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

Good thinkers are curious and ask good questions. They are excited by new ideas and are keen to explore and investigate them.

Want to become a more curious mathematician?

We hope these problems will provoke you to ask good mathematical questions. Take a look, we think you'll get hooked on them!

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

### Five Steps to 50

### Next-door Numbers

### Eightness of Eight

### Digit Addition

### Shaping It

### If the World Were a Village

### 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?

### Ring a Ring of Numbers

### Colouring Triangles

### Chain of Changes

### Little Man

### More Numbers in the Ring

### Brush Loads

### 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

### The Number Jumbler

### Consecutive Numbers

### Number Differences

### Three neighbours

### Pouring Problem

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

### Two Clocks

### Curious number

### 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?

### Elevenses

### Satisfying Statements

### Can they be equal?

### Special Numbers

### 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

### 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?

### 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

### 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

### Think of Two Numbers

### Estimating time

### 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?

### 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

### Litov's Mean Value Theorem

### A Chance to Win?

### Cola Can

### Which solids can we make?

### Which spinners?

### Curvy areas

### Pair Products

### 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?

### Vector journeys

### How old am I?

### Beelines

### What's Possible?

### Arclets

### Odds and Evens made fair

### Trapezium Four

### Pick's Theorem

### Triangles and petals

### Partly Painted Cube

### Same Number!

### Where to Land

### 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?