Problems
Little Squares
Stage:1 Challenge Level:
Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?
What's Left?
Stage:1 Challenge Level:
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Polydron
Stage:2 Challenge Level:
This activity investigates how you might make squares and pentominoes from Polydron.
Geoboards
Stage:2 Challenge Level:
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Two Primes Make One Square
Stage:2 Challenge Level:
Can you make square numbers by adding two prime numbers together?
Seven Square Numbers
Stage:2 Challenge Level:
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Cycling Squares
Stage:2 Challenge Level:
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Penta Primes
Stage:2 Challenge Level:
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
Squaring the Circle
Stage:3 Challenge Level:
Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an. . . .
Overlap
Stage:3 Challenge Level:
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
NRICH Prime Squared
Stage:3 Challenge Level:
What is the first prime number greater than 3? Square it and subtract 1. What do you get? Do ths for the second prime number, then the third. Look at the three numbers you have ended up with. What do. . . .
LOGO Challenge 7 - More Stars and Squares
Stage:3 and 4 Challenge Level:
Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.
Excel Investigation: Number Pyramids
Stage:3 and 4 Challenge Level:
Use Excel to create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.
Excel Investigation: Pascal Multiples
Stage:3 and 4 Challenge Level:
This spreadsheet highlights multiples of numbers up to 20 in Pascal's triangle. What patterns can you see?
Excel Interactive Resource: Number Grid Functions
Stage:3 and 4 Challenge Level:
Use Excel to investigate the effect of translations around a number grid.
Excel Technique: Triangular Arrays by Turning Off Zeros
Stage:3 and 4 Challenge Level:
Learn how to use Excel to create triangular arrays.
Tree Graphs
Stage:4 Challenge Level:
A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops). Prove that every tree. . . .
A Tilted Square
Stage:4 Challenge Level:
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Square Pizza
Stage:4 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?
Semi-square
Stage:4 Challenge Level:
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
Take a Square
Stage:4 Challenge Level:
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
Modular Knights
Stage:5 Challenge Level:
Try to move the knight to visit each square once and return to the starting point. Move either 2 steps one way and one perpendicular (as in chess) or generalise to a steps one way and b the other.
Cocked Hat
Stage:5 Challenge Level:
A new solution to a Tough Nut problem. Aleksander has drawn graphs for members of the family of functions given by the implicit equation (x^2 + 2ay -a^2)^2 = y^2(a^2 - x^2) corresponding to different. . . .
