Other tags that relate to Square Pizza
Mathematical reasoning & proof. Creating and manipulating expressions and formulae. Describing patterns and sequences. Interactivities. Area - triangles, quadrilaterals, compound shapes. Visualising. Symmetry. Generalising. Factors and multiples. Pythagoras' theorem.There are 131 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?
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?
Mindreader
Age 11 to 14
Challenge Level
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
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?
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.
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?
Quadratic Patterns
Age 11 to 14
Challenge Level
Surprising numerical patterns can be explained using algebra and diagrams...
Harmonic Triangle
Age 14 to 16
Challenge Level
Can you see how to build a harmonic triangle? Can you work out the next two rows?
More Number Pyramids
Age 11 to 14
Challenge Level
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Areas of Parallelograms
Age 14 to 16
Challenge Level
Can you find the area of a parallelogram defined by two vectors?
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?”
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 =
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?
Partitioning Revisited
Age 11 to 14
Challenge Level
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
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?
Regular Hexagon Loops
Age 11 to 14
Challenge Level
Make some loops out of regular hexagons. What rules can you discover?
Chocolate 2010
Age 14 to 16
Challenge Level
First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...
Interactive Number Patterns
Age 14 to 16
Challenge Level
How good are you at finding the formula for a number pattern ?
Mind Reading
Age 11 to 14
Challenge Level
Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .
Sum Equals Product
Age 11 to 14
Challenge Level
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so. . . .
Christmas Chocolates
Age 11 to 14
Challenge Level
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
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?
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?
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. . . .
Summing Consecutive Numbers
Age 11 to 14
Challenge Level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Magic Squares for Special Occasions
Age 11 to 16
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
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?
Algebra from Geometry
Age 11 to 16
Challenge Level
Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.
Always the Same
Age 11 to 14
Challenge Level
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
Puzzling Place Value
Age 14 to 16
Challenge Level
Can you explain what is going on in these puzzling number tricks?
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Seven Squares
Age 11 to 14
Challenge Level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
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?
Difference of Two Squares
Age 14 to 16
Challenge Level
What is special about the difference between squares of numbers adjacent to multiples of three?
Special Sums and Products
Age 11 to 14
Challenge Level
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
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?
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?
Square Number Surprises
Age 14 to 16
Challenge Level
There are unexpected discoveries to be made about square numbers...
Number Pyramids
Age 11 to 14
Challenge Level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
How Much Can We Spend?
Age 11 to 14
Challenge Level
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Your Number Is...
Age 7 to 14
Challenge Level
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
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. . . .
Cubes Within Cubes Revisited
Age 11 to 14
Challenge Level
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
Pythagoras Proofs
Age 14 to 16
Challenge Level
Can you make sense of these three proofs of Pythagoras' Theorem?
Algebra Match
Age 11 to 16
Challenge Level
A task which depends on members of the group noticing the needs of others and responding.
Fibonacci Surprises
Age 11 to 14
Challenge Level
Play around with the Fibonacci sequence and discover some surprising results!
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.