open ended problem solving year 6

Open-Ended Maths Problems Task Cards

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Are you looking to extend your students’ mathematical thinking? Are you seeking ways to apply maths concepts you have taught engagingly and authentically? Are you after easy yet effective ways to differentiate and assess mathematical understandings? If so, these open-ended maths task cards are the perfect resource for your class.  

With 24 open-ended problems across a range of mathematics content areas, this set of cards challenges students to flexibly combine and apply a range of mathematical skills, with the opportunity to demonstrate multiple answers.

These task cards can be used for independent or guided practice. Selected cards can be used as formative assessment tools within focused units, or the set can be used throughout the year to continue to consolidate prior learning, regardless of your classroom’s current topic.

Designed with four problems per page and with the option of colour or black and white cards, simply print, cut and distribute to students. (They can also be laminated to be used again and again with different students).

Ensure your students get the most out of these challenges and know how to show their best thinking with our Solving Open-Ended Problems PowerPoint. Or you can have all the open-ended challenges in one place in our Open-Ended Maths Problems Booklet.

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KS2 Maths Investigations Based On Real Life In Primary School

Sophie Bessemer

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

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

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

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

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

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

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

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

KS2 Maths Investigations: Problem solving in context

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

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

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

KS2 Topical Maths Problems

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

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

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

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

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

1. KS2 Maths Investigations Involve Pupils Talking and Reasoning

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

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

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

2. KS2 Maths Investigations Cement Higher Order Reasoning Skills

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

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

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

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

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

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

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

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

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

More problem solving and reasoning articles

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

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

1. Date-based themes for maths problem solving activities

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

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

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

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

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

2. Trends and pop-culture KS2 maths investigations

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

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

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

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

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

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

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

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

4. Cool factor for primary teachers – even in maths

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

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

5. Make your maths investigations REALLY relevant

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

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

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

Instead of apples, why not their favourite snack?

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

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

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

Autumn Term maths investigations year 6 and year 5

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

Spring Term maths investigations year 6 and year 5

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

Summer term maths investigations year 6 and year 5

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

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

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

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

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Open-Ended Tasks and Questions in Mathematics

by CristinaM. | Sep 13, 2014 | inquiry , math , thinking | 5 comments

One way to differentiate in math class is creating open-ended tasks and questions (I talked about several differentiation strategies I use here – Mathematically Speaking ).

I think it is useful to clarify the scheme of mathematical problems – below I used Foong Pui’s research paper:

“Problems in this classification scheme have their different roles in mathematics instruction as in teaching for problem solving, teaching about problem solving, or teaching via problem solving.”

1.   CLOSED problems   are well-structured problems in terms of clearly formulated tasks where the one correct answer can always be determined in some fixed ways from the necessary data given in the problem situation.

 A. Routine closed problems – are usually multi-step challenging problems that require the use of a specific procedure to arrive to the correct, unique, answer.

B. Non-routine closed problems – imply the use of heuristics strategies * in order to determine, again, a single correct answer.

*Problem-solving heuristics: work systematically, tabulate the data, try simpler examples, look for a pattern, generalize a rule etc.

Routine problem : Minah had a bag of rice. Her family ate an equal amount of rice each day. After 3 days, she had 1/3 of the rice left. After another 7 days, she had 24 kg of rice left. How much rice was in the bag at first?

Non-routine problem : How many squares are there in a chess board?

2. OPEN –ENDED problems – are often named “ill-structured” problems as they involve a higher degree of ambiguity and may allow for several correct solutions. Real-life mathematical problems or mathematical investigations are of this type – e.g. “How much water can our school save on a period of four months?” or “Design a better gym room considering the amount of money we can spend.”

FEATURES of open-ended problems :

• There is no fixed answer (many possible answers)
• Solved in different ways and on different levels (accessible to mixed abilities)
• Empower students to make their own mathematical decisions and make room for own mathematical thinking
• Develop reasoning and communication skills

HOW do you create open-ended tasks?

