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- Authentic tasks
- F - 10 Resources
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:
| Criteria | Elaboration |
|---|---|
| Intriguing contexts capture the students’ interests and curiosities | An opportunity for students to relate learning to their own lives and communities. High student motivation/enjoyment and sense of purpose can be anticipated or observed. |
| Problem solving is required to overcome obstacles | Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
| Low entry/ high ceiling, and an open-middle encourages different strategies | Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
| Opportunities for creative thinking and or visualising | Students invent, discover and imagine new ways to solve a problem. Students make connections and see relationships by visualising the problem or representing solutions visually. |
| Encourages reasoning and critical thinking | Logical, rational and critical thinking. eg: estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| Opportunity to collaborate and see others working mathematically | Students challenge each other, the computer, the teacher etc and observe how they work mathematically. Make decisions in groups to communicate findings, engage with different ideas, monitor and regulate each other's thinking. |
| Opportunities for students to develop fluency | Estimating, collecting and interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Promotes feedback and metacognition. | Self and peer reflection targeted at specific aspects of the work. eg: knowledge; how your thinking is changed as a result of lesson. Affective traits eg: problem solving attitude, collaborative skills. |
| Extends knowledge or applies knowledge in new contexts | Provides students with access to forms of knowledge beyond what they can pick up in everyday life or via the Internet. |
| Promotes an understanding of the ‘why’ and ‘how’ of mathematics | Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big Ideas) in different ways eg: developing number sense, place value. |
| Guides future learning | Provides data on student growth to guide future direction. eg: identifies patterns or errors, level of progress towards goal. Makes suggestions for future learning. |
Used with permission © Martin Holt Educational Consultant 2017
If you would like to learn more about this approach to assessing or using tasks contact [email protected]
Statistics and probability
| NRICH problem solving task: | Scootle lesson sequence: |
| Target Level: F - 2 | Target Level: 1 - 6 |
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Measurement and geometry
| Wildmaths interactive game: | Teach Engineering investigation: |
| Target Level: 2-4 | Target Level: F-2 |
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Number and algebra
| NZMaths lesson sequence: | MAV problem solving task: | ReSolve Maths by Inquiry lesson sequence: |
| Target Level: 5-6 | Target Level: 1-6 | Target Level: 5-6 |
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These support pages were produced using Strategic Partnership Program funding from the Department of Education and Training.
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Learning Path
Maths week pdst problem solving - junior and senior infants learning path.
Click on the Title to open the problem...Upload pictures or answers to the Padlet to enter the Maths Week competition for PDST Numeracy Manuals and a class set of Active Learning Boards. 5 resources in this Learning Path
Incey Wincey Spider
An interactive game encouraging students to move along tracks - forward & back. Nice introduction to negative numbers. Resource can be used on the interactive whiteboard (Flash required) or worksheet downloaded. Teacher guide provided within the link. Dice needed.
How it maps to the curriculum
Strand: Number
Strand unit: Comparing & Ordering
Content objective: This resource should enable a child to:
- use the language of ordinal number: first, last
- use the language of ordinal number: first, second, third, last
Suggestions for use: Use as part of Maths Week Problem Solving activity. Submit problem solving pictures to the Scoilnet-PDST Padlet
Strand unit: Analysis of Number: Numeration
Three Block Towers - Teacher Guide to Activity
Nrich problem solving activity. Link explains the activity, provides worksheets for 3 blocks and 4 blocks challenge and a poster for the problem solving challenge.
Strand: Early Maths Activities
Strand unit: Classifying
Suggestions for use: Problem for Maths Week. Take pictures of the problem solving process and submit the PDST - Scoilnet Padlet.
Strand: Algebra
Lollipop Stick Shapes - PDST
A great problem solving challenge from the Shape and Space Manual, page 72. Pupils are given lollipop sticks to create as many 2D shapes as they can.
Strand: Shape & Space
Strand unit: 2-D Shapes
- combine and divide 2-D shapes to make larger or smaller shapes
Worms (Length) - PDST
A great problem solving challenge from the Measures Manual, page 37. Pupils are given play dough to make a worm. Pupils describe their worm with keywords, long, short, longer than, shorter than..etc
Strand: Measures
Strand unit: Length
Suggestions for use: Maths week problem solving challenge. Submit pictures of the problem solving challenge to the PDST-Scoilnet Padlet.
Noah - Nrich
A problem solving question from Nrich website for the PDST Numeracy - Maths Week Challenge. A very good problem to use when practicing counting.
Suggestions for use: Maths week problem solving challenge. Submit pictures of problem solving techniques to the PDST-Scoilnet Padlet.
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Number and algebra
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Working mathematically
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For younger learners
- Early Years Foundation Stage
Addition and Subtraction
These activities are part of our Primary collections , which are problems grouped by topic.
Number Balance
Can you hang weights in the right place to make the the number balance balanced?
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
Domino Sorting
Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
What Was in the Box?
This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?
One Big Triangle
Make one big triangle so the numbers that touch on the small triangles add to 10.
Arranging Additions and Sorting Subtractions
Order these four calculations from easiest to hardest. How did you decide?
Pairs of Numbers
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Butterfly Flowers
Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?
Subtraction Slip
Can you spot the mistake in this video? How would you work out the answer to this calculation?
Number Lines
A resource to try once children are familiar with number lines, and they have begun to use them for addition. It could be a good way to talk about subtraction. Leah and Tom each have a number line. Can you work out where their counters will land?
The Add and Take-away Path
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Equivalent Pairs
Can you match pairs of cards which show the same amount?
