*Reasoning, Convincing and Proving is part of our Thinking Mathematically collection.*

### Statement Snap

### Fruity Totals

### Your number is...

### The Number Jumbler

### Missing Multipliers

### 5 by 5 Mathdokus

### More Less is More

### Remainders

### Number Lines in Disguise

### 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?

### Olympic Measures

### Strange Bank Account

Imagine a very strange bank account where you are only allowed to do two things...

### American Billions

### Crossed Ends

### Multiples Sudoku

### Polygon Pictures

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

### Gabriel's Problem

### Special Numbers

### Tilted Squares

### Cyclic Quadrilaterals

### 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?

### Arithmagons

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

### Place your orders

### Triangles in circles

Can you find triangles on a 9-point circle? Can you work out their angles?

### What numbers can we make now?

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

### Legs Eleven

### Squares in rectangles

### Product Sudoku

### Triangle Numbers

### Impossibilities

### Overlaps

### All in a jumble

### Same length

### Marbles in a box

### Fibonacci Surprises

### Think of Two Numbers

### Power mad!

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

### 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?

### Always a multiple?

### More Number Pyramids

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

### Seven Squares - Group-worthy Task

### Pythagoras Proofs

Can you make sense of these three proofs of Pythagoras' Theorem?

### What does it all add up to?

### Tower of Hanoi

### Fill Me Up

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

### Differences

### Consecutive negative numbers

### Shopping Basket

### the greedy algorithm

### Mega Quadratic Equations

### How old am I?

### Curvy areas

### 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?

### Speeding boats

### Common Divisor

Can you find out what numbers divide these expressions? Can you prove that they are always divisors?

### Circles in quadrilaterals

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

### Generating Triples

### Speed-time problems at the Olympics

### Salinon

### Finding factors

### Factorising with Multilink

### Nutrition and Cycling

### Doesn't add up

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

### Kite in a Square

### Quad in Quad

### Pythagoras Perimeters

### Why 24?

### Iff

### LCM Sudoku

### Difference of Two Squares

### CD Heaven

### Puzzling Place Value

### Terminology

### Partly Painted Cube

### Always Perfect

### Back fitter

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

### Painted Cube

### Multiplication arithmagons

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