Other tags that relate to Square Pizza
Regular polygons and circles. Generalising. Sine, cosine, tangent. Mathematical reasoning & proof. Symmetry. Area - triangles, quadrilaterals, compound shapes. Making and proving conjectures. Polynomial functions and their roots. Creating and manipulating expressions and formulae. Inequalities.There are 125 results
Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae
Square Pizza
Age 14 to 16 Challenge Level:
Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
Screen Shot
Age 14 to 16 Challenge Level:
A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .
Steel Cables
Age 14 to 16 Challenge Level:
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Pick's Theorem
Age 14 to 16 Challenge Level:
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Triangles Within Triangles
Age 14 to 16 Challenge Level:
Can you find a rule which connects consecutive triangular numbers?
Always Perfect
Age 14 to 16 Challenge Level:
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
DOTS Division
Age 14 to 16 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Perfectly Square
Age 14 to 16 Challenge Level:
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Pair Products
Age 14 to 16 Challenge Level:
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Lens Angle
Age 14 to 16 Challenge Level:
Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
Gutter
Age 14 to 16 Challenge Level:
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
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?
Sums of Pairs
Age 11 to 16 Challenge Level:
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
What's Possible?
Age 14 to 16 Challenge Level:
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
The Pillar of Chios
Age 14 to 16 Challenge Level:
Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
Multiplication Square
Age 14 to 16 Challenge Level:
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Attractive Tablecloths
Age 14 to 16 Challenge Level:
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
2-digit Square
Age 14 to 16 Challenge Level:
A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
Lower Bound
Age 14 to 16 Challenge Level:
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
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?
Triangles Within Squares
Age 14 to 16 Challenge Level:
Can you find a rule which relates triangular numbers to square numbers?
Triangles Within Pentagons
Age 14 to 16 Challenge Level:
Show that all pentagonal numbers are one third of a triangular number.
Never Prime
Age 14 to 16 Challenge Level:
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
Generating Triples
Age 14 to 16 Challenge Level:
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Pinned Squares
Age 14 to 16 Challenge Level:
What is the total number of squares that can be made on a 5 by 5 geoboard?
Simplifying Doughnut
Age 14 to 18 Challenge Level:
An algebra task which depends on members of the group noticing the needs of others and responding.
Algebra Match
Age 11 to 16 Challenge Level:
A task which depends on members of the group noticing the needs of others and responding.
Series Sums
Age 14 to 16 Challenge Level:
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
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. . . .
Diophantine N-tuples
Age 14 to 16 Challenge Level:
Can you explain why a sequence of operations always gives you perfect squares?
Sixational
Age 14 to 18 Challenge Level:
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
Pythagoras Proofs
Age 14 to 16 Challenge Level:
Can you make sense of these three proofs of Pythagoras' Theorem?
Terminology
Age 14 to 16 Challenge Level:
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
There and Back
Age 14 to 16 Challenge Level:
Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?
Consecutive Squares
Age 14 to 16 Challenge Level:
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
Always Two
Age 14 to 18 Challenge Level:
Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
Training Schedule
Age 14 to 16 Challenge Level:
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
Partly Painted Cube
Age 14 to 16 Challenge Level:
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Robert's Spreadsheet
Age 14 to 16 Challenge Level:
Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
Hand Swap
Age 14 to 16 Challenge Level:
My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .
One and Three
Age 14 to 16 Challenge Level:
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
Painted Cube
Age 14 to 16 Challenge Level:
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Sitting Pretty
Age 14 to 16 Challenge Level:
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
Three Four Five
Age 14 to 16 Challenge Level:
Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
Balance Point
Age 14 to 16 Challenge Level:
Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?
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?
Interactive Number Patterns
Age 14 to 16 Challenge Level:
How good are you at finding the formula for a number pattern ?
NRICH is part of the family of activities in the Millennium Mathematics Project.