Usually, in order to create open-ended questions or problems, the teacher has to work backwards :

• Indentify a mathematical topic or concept.
• Think of a closed question and write down the answer.
• Make up a new question that includes (or addresses) the answer.

STRATEGIES to convert closed problems/questions

• Turning around a question

CLOSED: What is half of 20?

OPEN: 10 is the fraction of a number. What could the fraction and the number be? Explain.

CLOSED:  Find the difference between 23 and 7.

OPEN: The difference between two numbers is 16. What might the numbers be? Explain your thinking.

CLOSED: Round this decimal to the decimal place 5.7347

OPEN: A number has been rounded to 5.8. What might the number be?

CLOSED: There are 12 apples on the table and some in a basket. In all there are 50 apples. How many apples are in the basket?

OPEN: There are some apples on the table and some in a basket. In all there are 50 apples. How many apples might be on the table? Explain your thinking.

• Asking for similarities and differences.

Choose two numbers, shapes, graphs, probabilities, measurements etc. and ask students how they are alike and how they are different.

Example: How are 95 and 100 alike? How are they different?

Possible answers:

They are alike because you can skip count by 5s, both are less than 200, both are greater than 90 etc.

They are different because one is a three-digit number, only one ends in 5, only one is greater than 99 etc.

Example: How are the numbers 6.001 and 1.006 alike? How are they different?

• Asking for explanations.

Example: Compare two fractions with different denominators. Tell how you compare them.

Example: 4 is a factor for two different numbers. What else might be true about both numbers?

• Creating a sentence

Students are asked to create a mathematical sentence that includes certain numbers and words.

Example: Create a sentence that includes numbers 3 and 4 along with the words “more” and “and”.

• 3 and 4 are more than 2
• 3 and 4 together are more than 6
• 34 and 26 are more than 34 and 20 etc.

Example: Create a question involving multiplication or division of decimals where the digits 4, 9, and 2 appear somewhere.

Example: Create a sentence involving ½  and 64 and the words “less” and “twice as much”.

• Using “soft” words.

Using the word “close” (or other equivalents) allows for a richer, more interesting mathematical discussion.

Example: You multiply two numbers and the product is almost 600. What could the numbers have been? Explain.

Example: Add two numbers whose sum is close to 750. What can the numbers be? Explain.

Example: Create two triangles with different but close areas. (*instead of, “Create a triangle with an area of 20 square inches.”)

……………………………………………………………………………………………………………………………………………………………………………………………………

A few important considerations are to be made when creating open-ended problems or questions.

• Know your mathematical focus .
• Develop questions with the right degree of ambiguity (vague enough to be interesting and to allow for different responses, but not too vague so as students get frustrated).
• Plan for two types of prompts :
• enabling prompts (for students who seem unable to start working)
• extension prompts (for students who finish quickly)

High quality responses from students have the following features:

• Are systematic (e.g. may record responses in a table or pattern).
• If the solutions are finite, all solutions are found.
• If patterns can be found, then they are evident in the response.
• Where a student has challenged themselves and shown complex examples which satisfy the constraints.
• Make connections to other content areas.

……………………………………………………………………………………………………………………………………………………………………………………………………………….

References:

Designing Quality Open-Ended Tasks in Mathematics , Louise Hodgson, 2012

Using Short Open-ended Mathematics Questions to Promote Thinking and Understanding , Foong Pui Yee, National Institute of Education, Singapore

Good Questions – Great Ways to Differentiate Mathematics Instruction , Marian Small, 2012

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Thank you for posting this. I appreciate how there is a comparison between the two (closed and open ended) types of questions and the considerations that go along with each. Thanks!

You are welcome!

Wow, well-written, thank you. I’m excited that my teaching is getting great, clear, and organized at the level that I’m at. But this article reminds me there are many higher levels I can get to, including this area of more open-endedness. Thank you!

I am happy to have helped even in a small way!

