5th Grade) Geometry - Angles
• Area of Quadrilaterals
• 5th Grade Volume Worksheets
• Coordinate Worksheets (1st Quadrant)
• Coordinate Plane Worksheets (All 4 Quadrants)
• Parts of a Circle Worksheets

Measurement Zone, including Time & Money

Year 6 measurement worksheets.

Using these sheets will help your child understand how to:

• learn how to read a standard scale going up in different fractions: halves, quarters, eighths and sixteenths;
• learn how to read a metric scale going up in 0.1s, 5s, 10s, 25s, 50s & 100s;
• learn how to estimate a measurement of length, weight or liquid;
• convert temperatures in Celsius and Fahrenheit.
• (5th Grade) Measurement Worksheets

Time Puzzles - harder

Here you will find our selection of harder time puzzles.

• Time Word Problems Worksheets - Riddles (harder)

Using these sheets will help you to:

• find the mean of up to 5 numbers;
• find a missing data point when the mean is given.
• Mean Worksheets

Fun Zone: Puzzles, Games and Riddles

Year 6 maths games.

• Year 6 Math Games (5th Grade)

Year 6 Maths Puzzles

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

• Printable Math Puzzles

Math Salamanders Year 6 Maths Games Ebook

Our Year 6 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store - use the link below to find out more!

• Year 6 Maths Games Ebook

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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Problem-solving maths investigations for year 6.

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

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

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

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

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

You can find Hamilton's investigations for Year 6:

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

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

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

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20 Word Problems For Year 6: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma Johnson

Word problems for Year 6 are an important part of the curriculum. For children to achieve success in the Year 6 SATs, in particular the more challenging reasoning element of the SATs assessments, it is essential they have the confidence to tackle a wide range of word problems.

Key to this success is regular exposure to the style and type of questions, covering the topics children could be presented with. Our collection of year 6 maths worksheets are is a great place to start.

To help child practice their problem solving skills, we have put together a collection of 20 word problems , organised by topic. This collection encompasses the types of questions children may encounter in the two reasoning papers.

All Kinds of Word Problems Four Operations

Download this free pack of word problems. With questions covering all four operations, your students will have a great opportunity to practice their problem solving skills across KS2 topics.

Place value 

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The National Curriculum states that children need to be able to solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into simpler steps and persevering in seeking solutions. 

By Year 6, children can expect to be tackling a range of one-step, two-step and multi-step word problems. To achieve at least the expected standard in Year 6, pupils need to demonstrate the ability to solve word problems across a range of topics.

Solving problems including ordering, rounding and negative numbers.

Solving multiplication, division and addition and subtraction word problems including one and two-step word problems and multi-step word problems in context, deciding which operations and methods to use and why.

Solving problems involving comparing, ordering and sequencing fractions; using the four operations and problems which require answers to be rounded to specified degrees of accuracy.

Solving problems involving the relative sizes of two quantities; the calculation of percentages; involving similar shapes where the scale factor is known and can be found; and unequal sharing and grouping, using knowledge of fractions and multiples.

Solving problems including time word problems and involving the calculation and conversion of units of measure, using decimal notation up to three decimal places, where appropriate.

Interpret and construct pie and line graphs and use these to solve problems.

Word problems are an essential element of the Year 6 curriculum, because they require children to apply the knowledge they have learnt to ‘real life’ situations, for example, in money word problems . They shouldn’t just be taught as stand alone topics, but should be incorporated in lessons throughout the year, to ensure children have as much exposure as possible. 

Solving word problems helps children learn the skills needed to apply their knowledge of maths beyond the classroom and into the real world.

When teaching problem solving in Year 6, children need to firstly look carefully at the key information and think about what they already know. Secondly, what is the word problem actually asking? Which calculation(s) would be required and would it help to draw/represent the problem pictorially?

Here is an example:

Ahmed is buying clothes. He buys a t-shirt for £12.99 and a pair of jeans which cost £12.26 more than the T-shirt. He pays with a £50 note. What change does Ahmed get?

How to solve:

What do you already know?

• More than means I will need to add the price of the T-shirt and jeans together.
• Decimals numbers means I need to remember to line up the decimal points in my calculations.
• Calculating change means I will need to subtract the total for the jeans and T-shirt from the original amount. 

