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For younger learners

  • Early Years Foundation Stage

Being Collaborative - Secondary Teachers

Being Collaborative is part of our Developing Mathematical Habits of Mind collection.

Good thinkers collaborate and communicate. They work productively with other people, valuing different points of view. They are willing to change their mind when presented with convincing arguments. They know when to seek help, when to support others, when to speak up and when to compromise.

How do we help our students to become better at collaborating mathematically?

These problems are ideal to work on with others. If you encourage your students to work in pairs or small groups and share ideas, they may learn to recognise that two heads can be better than one.

You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.

Being Collaborative - Number

Number problems to work on with others.

Being Collaborative - Algebra

Algebra problems to work on with others.

Being Collaborative - Geometry

Geometry problems to work on with others.

Being Collaborative - Statistics

Statistics problems to work on with others.

American Billions

Age 11 to 14
Challenge Level Yellow star

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

What's it Worth?

Age 11 to 16
Challenge Level Yellow star

There are lots of different methods to find out what the shapes are worth - how many can you find?

Estimating Angles

Age 7 to 14
Challenge Level Yellow star

How good are you at estimating angles?

Got It

Age 7 to 14
Challenge Level Yellow starYellow star

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Stringy Quads

Age 7 to 11
Challenge Level Yellow starYellow star

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Quadrilaterals Game

Age 11 to 14
Challenge Level Yellow star

A game for 2 or more people, based on the traditional card game Rummy.

Shapely Pairs

Age 11 to 14
Challenge Level Yellow starYellow star

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

Property Chart

Age 11 to 14
Challenge Level Yellow starYellow star

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

Transformation Game

Age 11 to 14
Challenge Level Yellow starYellow star

Why not challenge a friend to play this transformation game?

Factors and Multiples Game

Age 7 to 16
Challenge Level Yellow star

A game in which players take it in turns to choose a number. Can you block your opponent?

Diamond Collector

Age 11 to 16
Challenge Level Yellow star

Collect as many diamonds as you can by drawing three straight lines.

Connect Three

Age 11 to 16
Challenge Level Yellow starYellow star

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

First Connect Three

Age 7 to 11
Challenge Level Yellow star

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?

Big and Small Numbers in Physics - Group Task

Age 16 to 18
Challenge Level Yellow star

Work in groups to try to create the best approximations to these physical quantities.

All in a Jumble

Age 11 to 14
Challenge Level Yellow starYellow star

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Reflecting Lines

Age 11 to 14
Challenge Level Yellow star

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Translating Lines

Age 11 to 14
Challenge Level Yellow star

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

Surprising Transformations

Age 14 to 16
Challenge Level Yellow starYellow star

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Jig Shapes

Age 5 to 11
Challenge Level Yellow star

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Developing Good Team-working Skills

Age 5 to 18

Group work depends on effective team work. This article describes attributes of effective team work and links to "Team Building" problems that can be used to develop learners' team working skills.

Making Rectangles

Age 7 to 14
Challenge Level Yellow starYellow star

A task which depends on members of the group noticing the needs of others and responding.

Number Match

Age 5 to 11
Challenge Level Yellow star

A task which depends on members of the group noticing the needs of others and responding.

Fraction Match

Age 5 to 11
Challenge Level Yellow star

A task which depends on members of the group noticing the needs of others and responding.

Algebra Match

Age 11 to 16
Challenge Level Yellow star

A task which depends on members of the group noticing the needs of others and responding.

Simplifying Doughnut

Age 14 to 18
Challenge Level Yellow starYellow starYellow star

An algebra task which depends on members of the group noticing the needs of others and responding.

Doughnut Percents

Age 7 to 14
Challenge Level Yellow starYellow star

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

How Would You Score It?

Age 11 to 14
Challenge Level Yellow star

Invent a scoring system for a 'guess the weight' competition.

Thirsty?

Age 5 to 7
Challenge Level Yellow star

Can you lay out the pictures of the drinks in the way described by the clue cards?

Arranging Cubes

Age 7 to 11
Challenge Level Yellow starYellow star

A task which depends on members of the group working collaboratively to reach a single goal.