Thank you so much

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Problem Solving

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

Problem Solving in Primary Maths - the Session

Quality Assured Category: Mathematics Publisher: Teachers TV

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

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

Cards for Cubes: Problem Solving Activities for Young Children

Quality Assured Category: Mathematics Publisher: Claire Publications

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

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

Quality Assured Category: Computing Publisher: Department for Education

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

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

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

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

Primary mathematics classroom resources

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

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

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

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

Number Picnic: The problems make ideal starter activities

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

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

GAIM Activities: Practical Problems

Quality Assured Category: Mathematics Publisher: Nelson Thornes

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

Examples include:

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

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

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

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

Go Further with Investigations

Quality Assured Category: Mathematics Publisher: Collins Educational

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

Starting Investigations

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

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

NRICH Primary Activities

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

Mathematical reasoning: activities for developing thinking skills

Quality Assured Category: Mathematics Publisher: SMILE

Problem Solving 2

Reasoning about numbers, with challenges and simplifications.

Quality Assured Category: Mathematics Publisher: Department for Education

Popular searches in the last week:

Problem-solving maths investigations for year 6.

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

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

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

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

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

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

You can find Hamilton's investigations for Year 6:

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

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

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

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

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Year 6 Maths Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

22 February 2018

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Year 6 Maths Scheme of Work (based on White Rose Maths)

A scheme of learning with planning and worksheets included for Year 6 Maths. Included are 90 lessons that cover: Place Value Rounding Negative Numbers Roman Numerals Indices Inverse operations Written addition and subtraction Mental addition and subtraction Written multiplication and division Order of operations Finding fractions of amounts Comparing fractions Converting between improper and mixed number fractions Add and subtract fractions Multiply fractions together Multiply fractions by whole numbers Divide fractions by whole numbers Percentages Fraction, decimal and percentages Ratio Algebra including missing information, expressing problems, satisfying equations, satisfying two variables and sequences Multiplying and dividing by 10, 100 and 1000 Multiplying decimal numbers Finding percentages of amounts x 2 Fraction, decimal and percentage equivalents Converting measurements Miles and kms Time Shape with same area but different perimeter and vice versa Volume Area Area of triangles Addition and subtraction (Same as 1st planning scheme as it is revision) Multiplication (Same as 1st planning scheme as it is revision) Division (Same as 1st planning scheme as it is revision) Worksheets are differentiated three ways with a mastery aim running throughout. Having used a similar format in my own lessons, these sheets often provide enough challenge for two days lessons, with children taking on the easier work then moving on to harder challenges within the other sheets. These have all been made with mastery in mind and so follow this pattern. Worksheet One - Works on practise and fluency (LA) Worksheet Two - Practise, fluency and reasoning (MA) Worksheet Three - Practise, fluency, reasoning and problem solving (HA) Worksheet Four - Same as worksheet three as a spare for anybody who finishes problem solving Answers are included for each sheet.

Maths resources

A range of Maths resources including fully planned and resourced lessons that can all be used in Years 5 and 6.

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April 27, 2012 / 7 Comments

Open-ended problems in elementary school mathematics

I’m hoping to find (or potentially build, given how well my search is going) some open-ended problems appropriate for elementary school math classes. By open-ended problems, I mean problems which:

• do not have an obvious solution,
• require some time to figure out,
• have multiple solutions,
• may require some assumptions are made by the students,
• are extendable in some way,
• require that the solution be explained, rather than a single number given as the answer.

I’ve found that the definition of open-ended problem seems to vary quite a bit, with many sources that I’ve found using free-response or open-response as a synonym for open-ended.

Here’s a sample question (forgive the wording, it may need improvement).

Ellen is planning a party for her friends. She has invited 100 of them, but she doesn’t know exactly how many of her friends will attend. She wants to put out tables for her friends, and she wants to put enough chairs at each table so that none of her friends has to sit alone. Assume that her friends will fill up each table as they arrive. How many tables should she put out, with how many chairs at each table?

