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# 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 thatÂ 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.*
### American Billions

### What's it Worth?

### Got It

### Stringy Quads

### Quadrilaterals Game

### Shapely Pairs

### Property Chart

### Transformation Game

### Factors and Multiples Game

### Diamond Collector

### Connect Three

### First Connect Three

### Big and Small Numbers in Physics - Group Task

### All in a Jumble

### Reflecting Lines

### Translating Lines

### Surprising Transformations

### Jig Shapes

### Developing Good Team-working Skills

### Making Rectangles

### Number Match

### Fraction Match

### Algebra Match

### Simplifying Doughnut

### Doughnut Percents

### How Would You Score It?

### Thirsty?

### Arranging Cubes

### Arranging Counters

### Arranging Squares

### The Solid

### Solids

### Counters in the Middle

### Triangles in the Middle

### Stick Images

### En-counters

### Coordinate Designs

### Guess the Houses

### What Shape?

### Which Quadratic?

### Guess the Function

### Castles in the Middle

### Guess the Dominoes

### Which Solid?

### Quad Match

### Sociable Cards

### What Does Random Look Like?

### Olympic Records

### What's That Graph?

### Sticky Data

### Magic Letters

### Constructing Triangles

### Developing Good Team-working Skills in Primary Schools

### Olympic Measures

### Dice in a Corner

### The Dice Train

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

### Up, Down, Flying Around

### Shape Draw

### Picturing the World

### Perception Versus Reality

### Box Plot Match

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

## Related Collections

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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 thatÂ two heads can be better than one.

Age 11 to 14

Challenge Level

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...

Age 11 to 16

Challenge Level

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

Age 7 to 14

Challenge Level

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.

Age 7 to 11

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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...

Age 11 to 14

Challenge Level

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?

Age 11 to 14

Challenge Level

Why not challenge a friend to play this transformation game?

Age 7 to 16

Challenge Level

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

Age 11 to 16

Challenge Level

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

Age 11 to 16

Challenge Level

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

Age 7 to 11

Challenge Level

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?

Age 16 to 18

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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.

Age 11 to 14

Challenge Level

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

Age 14 to 16

Challenge Level

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?

Age 5 to 11

Challenge Level

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

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.

Age 7 to 14

Challenge Level

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

Age 5 to 11

Challenge Level

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

Age 5 to 11

Challenge Level

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

Age 11 to 16

Challenge Level

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

Age 14 to 18

Challenge Level

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

Age 7 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 5 to 7

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 11 to 18

Challenge Level

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

Age 11 to 16

Challenge Level

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

Age 11 to 16

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 11 to 18

Challenge Level

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

Age 7 to 14

Challenge Level

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

Age 5 to 7

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 5 to 7

Challenge Level

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

Age 7 to 14

Challenge Level

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.

Age 14 to 18

Challenge Level

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.

Age 16 to 18

Challenge Level

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

Age 7 to 14

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 16

Challenge Level

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.

Age 7 to 11

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 14 to 18

Challenge Level

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

Age 5 to 7

Challenge Level

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?'.

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 5 to 11

This article looks at team building in the primary context.

Age 11 to 14

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

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.

Age 11 to 14

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 14 to 16

Challenge Level

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

Age 14 to 18

Challenge Level

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

Age 14 to 16

Challenge Level

Match the cumulative frequency curves with their corresponding box plots.

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.