Reasoning, Convincing and Proving is part of our Thinking Mathematically collection.
Fruity Totals
The Number Jumbler
Missing Multipliers
5 by 5 Mathdokus
More Less is More
Your number is...
Statement Snap
Remainders
Number Lines in Disguise
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?
Triangles in circles
Can you find triangles on a 9-point circle? Can you work out their angles?
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?
Place your orders
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
Special Numbers
Polygon Pictures
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
Gabriel's Problem
Tilted Squares
Cyclic Quadrilaterals
Tower of Hanoi
What does it all add up to?
Fill Me Up
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
Legs Eleven
Squares in rectangles
Product Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.
Triangle Numbers
What numbers can we make now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
All in a jumble
Marbles in a box
Impossibilities
Just because a problem is impossible doesn't mean it's difficult...
Overlaps
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.
Same length
Fibonacci Surprises
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?
More Number Pyramids
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Pythagoras Proofs
Can you make sense of these three proofs of Pythagoras' Theorem?
Seven Squares - Group-worthy Task
Always a multiple?
Differences
Consecutive negative numbers
Shopping Basket
the greedy algorithm
Generating Triples
Speed-time problems at the Olympics
Salinon
Finding factors
Factorising with Multilink
Nutrition and Cycling
How old am I?
Mega Quadratic Equations
Curvy areas
Speeding boats
Circles in quadrilaterals
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
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?
Common Divisor
Can you find out what numbers divide these expressions? Can you prove that they are always divisors?
Painted Cube
Multiplication square
Picture Story
Multiplication arithmagons
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Doesn't add up
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Quad in Quad
Kite in a Square
Why 24?
Iff
LCM Sudoku
Pythagoras Perimeters
CD Heaven
Difference of Two Squares
Terminology
Always Perfect
Puzzling Place Value
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?