Resources tagged with Generalising similar to Charlie's Mapping:
Other tags that relate to Charlie's Mapping
Gradients. Quadratic functions. Video. Generalising. Mathematical reasoning & proof. Speed. Linear functions. Dynamic geometry. Graphs. Making and proving conjectures.There are 122 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising
Beelines
Stage: 4 Challenge Level: 
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Sliding Puzzle
Stage: 1, 2, 3 and 4 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.
Sums of Pairs
Stage: 3 and 4 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?”
Jam
Stage: 4 Challenge Level:
To avoid losing think of another very well known game where the patterns of play are similar.
Polycircles
Stage: 4 Challenge Level:
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
Loopy
Stage: 4 Challenge Level:
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
Of All the Areas
Stage: 4 Challenge Level:
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
Arithmagons
Stage: 4 Challenge Level:
Can you find the values at the vertices when you know the values on the edges?
What's Possible?
Stage: 4 Challenge Level:
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Seven Squares - Group-worthy Task
Stage: 3 Challenge Level:
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Happy Numbers
Stage: 3 Challenge Level:
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.
Multiplication Square
Stage: 4 Challenge Level:
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
For Richer for Poorer
Stage: 4 Challenge Level:
Charlie has moved between countries and the average income of both has increased. How can this be so?
Janine's Conjecture
Stage: 4 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. . . .
Games Related to Nim
Stage: 1, 2, 3 and 4
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Pentanim
Stage: 2, 3 and 4 Challenge Level:
A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
Take Three from Five
Stage: 4 Challenge Level:
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Hypotenuse Lattice Points
Stage: 4 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?
Winning Lines
Stage: 2, 3 and 4
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Pair Products
Stage: 4 Challenge Level:
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Nim
Stage: 4 Challenge Level:
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Nim-interactive
Stage: 3 and 4 Challenge Level:
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.
Odd Differences
Stage: 4 Challenge Level:
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
One, Three, Five, Seven
Stage: 3 and 4 Challenge Level:
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
In a Spin
Stage: 4 Challenge Level:
What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
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?
Equilateral Areas
Stage: 4 Challenge Level:
ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
Mystic Rose
Stage: 4 Challenge Level:
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Multiplication Arithmagons
Stage: 4 Challenge Level:
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Generating Triples
Stage: 4 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?
Gnomon Dimensions
Stage: 4 Challenge Level:
These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
Magic Squares
Stage: 4 and 5
An account of some magic squares and their properties and and how to construct them for yourself.
Building Gnomons
Stage: 4 Challenge Level:
Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
Plus Minus
Stage: 4 Challenge Level:
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
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?
Problem Solving, Using and Applying and Functional Mathematics
Stage: 1, 2, 3, 4 and 5 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.
Magic Squares II
Stage: 4 and 5
An article which gives an account of some properties of magic squares.
Steel Cables
Stage: 4 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
Stage: 4 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?
Magic Letters
Stage: 3 Challenge Level:
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Picturing Square Numbers
Stage: 3 Challenge Level:
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
What Numbers Can We Make?
Stage: 3 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Picturing Triangular Numbers
Stage: 3 Challenge Level:
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Painted Cube
Stage: 3 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?
Frogs
Stage: 3 Challenge Level:
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Tourism
Stage: 3 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.
Number Pyramids
Stage: 3 Challenge Level:
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
NRICH is part of the family of activities in the Millennium Mathematics Project.