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

• To calculate the cost of the jeans, we need to add £12.99 and £12.26 = £25.25
• Ahmed pays using a £50 note. 
• To calculate the change Ahmed will get, we need to subtract £25.25 from £50.
• £50 – £25.25 = £24.75

Problem solving is an important part of the preparation for the Key Stage 2 SATs, as this is the area children tend to find the most challenging. With two reasoning papers to complete, children will be expected to answer a wide range of word and number problem style questions. The best preparation for this is through regular exposure to these types of questions.

Addition word problems at Year 6 include larger 6 or 7 digit numbers, decimal numbers and problems involving finding the inverse. These can be one, two and multi-step problems

Addition question 1

A shopping centre had 124,713 visitors in January, 102,539 in February and 118,768 in March. How many shoppers visited the shopping centre from January to March?

Answer (1 mark): 346,020

Addition question 2

A shop has an offer on all T-shirts. 

Buy one T-shirt, get one for half price.

If Tom buys 2 T-shirts, how much does he pay altogether?

Answer (2 marks): £7.35

Addition question 3

The table below shows the number of visitors to the planetarium and the transport museum each day. Which day had the most visitors?

Answer (2 marks): Saturday

Subtraction word problems in Year 6 include larger 6 or 7 digit numbers, decimal numbers and problems involving finding the inverse. These can be one, two and multi-step problems

Subtraction question 1

In the Autumn term, the total number of English and maths worksheets printed by a school was 63,502. 39,756 were maths worksheets. How many worksheets were printed out for English?

Answer (1 mark): 23,746

Subtraction question 2

6 cars were weighed before being loaded onto the car transporter. 

They weight of the cars was:

What is the difference in weight between the heaviest and lightest car?

Answer (1 mark): 1043kg

Subtraction question 3

Two decimal numbers add together to make 37.53.

One number is 23.86.

What is the other number?

Answer (1 mark): 13.67

Multiplication word problems can include multiplying whole and decimal numbers by 1 and 2-digit numbers. A secure knowledge of times tables is helpful for children solving these questions confidently. 

Multiplication question 1

A box of chocolate contains 2 trays of chocolates.

There are 18 chocolates on each tray.

How many chocolates are there in 35 boxes of chocolates?

Answer (2 marks): 1260

Multiplication question 2

Zara buys 4 large boxes of cupcakes and 3 small boxes of cupcakes.

Each large box contains 28 cupcakes. Each small box contains 16 cupcakes.

How many cupcakes does Zara buy altogether?

Answer (2 marks): 160

Multiplication question 3

A cyclist cycled a route of 123.6 miles once a week for a year. How far did he cycle over the whole year?

Answer (2 marks): 6427.2

Division word problems in Year 6 can include division with whole numbers and decimal numbers, dividing by 1 and 2-digit numbers.

Division question 1

A 940ml bottle of blackcurrant makes 20 drinks.

How many millilitres of blackcurrant are in each drink?

Answer (2 marks): 47

Division question 2

Mr Jones is organising mini buses for a Year 6 school trip. Each minibus seats 12 people

120 Year 6 pupils are going on a school trip. 

There needs to be one adult for every 10 pupils

How many coaches will Mr Jones need to book?

Answer (2 marks): 12 mini buses

125 pupils will need 13 adults = 138 in total

Division question 3

A factory is packaging eggs in boxes of 12.

The factory has 878 eggs to box-up. 

How many boxes will they have, to send to the supermarket?

Answer (2 marks): 73 boxes

Decimals, percentage word problems and fraction word problems can be stand alone, or they can involve converting between. For example, in questions using measures.

Fractions, decimals and percentages question 1

By the end of the Autumn term, Chloe had used ⅔ of her maths book. If the book had 96 pages, how many pages had she used?

Answer (1 mark): 64 pages

⅓ of 96 = 32

⅔ of 96 = 64

Fractions, decimals and percentages question 2

Abdullah received £600 for his birthday. He spent 45% of him money on a VR headset. How much did the headset cost him?

Answer (1 mark): £270

Fractions, decimals and percentages question 3

Mrs Jones went to the local supermarket to buy some vegetables.

