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There are **71** NRICH Mathematical resources connected to **Posing questions and making conjectures**, you may find related items under Thinking mathematically.

Problem
Primary curriculum
Secondary curriculum
### Guess What?

Can you find out which 3D shape your partner has chosen before they work out your shape?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Six Numbered Cubes

This task combines spatial awareness with addition and multiplication.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Six Ten Total

This challenge combines addition, multiplication, perseverance and even proof.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Division Rules

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magic Letters

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

Problem
Primary curriculum
Secondary curriculum
### Sticky Data

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 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multiplication Arithmagons

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Numbers Can We Make?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Count the Digits

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sorting Logic Blocks

This activity focuses on similarities and differences between shapes.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Light the Lights

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Light the Lights Again

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Charlie's Delightful Machine

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Little Light Thinking

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Our Numbers

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Shape?

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 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### En-counters

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stick Images

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

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Counters in the Middle

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### I Like ...

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Table Patterns Go Wild!

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Much Can We Spend?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cuboid Challenge

What's the largest volume of box you can make from a square of paper?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Can They Be Equal?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Searching for Mean(ing)

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magic Vs

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Age 7 to 11

Challenge Level

General
Primary curriculum
Secondary curriculum
### Interactive Spinners

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Consecutive Negative Numbers

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Spaces for Exploration

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

Age 11 to 14

Problem
Primary curriculum
Secondary curriculum
### Arithmagons

Can you find the values at the vertices when you know the values on the edges?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tilted Squares

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pair Products

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pick's Theorem

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Where Can We Visit?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tiling

An investigation that gives you the opportunity to make and justify predictions.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Logic Block Collections

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Least of All

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Impossible Triangles?

Which of these triangular jigsaws are impossible to finish?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tables Without Tens

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Trig Rules OK

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sheep Talk

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polite Numbers

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Marvellous Matrix

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

Age 7 to 11

Challenge Level

General
Primary curriculum
Secondary curriculum
### Folding, Cutting and Punching

Exploring and predicting folding, cutting and punching holes and making spirals.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Path to the Stars

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polycircles

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Age 14 to 16

Challenge Level