Two Spinners
What two-digit numbers can you make with these two dice? What can't you make?
Cuisenaire Counting
Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
Find all the numbers that can be made by adding the dots on two dice.
What Could It Be?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
What's in a Name?
What do you notice about these squares of numbers? What is the same? What is different?
Sort Them Out (1)
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Unit Differences
This challenge is about finding the difference between numbers which have the same tens digit.
Poly Plug Rectangles
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Dicey Addition
Who said that adding couldn't be fun?
Sitting Round the Party Tables
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Doing and Undoing
An investigation looking at doing and undoing mathematical operations focusing on doubling, halving, adding and subtracting.
How Do You See It?
Here are some short problems for you to try. Talk to your friends about how you work them out.
What could the half time scores have been in these Olympic hockey matches?
Strike it Out
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Cuisenaire Environment
An environment which simulates working with Cuisenaire rods.
Ladybirds in the Garden
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Eggs in Baskets
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?
Secret Number
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
Birthday Cakes
Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
Find the Difference
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Heads and Feet
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Jumping Squares
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Number Round Up
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
The Brown Family
Use the information about Sally and her brother to find out how many children there are in the Brown family.
The Tall Tower
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
IMAGES
VIDEO
COMMENTS
Developing excellence in problem solving with young learners. Becoming confident and competent as a problem solver is a complex process that requires a range of skills and experience. In this article, Jennie suggests that we can support this process in three principal ways.
A Guide to Problem Solving. When confronted with a problem, in which the solution is not clear, you need to be a skilled problem-solver to know how to proceed. When you look at STEP problems for the first time, it may seem like this problem-solving skill is out of your reach, but like any skill, you can improve your problem-solving with practice.
The focus of this feature is to show that every lesson can be a problem solving lesson. In planning for problem solving there are several areas to consider: 1. The type of problem you want to focus on 2. The problem-solving strategy or skill you wish the children to develop 3. The NRICH four stage problem-solving process This feature offers ...
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles. Skip over navigation. menu search ... Collections of NRICH tasks designed to develop learners' key problem-solving skills. Developing positive attitudes.
In planning for problem solving there are several areas to consider: 1. The type of problem you want to focus on. 2. The problem-solving strategy or skill you wish the children to develop. 3. The NRICH four stage problem-solving process. This feature offers ideas on all of these aspects and also links different NRICH activities to each.
The Problem-solving Classroom By NRICH Primary Team and Jenny Earl This article forms part of our Problem-solving Classroom Feature, exploring how to create ... The length of student response increases (300-700%) 2. More responses are supported by logical argument. 3. An increased number of speculative responses.
A selection of rich tasks ideal for developing subject content knowledge, mathematical thinking, and problem-solving skills. The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.
Primary Teachers. Our favourite rich tasks, organised by curriculum topic and age group. Collections of NRICH tasks designed to develop learners' key problem-solving skills. Collections of tasks designed to encourage learners to be curious, resourceful, resilient and collaborative. Problems inviting solutions, together with our most recently ...
Curriculum, pedagogy and assessment. We are committed to: Regularly embedding non-standard problem-solving opportunities in our maths curriculum for all. Ensuring that problems, and classroom support, offer opportunities for all to experience both struggle and success. Allocating time to developing key problem-solving skills and positive attitudes.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. NRICH is part of the family of activities in the ...
Authentic tasks. 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 ...
A collaboration between the Mathematics and Education Faculties, NRICH focuses on developing problem-solving, supporting every stage of school education with free online resources for ages 3-19 and their teachers. NRICH's materials have always been shared online, free of charge and without any barriers, internationally, and the site welcomed ...
30 Nov 2023. Our NRICH programme has launched a new initiative to help schools prioritise problem-solving in maths. The NRICH Problem-Solving Schools programme will offer free resources, advice and teacher professional development training. Problem-solving is a critical skill when it comes to empowering students for the future. It opens up a ...
Enriching mathematics for all learners. We offer curriculum-linked resources for students aged 3-18, designed to nurture curious, resourceful and confident learners of school mathematics. All of our resources are free to use by everyone. We are based in the Faculty of Mathematics at the University of Cambridge.
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles. ... We aim to help you raise the profile of mathematical problem-solving in your school. Our Charter offers a framework intended to inform policy and practice.
Reasoning and Problem Solving Measure Length (m) Reasoning and Problem Solving Measure Length (m) Developing 1a. Various possibilities, any reasonable answer acceptable, for example: bus 8m and 70cm; scooter 1m and 20cm 2a. The sweet should be measured in cm. 3a. No, Alfie has not aligned the snake's tail with the 0 on the scale. Expected 4a.
Nrich problem solving activity. Link explains the activity, provides worksheets for 3 blocks and 4 blocks challenge and a poster for the problem solving challenge. View full description . in Mathematics. ... Strand unit: Length. Suggestions for use: Maths week problem solving challenge. Submit pictures of the problem solving challenge to the ...
About Nrich. We believe that successful mathematicians understand curriculum concepts and are fluent in mathematical skills and procedures, and can also solve problems, explain and justify their thinking, and have a positive attitude towards mathematics and to themselves as learners of mathematics. With this in mind, we offer rich mathematical ...
Early Years Practitioners. Our Early Years resources will support you as you develop the initial building blocks for young children's mathematical thinking, reasoning and problem solving. Browse this section to find activities for children, the latest articles for Early Years practitioners, and examples of children's thinking.
Strike it Out. Age 5 to 11. Challenge Level. Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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? Age 7 to 11. Challenge Level. Problem Primary curriculum.