She bought:

• 1 3/10kg of potatoes
• 840.5g of apples
• 4/5kg of peaches
• 520.6g of grapes

What was the total weight of the shopping Mrs Jones bought?

Answer (1 mark):

• 1.3kg potatoes
• 0.8405kg apples
• 0.8kg peaches
• 0.520kg grapes

Ratio word problems are often linked with measures. Children should be encouraged to draw bar models to solve problems involving ratio, as these question really benefit from a visual representation.

Ratio question 1

Sam and Zeyn were making drinks for the school fair. To make the jugs of squash, they were mixing 300ml of orange squash with 1500ml of water.

If they have 900ml of orange squash

• How much water will they need altogether? 
• What will be the total volume of the squash?

Answer (2 marks):

• 4500ml of water
• 5400ml of squash

Ratio question 2

A piece of ribbon is 72cm long. It is cut into pieces in the ratio of 2:3:4.

How long is each piece of ribbon?

Answer (1 mark): 16cm:24cm:32cm

Mixed operation word problems require two or more operations to solve. Alongside the four operations, they can also include other topics, including fractions and percentages These can be two-step or multi-step questions and are worth 2 or 3 marks in SATs papers. 

Third Space Learning’s online one-to-one tutoring programmes include questions that combine skills students have learnt and test their understanding across a range of topics. Personalised to the needs of each individual student, our online tutoring programme works to identify gaps in learning, fill those gaps and reinforce students’ maths knowledge.

Mixed four operations question 1

One bank-holiday weekend, a total of 346,728 people visited a theme park.

134,235 visited on Saturday

121,689 visited on Sunday.

How many visited on bank holiday Monday?

Answer (2 marks): 90,804

Mixed four operations question 2

A pair of jeans in a shop cost £28.

In the sale, they were reduced in price by 25%.

What was the reduced price?

Answer (2 marks): £21

Mixed four operations question 3

Sophie thinks of a number.

She multiplies her number by 6.

Then she adds 10

Finally she divides by 4.

Her answer is 13. 

What was her original number?

Answer (1 mark): 7

Third Space Learning also offers a wide array of maths and word problems resources for other year groups such as word problems for Year 5 , word problems for Year 4 and word problems for Year 3

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Learn how tutors develop pupils’ maths fluency 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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Australian Curriculum: Mathematics

Students are entering a new section of math that consists of algebra, geometry, decimals, and more complicated division problems. When there is not a parent or teacher around, students have access to on-demand videos for their sixth-grade mathematical lessons. Our video tutorials are taught by math teachers who go through the problem solving process.

• The key to learning math is repetition, and our math teachers go through multiple examples. 
• Math teachers show students step-by-step directions on how to solve these more complex problems.
• Students learn money, ratios, decimals, graphing, and other concepts from the 6th grade curriculum.

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Extending Fraction Bars

Can you compare these bars with each other and express their lengths as fractions of the black bar?

More Fraction Bars

What fraction of the black bar are the other bars? Have a go at this challenging task!

Always, Sometimes or Never? Shape

Are these statements always true, sometimes true or never true?

Always, Sometimes or Never? Number

Round the Three Dice

What happens when you round these three-digit numbers to the nearest 100?

Round the Four Dice

This activity involves rounding four-digit numbers to the nearest thousand.

Use the information on these cards to draw the shape that is being described.

Dicey Perimeter, Dicey Area

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Domino Sets

How do you know if your set of dominoes is complete?

Making Spirals

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

Round a Hexagon

This problem shows that the external angles of an irregular hexagon add to a circle.

Have a look at this data from the RSPB 2011 Birdwatch. What can you say about the data?

So It's Times!

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

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

Button-up Some More

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Counting Cogs

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Doughnut Percents

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.

Next Size Up

The challenge for you is to make a string of six (or more!) graded cubes.

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

What can you see? What do you notice? What questions can you ask?

Treasure Hunt

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

First Connect Three

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Factor-multiple Chains

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Fraction Fascination

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

Triangles All Around

Can you find all the different triangles on these peg boards, and find their angles?

Diagonal Sums

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Ten Hidden Squares

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Orange Drink

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Sponge Sections

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Factor Lines

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Would You Rather?

