*Being Curious is part of our Developing Mathematical Habits of Mind collection.*

In Nurturing Students' Curiosity, we offer you support and advice on how to encourage your students to be curious mathematicians.

All humans are naturally curious, and good mathematicians get excited by new ideas and are keen to explore and investigate them. As teachers, we want to nurture our students' mathematical curiosity so they grow into creative, flexible problem-solvers. One way to nurture this curiosity is by providing the right hook to draw students in.

We hope that the problems below will exploit students' natural curiosity and provoke them to ask good mathematical questions.*You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.*

### Shaping It

### If the World Were a Village

This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?

### Five Steps to 50

### Next-door Numbers

### Eightness of Eight

### Digit Addition

Try out this number trick. What happens with different starting numbers? What do you notice?

### Ring a Ring of Numbers

### Colouring Triangles

### Chain of Changes

### Little Man

### 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?

### More Numbers in the Ring

### Consecutive Numbers

### Number Differences

### Brush Loads

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

### Statement Snap

### Nice or Nasty

### Tumbling Down

Watch this animation. What do you see? Can you explain why this happens?

### Your number is...

### Fruity Totals

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

### The Number Jumbler

### Two Clocks

These clocks have only one hand, but can you work out what time they are showing from the information?

### Three neighbours

### Pouring Problem

What do you think is going to happen in this video clip? Are you surprised?

### Curious number

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

### Dicey Operations

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

### Arithmagons

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

### 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?

### 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?

### Semi-regular Tessellations

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Blue and White

### Perimeter Possibilities

### What's it worth?

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

### Elevenses

### Satisfying Statements

### Can they be equal?

### Special Numbers

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

### Number Pyramids

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

### How much can we spend?

### Shifting Times Tables

Can you find a way to identify times tables after they have been shifted up or down?

### Your number was...

### Tilted Squares

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

### 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?

### Stars

### Opposite vertices

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

### Right angles

### Two's company

### Cosy corner

### Non-Transitive Dice

### What numbers can we make now?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

### Marbles in a box

### Estimating time

### Think of Two Numbers

### Wipeout

### Take Three From Five

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

### Searching for mean(ing)

### Unequal Averages

### Cuboid Challenge

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

### More Number Pyramids

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### On the Edge

### Sending a Parcel

### Square coordinates

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

### Which solids can we make?

### Litov's Mean Value Theorem

### A Chance to Win?

### Cola Can

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

### Vector journeys

### How old am I?

### Beelines

### Which spinners?

### Curvy areas

### Pair Products

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

### Circles in quadrilaterals

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

### Last one standing

### 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?

### Multiplication arithmagons

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

### Triangle midpoints

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?