Other tags that relate to LOGO Challenge - Sequences and Pentagrams
Games. Practical Activity. Combinatorics. Logo. Working systematically. STEM - General. Networks/Graph Theory. Mathematical reasoning & proof. Visualising. Programming.There are 179 results
Broad Topics > Thinking Mathematically > Visualising
Ding Dong Bell
Age 11 to 18
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
Instant Insanity
Age 11 to 18
Challenge Level
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Sprouts
Age 7 to 18
Challenge Level
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Alquerque
Age 5 to 18
This game for two, was played in ancient Egypt as far back as 1400 BC. The game was taken by the Moors to Spain, where it is mentioned in 13th century manuscripts, and the Spanish name Alquerque. . . .
Pumpkin Patch
Age 5 to 18
A game for two players based on a game from the Somali people of Africa. The first player to pick all the other's 'pumpkins' is the winner.
Sea Defences
Age 7 to 14
Challenge Level
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
Königsberg
Age 11 to 14
Challenge Level
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
LOGO Challenge - Triangles-squares-stars
Age 11 to 16
Challenge Level
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Seega
Age 5 to 18
An ancient game for two from Egypt. You'll need twelve distinctive 'stones' each to play. You could chalk out the board on the ground - do ask permission first.
Triangles to Tetrahedra
Age 11 to 14
Challenge Level
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Yih or Luk Tsut K'i or Three Men's Morris
Age 11 to 18
Challenge Level
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
Khun Phaen Escapes to Freedom
Age 11 to 14
Challenge Level
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Dice, Routes and Pathways
Age 5 to 14
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
Changing Places
Age 14 to 16
Challenge Level
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
Sliding Puzzle
Age 11 to 16
Challenge Level
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Rolling Triangle
Age 11 to 14
Challenge Level
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
Square It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Tourism
Age 11 to 14
Challenge Level
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Wari
Age 14 to 16
Challenge Level
This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
One Out One Under
Age 14 to 16
Challenge Level
Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
Konigsberg Plus
Age 11 to 14
Challenge Level
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Travelling Salesman
Age 11 to 14
Challenge Level
A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?
Tetrahedra Tester
Age 11 to 14
Challenge Level
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
Fermat's Poser
Age 14 to 16
Challenge Level
Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
Cube Paths
Age 11 to 14
Challenge Level
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
How Many Dice?
Age 11 to 14
Challenge Level
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
Jam
Age 14 to 16
Challenge Level
To avoid losing think of another very well known game where the patterns of play are similar.
Painting Cubes
Age 11 to 14
Challenge Level
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
Paving Paths
Age 11 to 14
Challenge Level
How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
Isosceles Triangles
Age 11 to 14
Challenge Level
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Bands and Bridges: Bringing Topology Back
Age 7 to 14
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
The Development of Spatial and Geometric Thinking: 5 to 18
Age 5 to 16
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .
There and Back Again
Age 11 to 14
Challenge Level
Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
Shady Symmetry
Age 11 to 14
Challenge Level
How many different symmetrical shapes can you make by shading triangles or squares?
Shaping the Universe I - Planet Earth
Age 11 to 16
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
Hidden Rectangles
Age 11 to 14
Challenge Level
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Squares in Rectangles
Age 11 to 14
Challenge Level
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Nine Colours
Age 11 to 16
Challenge Level
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Shaping the Universe II - the Solar System
Age 11 to 16
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
Tower of Hanoi
Age 11 to 14
Challenge Level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Penta Colour
Age 14 to 16
Challenge Level
In how many different ways can I colour the five edges of a pentagon red, blue and green so that no two adjacent edges are the same colour?
Euromaths
Age 11 to 14
Challenge Level
How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?
Constructing Triangles
Age 11 to 14
Challenge Level
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Triangles in the Middle
Age 11 to 18
Challenge Level
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Hypotenuse Lattice Points
Age 14 to 16
Challenge Level
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
3D Treasure Hunt
Age 14 to 18
Challenge Level
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
Getting an Angle
Age 11 to 14
Challenge Level
How can you make an angle of 60 degrees by folding a sheet of paper twice?
NRICH is part of the family of activities in the Millennium Mathematics Project.