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

Plenty of Pens

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

Mystery Matrix

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

The Moons of Vuvv

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Where Are They?

Use the isometric grid paper to find the different polygons.

Rectangle Tangle

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

Pumpkin Pie Problem

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

Quadrilaterals

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Two and Two

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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?

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.

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?

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Authentic tasks are designed to help students see mathematics as worthwhile and important. When students understand the purpose of a given problem in mathematics, they are more likely to persist when challenged. Authentic tasks generally have an ‘open middle’ which means that students can use different representations and solutions to communicate their knowledge and reasoning.

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

The following criteria was used to select the tasks based on their potential:

Used with permission © Martin Holt Educational Consultant 2017

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17 Fun Problem Solving Activities for Kids

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As a child, I would spend hours putting together puzzles… whether it was 3-D puzzles or figuring out a crossword. I also loved it when teachers would give the class an open-ended question and we had to work in groups to figure out the answer in our own way.

Even something as simple as playing checkers with my brothers gave me the chance to use strategy as a way to win the game. I honestly believe that it’s so important for kids to solve problems at a young age, as it helps them think critically and outside the box.

Table of Contents

So, Why Is It Important To Teach Kids Problem Solving?

I think these kinds of activities are so important for kids to do because it helps them learn how to think analytically and solve problems on their own. It's a great way to get kids to use their imaginations and be creative.

Rote memorization simply does not have the same effect. This type of learning is great for learning facts like historical dates, but it’s not going to help kids figure out how events in history happened and the results.

We take these problem-solving skills into college, the workforce, and travel . My ability to problem solve since childhood has certainly got me through many sticky situations while in a new city or country.

Additionally, problem-solving helps children learn how to find creative solutions to challenges they may face both in and out of the classroom . These activities can also be fun and used in cohesion with school or playtime.

17 Fun Problem-Solving Activities for Kids

1. marble mazes.

This activity was selected because it requires them to think spatially. Spatial learning will benefit kids when they start driving, riding a bike, playing sports,etc.

To do this activity in its simplest form, you will need a piece of paper, a pencil, and some marbles. First, draw a maze on a piece of paper using a pencil.

Make sure to create a start and finish point. Then, place the marbles at the start of the maze. The goal is to get the marbles from the start to the finish by tilting the paper and using gravity to guide the marbles through the maze.

Another example of a marble maze can involve using toilet paper rolls taped together to create a three-dimensional maze. The larger the maze, the harder you can make it.

Check Price on Amazon!

If you are not into the DIY method, you can always buy a toy maze on Amazon. A good 48 piece puzzle is the Melissa & Doug Underwater Ocean Floor puzzle.

2. The Tower Challenge

Building a tower gives kids the chance to think about gravity, structure, and balance.

To do this activity, you will need some building materials like legos, blocks, or even toilet paper rolls. The challenge is to see how high they can stack the materials without the tower toppling over.

This can be done individually or in teams. An activity like this is good for younger kids and is the building block to learning about harder topics like engineering.

3. The Egg Drop Challenge

The egg drop challenge helps kids learn how to engineer a solution that prevents something from breaking. It requires them to think critically about which materials will best protect something fragile like an egg when dropped from a height.

To do this activity, you will need some eggs and various materials such as straws, cotton balls, bubble wrap, etc. The goal is to construct a device that will protect an egg from breaking upon impact.

This can be done individually or in teams . Teams can even have a competition for the best egg drop device.

As children begin handling, shopping for, and cooking their own food, activities like this will help them understand how to handle breakable items like bottles, eggs, delicate fruit,.etc. Ideally, this is best for age groups 8 and up.

4. The Penny Drop Challenge

This activity was selected because it requires kids to think about physics and how different materials affect sound.

To do this activity, you will need a penny ( or another coin), a cup, and various materials such as paper towels, cotton balls, etc.

The goal is to drop the penny into the cup without making any noise. Begin by placing different materials into the cup and then drop the penny into it. The children should also drop the penny from different heights into the same material to see if/how the impact from a higher drop affects sound.

Group kids into teams or let them try it on their own.

Kids should make note of what type of sounds are made when the penny hits different materials. This is a great activity for kids who are interested in science and physics.

