Resources tagged with Generalising similar to Mindreader:
Other tags that relate to Mindreader
Creating and manipulating expressions. Curious. Mathematical reasoning & proof. Visualising. Patterned numbers. Interactivities. Algebra - generally. Generalising. Games. Creating expressions/formulae.There are 123 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising
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. . . .
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?
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 for. . . .
Handshakes
Age 11 to 14 Challenge Level:
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
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
Triangle Numbers
Age 11 to 14 Challenge Level:
Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
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. . . .
Make 37
Age 7 to 14 Challenge Level:
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Picturing Triangular Numbers
Age 11 to 14 Challenge Level:
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Enclosing Squares
Age 11 to 14 Challenge Level:
Can you find sets of sloping lines that enclose a square?
Shear Magic
Age 11 to 14 Challenge Level:
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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.
Converging Means
Age 11 to 14 Challenge Level:
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .
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?
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?
Magic Letters
Age 11 to 14 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?
Steps to the Podium
Age 7 to 14 Challenge Level:
It starts quite simple but great opportunities for number discoveries and patterns!
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?
More Number Pyramids
Age 11 to 14 Challenge Level:
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
Nim-7
Age 5 to 14 Challenge Level:
Can you work out how to win this game of Nim? Does it matter if you go first or second?
More Twisting and Turning
Age 11 to 14 Challenge Level:
It would be nice to have a strategy for disentangling any tangled ropes...
Go Forth and Generalise
Age 11 to 14
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
Adding in Rows
Age 11 to 14 Challenge Level:
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Who Is the Fairest of Them All ?
Age 11 to 14 Challenge Level:
Explore the effect of combining enlargements.
Dicing with Numbers
Age 11 to 14 Challenge Level:
In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?
...on the Wall
Age 11 to 14 Challenge Level:
Explore the effect of reflecting in two intersecting mirror lines.
Chocolate Maths
Age 11 to 14 Challenge Level:
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
One O Five
Age 11 to 14 Challenge Level:
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
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.
Chess
Age 11 to 14 Challenge Level:
What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?
Games Related to Nim
Age 5 to 16
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.
Lower Bound
Age 11 to 14 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 =
Three Times Seven
Age 11 to 14 Challenge Level:
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Great Granddad
Age 11 to 14 Challenge Level:
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
Pick's Theorem
Age 11 to 14 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.
Consecutive Negative Numbers
Age 11 to 14 Challenge Level:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Picturing Square Numbers
Age 11 to 14 Challenge Level:
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Mini-max
Age 11 to 14 Challenge Level:
Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .
2001 Spatial Oddity
Age 11 to 14 Challenge Level:
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
Nim
Age 14 to 16 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
Age 11 to 16 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.
Tilted Squares
Age 11 to 14 Challenge Level:
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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.
Pinned Squares
Age 11 to 14 Challenge Level:
The diagram shows a 5 by 5 geoboard with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins. What is the total number of squares that can be made on a. . . .
Painted Cube
Age 11 to 14 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?
NRICH is part of the family of activities in the Millennium Mathematics Project.