Other tags that relate to Burning Down
Real world. Physics. Linear equations. Quadratic equations. Simultaneous equations. Area - triangles, quadrilaterals, compound shapes. Biology. Calculating with ratio & proportion. Mathematical reasoning & proof. Chemistry.There are 162 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof
Gift of Gems
Age 14 to 16 Challenge Level:
Four jewellers share their stock. Can you work out the relative values of their gems?
Leonardo's Problem
Age 14 to 18 Challenge Level:
A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
Truth Tables and Electronic Circuits
Age 11 to 18
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Rhombus in Rectangle
Age 14 to 16 Challenge Level:
Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
Problem Solving, Using and Applying and Functional Mathematics
Age 5 to 18 Challenge Level:
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Towering Trapeziums
Age 14 to 16 Challenge Level:
Can you find the areas of the trapezia in this sequence?
Kite in a Square
Age 14 to 16 Challenge Level:
Can you make sense of the three methods to work out the area of the kite in the square?
Pent
Age 14 to 18 Challenge Level:
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
Ordered Sums
Age 14 to 16 Challenge Level:
Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .
Dalmatians
Age 14 to 18 Challenge Level:
Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.
Disappearing Square
Age 11 to 14 Challenge Level:
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
Our Ages
Age 14 to 16 Challenge Level:
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
Matter of Scale
Age 14 to 16 Challenge Level:
Prove Pythagoras' Theorem using enlargements and scale factors.
To Prove or Not to Prove
Age 14 to 18
A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.
Pareq Exists
Age 14 to 16 Challenge Level:
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
Unit Interval
Age 14 to 18 Challenge Level:
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
Pythagorean Triples I
Age 11 to 16
The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!
Parallel Universe
Age 14 to 16 Challenge Level:
An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.
Proof Sorter - Quadratic Equation
Age 14 to 18 Challenge Level:
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
Children at Large
Age 11 to 14 Challenge Level:
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Janine's Conjecture
Age 14 to 16 Challenge Level:
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
Salinon
Age 14 to 16 Challenge Level:
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Composite Notions
Age 14 to 16 Challenge Level:
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
Proof: A Brief Historical Survey
Age 14 to 18
If you think that mathematical proof is really clearcut and universal then you should read this article.
Cosines Rule
Age 14 to 16 Challenge Level:
Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.
Square Mean
Age 14 to 16 Challenge Level:
Is the mean of the squares of two numbers greater than, or less than, the square of their means?
There's a Limit
Age 14 to 18 Challenge Level:
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
Mouhefanggai
Age 14 to 16
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
Long Short
Age 14 to 16 Challenge Level:
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
Fitting In
Age 14 to 16 Challenge Level:
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .
Impossible Sandwiches
Age 11 to 18
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
The Frieze Tree
Age 11 to 16
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
Picturing Pythagorean Triples
Age 14 to 18
This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.
Angle Trisection
Age 14 to 16 Challenge Level:
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
Some Circuits in Graph or Network Theory
Age 14 to 18
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
Pythagorean Triples II
Age 11 to 16
This is the second article on right-angled triangles whose edge lengths are whole numbers.
The Golden Ratio, Fibonacci Numbers and Continued Fractions.
Age 14 to 16
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.
Air Nets
Age 7 to 18 Challenge Level:
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Geometric Parabola
Age 14 to 16 Challenge Level:
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
Cyclic Quadrilaterals
Age 11 to 16 Challenge Level:
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Encircling
Age 14 to 16 Challenge Level:
An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?
Pythagoras Proofs
Age 14 to 16 Challenge Level:
Can you make sense of these three proofs of Pythagoras' Theorem?
Zig Zag
Age 14 to 16 Challenge Level:
Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
Folding Fractions
Age 14 to 16 Challenge Level:
What fractions can you divide the diagonal of a square into by simple folding?
No Right Angle Here
Age 14 to 16 Challenge Level:
Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.
Folding Squares
Age 14 to 16 Challenge Level:
The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
Find the Fake
Age 14 to 16 Challenge Level:
There are 12 identical looking coins, one of which is a fake. The counterfeit coin is of a different weight to the rest. What is the minimum number of weighings needed to locate the fake coin?
Iffy Logic
Age 14 to 18 Challenge Level:
Can you rearrange the cards to make a series of correct mathematical statements?
Same Length
Age 11 to 16 Challenge Level:
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
NRICH is part of the family of activities in the Millennium Mathematics Project.