5. The Balloon Race Challenge

This activity was selected because it helps kids learn about aerodynamics and Bernoulli’s principle . It also requires them to think creatively about how to design a balloon-powered vehicle.

To do this activity, you will need balloons, straws, masking tape, and markers. The goal is to design a balloon-powered vehicle that can travel a distance of at least 10 feet. Kids can begin this activity by sketching out their designs on paper.

After they have a basic design, they can begin building their vehicle from various materials. Then kids can explain why they think the balloon traveled or did not travel as far as it did.

6. The Marshmallow Challenge

Marshmallows are not only delicious, but they are also soft and malleable. So kids can have fun using it for some construction projects.

This activity was selected because it requires kids to think creatively about how to build a structure using limited materials. It also helps them learn about engineering and work as a team.

To do this activity, you will need marshmallows and spaghetti noodles. The goal is to build the tallest free-standing structure possible using only marshmallows and spaghetti noodles. If you don't have spaghetti noodles, use something similar like pretzel sticks.

You may even want to establish certain rules like each team can only use a certain number of marshmallows or noodles. A time limit can also make it more fun and challenging.

For more fun activities, check out our post on problem solving exercises for team building .

7. The Balloon Pop Challenge

If you remember your childhood, you probably remember popping balloons for fun at times. But this activity is different because it requires kids to use strategy and critical thinking.

This activity was selected because it helps kids learn about patterns and problem-solving. It is also a lot of fun for kids who like popping balloons. The goal is to create a device that will allow them to pop a balloon without using their hands.

To do this activity, you will need balloons and various materials such as straws, string, paper clips, etc.

8. Picture Pieces Puzzle Game

As mentioned earlier, puzzles are a great pastime – especially in childhood. Kids must think critically about how to put the pieces together to create a certain picture. It also helps them learn about shapes, colors, and other concepts.

You can take a medium to large picture and cut it into pieces. If you have younger kids, you may want to make the pieces larger. However, if you have kids closer to the 8-11 age range, you should be able to provide a challenge and make the pieces smaller.

9. Copy the Block Model

For this challenge, you can build a model out of blocks for the kids to copy. Put kids into groups and make sure each group has the same number of blocks you used for your model.

Make your model block as simple or complex as needed for your child's age group.

Set a time limit and make sure each group starts at the same time.

10. Team Scavenger Hunt

A scavenger hunt is great for kids because they have to search for items and use investigative skills. It is also a lot of fun and can be done both indoors and outdoors .

To do this activity, you will need to create a list of items for the kids to find. The items can be anything from common household items to things you would find outside.

These types of activities can also revolve around a theme like a holiday, movie, or book. For example, if the kids are fans of “Harry Potter” you can make a list of items to find that are related to the movie.

11. Obstacle Course

This activity requires kids to think creatively about how to get from one point to another while maneuvering around obstacles. If you have outdoor space, this can be done with common objects such as hula hoops, cones, etc.

If you don't have access to an outdoor space, you can use common household items to create an indoor obstacle course. For example, you can use chairs, blankets, pillows, etc.

Begin by setting up the course and then timing each child as they complete it. You can also have them race against each other to make it more fun.

Obstacle courses are also great because kids get to be physically active while they are thinking critically.

12. Reading Storybooks

There are many great benefits for kids that read storybooks.  One of the excellent benefits is the ability to problem-solve.  When they read the stories in the books, they see scenarios that cause them to be attached to the various characters they read about. 

So, when they encounter a real-life problem, it is often productive to ask a child how their favorite character would solve that problem.  Your kids can also be encouraged to come up with various options and possible outcomes for some of the situations they may encounter. 

This not only helps kids solve various problems but become more independent as well. 

13. Ask Them Open-Ended Questions

A good way to improve a child's ability to think critically and creatively and improve their ability to solve problems is by asking open-ended questions.  It also helps them to develop healthy personalities .

There are no right or wrong answers to these questions.  In addition, the solution requires more than a simple “yes” or “no” answer.  Furthermore, it allows kids to put some extra thought into their responses. 

Here are some examples of open-ended questions you may want to ask. 

• What did this experience teach you?
• Was this easy?  What was easy about it?
• What this difficult?  What is complicated about it?
• What may happen next in this situation?
• How did you come to this solution?
• What, if anything, would you do differently next time?
• What can we do to make things more fun next time?

