year 2 problem solving nrich

Resource: Year Two Maths Problem Solving Activities Linked to NRICH

Add your heading text here, year two maths problem solving activities linked to nrich.

There are 22 maths problems which cover all of the maths objectives in the Year 2 curriculum for children to do independently. These are linked to the NRICH website .

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Phonics Phase 1 planning

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Helpful Phonics

Great Book, really helpful phonics planning. Would definitely recommend when teaching phonics to children.

Phonics 1 book

Highly recommend this informative phonics book. Everything you need to know about phase 1 and explained in good detail.

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Interactive Tasks and Games

Interactive tasks and games.

South Australia

Department for education.

Nrich - a website with maths activities and games

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Resources to develop mathematical reasoning and problem solving. Nrich aims to enrich the mathematical experiences of all learners and embeds rich mathematical tasks into everyday classroom practice.

Structure and features

Activities and games can be explored independently or together with families.

The website covers topic such as:

• measurement
• problem solving

The 'Thinking Mathematically' sections provide additional educational activities.

Links and files

Teacher notes.

The resources are grouped into levels. Level 1 aligns with early years, while level 4 aligns with lower secondary. Teachers can use the search functionality to find tasks that match the topic that they are teaching.

The tasks are not mapped to the Australian Curriculum but align well with the mathematical concepts.

Page last updated: 12 Oct 2022

learningathome [at] sa.gov.au

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Or search by topic

Number and algebra

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

Geometry and measure

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

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Developing positive attitudes
• Cross-curricular contexts
• Physical and digital manipulatives

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

For younger learners

• Early Years Foundation Stage

Addition and Subtraction

These activities are part of our Primary collections , which are problems grouped by topic.

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.

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?

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.

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.

Cuisenaire Environment

An environment which simulates working with Cuisenaire rods.

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.

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?

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?

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 Joint Mathematical Council of the United Kingdom

Addressing the five ‘big questions’ in problem-solving with NRICH

The importance of ensuring learners acquire the problem-solving skills which will enable them to thrive both socially and economically in their increasingly automated world is widely recognised (Luckin et al., 2017). Nevertheless, government inspectors have reported serious concerns about the quality and quantity of problem-solving in our schools (Ofsted, 2015). This summer schools were challenged to reflect on ‘Five big questions for problem-solving’ (EEF, 2021). In this blog, we will consider each of those five questions and explore the ways that the NRICH team is supporting schools to address them.

Question one: Do teachers in your school select genuine problem-solving tasks for which pupils do not already have a ready-made method available?

Too often, learners are presented with routine word problems which merely require the application of a known algorithm. ‘Genuine’ problems enable them to make their own problem-solving decisions by choosing their own strategies and enabling them to compare their approach with those of other learners, thus developing their problem-solving efficiency and flexibility. At NRICH , our award-winning activities allow learners to develop these key skills alongside the confidence to tackle genuine problems. Moreover, our ‘ low threshold, high ceiling ‘ approach enables everyone to get started on the problem while ensuring a suitable level of challenge too, making them ideal for whole-class teaching.

Question two: Are pupils given the opportunity to see – through multiple worked examples – to use, and to compare different approaches to solving a problem?

Many problems can be explored in more than one way. Working flexibly, making connections between different areas of the curriculum and reflecting on various problem-solving approaches are key steps towards becoming a more fluent mathematician. NRICH encourages learners to develop these skills in these two ways:

Our primary , secondary and post-16 Live Problems invite learners to explore and submit their ideas to the team. We review each submission that we receive and publish a selection on our website showcasing different approaches and the reasoning behind them.

Our NRIC H online activities sometimes feature ‘hide and reveal’ buttons showcasing different starting points towards a solution for learners to explore further for themselves. This approach enables learners to widen their range of strategies for solving unfamiliar problems and develop alternative approaches to explore when they get stuck using their first-choice strategy.

Question three: Are pupils encouraged to use visual representations to support them to solve a problem?

One of the most important approaches towards solving an unfamiliar problem is drawing a good diagram. Learning to draw diagrams is a skill which we encourage learners of all ages to develop alongside their other mathematical skills and knowledge. From sketching graphs to drawing a bar model, good diagrams can help learners clarify their understanding and identify possible ways forward.

Our four steps towards problem-solving feature highlights the importance of drawing a diagram to enable young learners to get started on a problem. We often highlight a useful diagram, table or sketch graph in the solutions chosen for publication. As learners progress through their learning, the team model more specific drawing skills, such as sketching a graph to help solve a STEP problem.

Question four: Are pupils supported to monitor, reflect on, and communicate their reasoning and choice of strategies, possibly through the use of prompt questions?

NRICH  encourages learners to reflect on their learning using this approach inspired by the Strands of Mathematical Proficiency model introduced by Kilpatrick et al. (2001).

Our approach uses child-friendly language that teachers and parents can share with students five key ingredients that characterise successful mathematicians. At NRICH , we believe that learning mathematics is about much more than just learning topics and routines. Successful mathematicians understand the curriculum content and are fluent in mathematical skills and procedures, but they can also solve problems, explain their thinking and have a positive attitude about themselves as learners of mathematics.

With this in mind, we have created  this self assessment tool  to help learners recognise where their mathematical strengths and weaknesses lie. We hope learners will explore NRICH activities and then take time to reflect on their own mathematical capabilities using our model.

Question 5: Is professional development time allocated to develop teachers’ pedagogical understanding of problem-solving, with particular support for early career teachers?

NRICH supports teachers to maximise the potential of our activities by offering free, regular professional development for teachers .  Each session is delivered online, enabling teachers to access the support wherever they are based, reducing teacher travel and cover costs for schools. We also record the sessions and upload them to our website so that schools can access them for future professional development days or staff/department meetings in their settings.

The live sessions are led by NRICH team members and they link directly to our latest primary , secondary and post-16 Live Problems. This approach enables teachers to consider the possibilities of the activities with the NRICH team before exploring them the next day with their own classes. Later, they are invited to share their classwork with our team for possible publication on the NRICH website.

The five ‘big questions’ provide excellent starting points for evaluating the teaching and learning of problem-solving in different settings. I hope that this blog shares an insight into the different ways that NRICH can support schools to address the five questions for themselves by engaging with our activities, Live Problems and teacher webinars.

Dr Ems Lord FCCT

Director of NRICH

Centre for Mathematical Sciences

University of Cambridge

Selected references

EEF. (2021). EEF Blog: Integrating evidence into maths teaching – guiding problem-solving. Accessed from https://educationendowmentfoundation.org.uk/news/eef-blog-integrating-evidence-into-mathematics-guiding-problem-solving /

Kilpatrick, J. Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics (Vol. 2101). J. Kilpatrick, & National research council (Eds.). Washington, DC: National Academy Press.

Luckin, R., Baines, E., Cukurova, M., Holmes, W., & Mann, M. (2017). Solved! Making the case for collaborative problem-solving. Accessed from http://oro.open.ac.uk/50105/1/solved-making-case-collaborative-problem-solving.pdf

Ofsted. (2015). Better Maths Conference Spring Keynote 2015. Accessed here https://www.slideshare.net/Ofstednews/better-mathematics-keynote-spring-2015