The curriculum link here is either counting (likely to be a slow technique so I’d recommend reducing the number of friends if this is the strategy your students are going to use), addition, multiplication, or division. Note that if you do questions like this, it is important for students to explain their reasoning, and you may need to help some students do this. You may also have to point out that since Ellen doesn’t know exactly how many of her friends will attend, this problem is harder than it looks. Also, I may or may not give the actual diagram as this likely gives away too much of the problem to students. Once students have drawn a diagram though, one could turn this into a bit of a probability question (given the diagram above, how likely is it that one of Ellen’s friends will have to sit alone?).

Does anyone else know a source of questions which are this open-ended, and are designed for elementary school students? 

Here are some resources I’ve been given or found so far:

• Numeracy tasks organized by Peter Liljedahl
• Good Questions: Great Ways to Differentiate Mathematics Instruction by Marian Small
• More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction by Marion Small
• Creative Problem Solving in School Mathematics by George Lenchner
• Galileo Math problems
• Nrich Maths
• Open ended questions in elementary school math  by Mary Kay Dyer and Christine Moynihan
• Open ended assessment tasks
• Author info

Add yours →

Matt Fletcher says:

This is exactly what we’re looking to do for our Grade 6 Math program next year. We’re trying to ditch our text and our ‘traditional’ way of teaching Math strand-by-strand, and instead focus on problem solving tasks involving multiple strands at one time and require the use of the Math Processes as outlined in the Ontario Curriculum.

We’ve found the same issue you have – that being there really isn’t a great resource out there. So far, it has involved a lot of searching on the internet and in some text books, and adapting problems which may come from a Secondary School, for our grade level.

One resource I have found useful is Math that Matters by David Stocker. While not always open-ended, the questions are based on Social Justice issues and are able to generate an incredible amount of discussion surrounding student answers.

April 30, 2012 — 8:09 pm

Gary Tupper says:

Having never taught elem, & being retired now for 12 yrs, the following may be a non-starter, but:

Little Johnnie is going to the store to buy a pair of Reeboks? which he knows will cost between $65 and $70. How much money (which denominations & coinage) should he take in order to pay the exact amount? Ie the least that will be sufficient.

Extension: The following week little Johnnie and his friend Willis are heading off to the mall to buy some game cartridges. Johnnies from Walmart will be between $20 and $25; Willis’ from Zellers will be between $35 and $40. If they pool their money, what is the least amount they need in order to pay for both exactly, without change.

April 30, 2012 — 8:41 pm

David Wees says:

I think those are both good examples of open-ended problems which fit into the curriculum nicely. I believe that in grade 1 they start looking at adding coin values together, and in grade 2 they continue that process. Thank you Gary.

May 2, 2012 — 11:47 am

Kristen Beck says:

Here are some resources I love using with my kiddos:

Just for the Fun of It! Book 1 and Book 2 – AIMS Education Foundation In the Balance Algebra Logic Puzzles – Creative Publications Get It Together Math Problems for Groups – EQUAL

I’m not sure if you can find this one but it is from Oregon Council of Teachers of Mathematics: OCTM Intermediate Problem Box Problems from TOMT, 1980 to 1992 Here is the link to their publications: http://bit.ly/Ivrrvq

I use these resources with my kiddos.

May 3, 2012 — 6:02 pm

Jerry says:

Thanks for sharing! I am a fan of open ended math questions for student to work on, because not only are they searching to solve the problem through critical thinking, but they are also creatively thinking in their own way, and I believe this type of example fits in well to a type of math examples students are personally engaged in as they are trying to find their own solution to the problem. Open ended math examples are great! Thank you for sharing!

October 4, 2016 — 2:59 am

Moriah says:

Thanks for sharing! I love open ended math questions as they give learners a chance to explore concepts for themselves and come to their own understandings and conclusions. As a tutor I find critical thinking to be one of the biggest skills kids lack across the board; this is a great task to help develop these skills.

February 9, 2017 — 2:58 am

Thanks for the post! The thing i love about open-ended math questions is that it really promotes the exploration of critical thinking, as well as creativity. These concepts are so important for the intellectual development of students, and help with all subjects and ways of life; not just math. This is something that I believe needs to be focused on more, as I agree with what Moriah said about students seeming to really lack/struggle with critical thinking.

February 23, 2017 — 12:25 am

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