14. Build Various Structures with Toys

Whether wooden blocks, LEGO blocks, or engineering blocks… giving your kid blocks to build whatever their minds can dream up is fun.  In addition, it requires them to think about how they will make a structure, put the pieces together, and creatively ensure the building's function and design. 

You may also want to challenge them to build something more complicated and watch them use their brain power to make it happen. 

15. Acting Out Skits

Impromptu activities like acting out skits help kids identify problems, develop solutions, and execute them.  This process works with multiple kids being divided into teams. 

First, you will want to write down different situations, such as resolving a disagreement between siblings or dealing with bullying on the playground on a piece of paper.  Second, you will fold the paper and place it in a hat or bowl.  

Third, each team will pick a scenario out of the hat.  Finally, you can give the kids a few minutes to discuss their solution and act out. 

16. Solving Moral Dilemmas   

In this simple game, you will help your kids solve simple dilemmas they may find themselves in.  You could write down a situation your child may find themselves in and help them learn the moral way to solve the problem.   

For instance, “The cashier gave them an additional $5 change back on my purchase.  What should they do?”  Another scenario could be, “I saw my friend cheating on a test.  Should I tell on them or let it go?”  A third one could be, “I caught my friends stealing some gum from the store.  What should I do?” 

After writing down the dilemmas and placing them in a bowl, get each child to select one and read it aloud.  Finally, you will help them devise morally correct solutions to the moral dilemma. 

17. Animal Pairing Game  

This is a fun and creative game to help your kids with focus, critical thinking, and team building skills .  In addition, this activity requires an even number of players to participate (4, 6, 8, etc.) 

Before starting the game, you will want to write the names of different animals twice, each on a separate slip of paper.  Then pass out the slips of paper to each individual or team member, instructing them not to share with anyone the name of the animal they received. 

Then the children will perform activities the animals might do without talking or making sounds.  Some of these activities might include:

• The way the animal cleans or grooms itself
• The way the animal sleeps
• The way the animal fights
• The way the animal eats or drinks
• The way the animal walks or runs

The goal is for each child to successfully pair up with the other child who has selected the same animal.

How Problem Solving in Childhood Helps in Adulthood

Children are not born with problem-solving skills. It is something that needs to be learned and developed over time .

From babies who learn how to communicate their needs to toddlers who figure out how to get what they want, to children who are starting to understand the consequences of their actions – problem-solving is a process that begins in childhood and continues into adulthood.

Some of the benefits of teaching problem-solving skills to children include:

• Improved critical thinking skills
• Better decision-making skills
• Enhanced creativity
• Improved communication and collaboration skills
• Increased confidence

There are many ways to teach problem-solving skills to children. The activities mentioned above are just a few examples. It is important to find activities that are appropriate for the age and abilities of the child.

With practice, children will develop these skills and be better prepared to face challenges in both childhood and adulthood.

Final Thoughts About Fun Problem Solving Activities For Kids

These are just a few ideas to get you started on teaching your child crucial problem solving skills. Perhaps they’ve inspired to come with some of your own, or seek out others? The important thing is to make sure the activity is age-appropriate and challenging enough to engage the kids.

Problem-solving skills are important for kids to learn because they can be applied to various situations in life. These skills also promote critical thinking, which is an important life skill.

There are many other problem-solving activities for kids out there. In time, you’ll find the ones that work best for your child.  And be sure not to forget about your own needs and self-improvement, both of which will make you a better parent and mentor. Here are some useful activities for adults to get your started.

Finally, if you want to level up your parenting skills, then check out this resource that will show you how to get your kids to listen WITHOUT yelling, nagging, or losing control .

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Geometry Math End of Year Project plus Problem Solving Tasks

Subject: Mathematics

Age range: 7-11

Resource type: Unit of work

Last updated

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This project based learning resource is an engaging Geometry based Math mini project revolving around designing a Gnome village or town using isometric paper and is a great back to school or end of term activity. The project lasts up to 5 lessons plus there are additional problem solving worksheets that could fill 2 more lessons. Includes fun geometric tasks, bursting with mathematical concepts and math skills such as isometric drawings, 3D shapes, elevation drawings and plans. It also offers opportunities to be creative and to develop number problem solving strategies.