Arranging Counters

Age 7 to 11
Challenge Level Yellow starYellow star

A task which depends on members of the group working collaboratively to reach a single goal.

Arranging Squares

Age 11 to 18
Challenge Level Yellow star

A task which depends on members of the group working collaboratively to reach a single goal.

The Solid

Age 11 to 16
Challenge Level Yellow star

A task which depends on members of the group working collaboratively to reach a single goal.

Solids

Age 11 to 16
Challenge Level Yellow star

A task which depends on members of the group working collaboratively to reach a single goal.

Counters in the Middle

Age 7 to 11
Challenge Level Yellow star

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Triangles in the Middle

Age 11 to 18
Challenge Level Yellow star

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Stick Images

Age 7 to 14
Challenge Level Yellow star

This task requires learners to explain and help others, asking and answering questions.

En-counters

Age 5 to 7
Challenge Level Yellow star

This task requires learners to explain and help others, asking and answering questions.

Coordinate Designs

Age 11 to 14
Challenge Level Yellow star

This task requires learners to explain and help others, asking and answering questions.

Guess the Houses

Age 5 to 7
Challenge Level Yellow star

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

What Shape?

Age 7 to 14
Challenge Level Yellow star

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Which Quadratic?

Age 14 to 18
Challenge Level Yellow star

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.

Guess the Function

Age 16 to 18
Challenge Level Yellow star

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Castles in the Middle

Age 7 to 14
Challenge Level Yellow starYellow star

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Guess the Dominoes

Age 7 to 11
Challenge Level Yellow star

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Which Solid?

Age 7 to 16
Challenge Level Yellow star

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Quad Match

Age 7 to 11
Challenge Level Yellow starYellow star

A task which depends on members of the group noticing the needs of others and responding.

Sociable Cards

Age 11 to 14
Challenge Level Yellow star

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

What Does Random Look Like?

Age 11 to 14
Challenge Level Yellow star

Engage in a little mathematical detective work to see if you can spot the fakes.

Olympic Records

Age 11 to 14
Challenge Level Yellow star

Can you deduce which Olympic athletics events are represented by the graphs?

What's That Graph?

Age 14 to 18
Challenge Level Yellow starYellow star

Can you work out which processes are represented by the graphs?

Sticky Data

Age 5 to 7
Challenge Level Yellow star

You'll need to work in a group on this problem. Use your sticky notes to show the answer to questions such as 'how many girls are there in your group?'.

Magic Letters

Age 11 to 14
Challenge Level Yellow star

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Constructing Triangles

Age 11 to 14
Challenge Level Yellow star

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Developing Good Team-working Skills in Primary Schools

Age 5 to 11

This article looks at team building in the primary context.

Olympic Measures

Age 11 to 14
Challenge Level Yellow star

These Olympic quantities have been jumbled up! Can you put them back together again?

Dice in a Corner

Age 7 to 11
Challenge Level Yellow starYellow starYellow star

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

The Dice Train

Age 7 to 11
Challenge Level Yellow starYellow starYellow star

This dice train has been made using specific rules. How many different trains can you make?

Group-worthy Tasks and Their Potential to Support Children to Develop Independent Problem-solving Skills

Age 5 to 11

In this article for teachers, Jennie Pennant outlines how group-worthy tasks support the development of children's problem-solving skills.

Up, Down, Flying Around

Age 11 to 14
Challenge Level Yellow star

Play this game to learn about adding and subtracting positive and negative numbers

Shape Draw

Age 7 to 11
Challenge Level Yellow star

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

Picturing the World

Age 14 to 16
Challenge Level Yellow star

How can we make sense of national and global statistics involving very large numbers?

Perception Versus Reality

Age 14 to 18
Challenge Level Yellow star

Infographics are a powerful way of communicating statistical information. Can you come up with your own?

Box Plot Match

Age 14 to 16
Challenge Level Yellow star

Match the cumulative frequency curves with their corresponding box plots.

Using National Young Mathematicians' Award Tasks to Develop Problem-solving and Group-working Skills

Age 7 to 11

This article for primary teachers uses National Young Mathematicians' Award tasks as contexts in which to develop learners' problem-solving and group-working skills.

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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 Millennium Mathematics Project.

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