I’m certain you and your students will enjoy Gnome Homes. My students always love it and still talk about it years later!

The aim of the task is to create all the 15 different shapes out of 4 Multilink cubes and then design a Gnomes village using these shapes as buildings. The village/town must be decorated in a theme and as this can be set as a competition within the class or year group, the student with the most creative Gnome Homes, wins.

Not only must students design their village, they must also work out the costs involved with each building relating to the ground rent, paint for the walls and tiles for the roofs.

There are activities and problem solving questions based on the task, that are available for students who need extension work.

Finished products can be laminated for a super wall display.

Can be set as a class or year group competition and entries displayed.

What’s Included Teacher Guide Starter activity Printable Isometric Paper Examples of previous work Student worksheets Problem Solving Tasks Answer Keys

**Here’s what others say ** “Students completed this at the end of the year and loved it. The directions were really clear and I love the built in differentiation. One of their favorite activities of the year!”

“My students’ creativity really came through with this activity. I had gnome villages with everything from carnivals to an IKEA store. The real-world connection of costs of building was great.”

“This was a super fun project for my enriched students. They were engaged and practicing without even realizing they were.”

“Amazing resource!”

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TES Resource Team

We are pleased to let you know that your resource Geometry and Math Creative Project Year 6 - 8, has been hand-picked by the Tes resources content team to be featured in https://www.tes.com/teaching-resources/blog/post-sats-projects-year-6-classes in May 2024 on https://www.tes.com/teaching-resources/blog. Congratulations on your resource being chosen and thank you for your ongoing contributions to the Tes Resources marketplace.

rachelbala3

Thank you so much. It is so nice for this resource to be picked. I have been doing it for over 25 years now and literally hundreds of students worldwide have created a Gnome Home. They talk about it for years afterwards so I am so pleased that perhaps many more students will have the opportunity . It is a real crowd pleaser! Many thanks again for the showcase . Much appreciated.

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Year 6 tasks

The Ministry is migrating nzmaths content to Tāhurangi.             Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz).  When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024.  e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

To solve maths problems at year 6 it is very important for your child to be able to instantly recall addition and subtraction facts up to 20, and multiplication and division facts up to 10 x 10.

e-ako maths provides free online basic fact learning tools which will help your child learn their basic facts, as well as a collection of games to improve their speed and accuracy. If you think this would benefit your child, click to read how to access this resource  (show instructions).

• To access e-ako maths, your child will need an account. You can make a new account for free, but check first whether they already have one that they use at school. If they do, they can use the same username and password to use e-ako maths at home.
• You can log in to e-ako maths or register a new account from the e-ako maths home page . If you are registering a new account to use at home you will need to click the "No join code? Click here." button and then "I am learning at home".

• The two large green boxes at the top are 'Learning tools' which will test the basic facts your child knows, and then help them learn the ones they don't already know.
• The blue buttons below are a collection of games designed to practise basic facts to improve speed and accuracy. 
• In Year 3 your child should mostly be concentrating on learning and practising their addition and subtraction facts, the buttons on the left.

Click to read about the purpose of the tasks below  (show purpose).

The tasks in this section are intended:

• for students in year 6 
• to complement similar class tasks
• to be a selection only of enjoyable learning opportunities for your child (and for you) 
• to generate useful explanations and discussions between you and your child.

The tasks in this section are NOT: 

• intended to be comprehensive in their coverage of all maths at year 6
• drill and practice exercises to learn basic facts.

These Year 6 tasks recognise that students:

• are mostly working at level 3 of the NZ Curriculum, growing in their understanding of number, algebra, geometry, measurement and statistics
• are all different, and some find parts of maths easier or harder than others
• are learning a range of approaches to solving problems that often involve several steps
• learn from and appreciate tasks presented in a variety of ways
• respond well to supportive questions from adults, such as, ‘What is the question asking you to do?’, or ‘What do you already know that might help you (solve the problem)?’
• enjoy exploring open tasks for which there can be a range of appropriate approaches and solutions (accordingly, set answers are not included for a number of these tasks).

We suggest that you ask your child what they are learning in maths at school, and select a task from this menu.

Click for  versions with Māori content .

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