Other tags that relate to Maximum Mean
Comparing data. Gradients. Handling data. Averages. Generalising. Measures of spread. Creating and manipulating expressions and formulae. Maths Supporting SET. Making and testing hypotheses. Percentages.There are 128 results
Broad Topics > Thinking Mathematically > Generalising
Searching for Mean(ing)
Age 11 to 16
Challenge Level
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
For Richer for Poorer
Age 14 to 16
Challenge Level
Charlie has moved between countries and the average income of both has increased. How can this be so?
Litov's Mean Value Theorem
Age 11 to 14
Challenge Level
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Arithmagons
Age 11 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges?
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?
Where Can We Visit?
Age 11 to 14
Challenge Level
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Cuboid Challenge
Age 11 to 16
Challenge Level
What's the largest volume of box you can make from a square of paper?
Got It
Age 7 to 14
Challenge Level
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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.
Seven Squares - Group-worthy Task
Age 11 to 14
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?
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?”
Take Three from Five
Age 11 to 16
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?
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?
More Twisting and Turning
Age 11 to 16
Challenge Level
It would be nice to have a strategy for disentangling any tangled ropes...
Semi-square
Age 14 to 16
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?
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?
Winning Lines
Age 7 to 16
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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.
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.
Frogs
Age 11 to 14
Challenge Level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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?
Shear Magic
Age 11 to 14
Challenge Level
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
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?
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?
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?
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.
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.
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. . . .
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. . . .
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.
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
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?
What Numbers Can We Make?
Age 11 to 14
Challenge Level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Charitable Pennies
Age 7 to 14
Challenge Level
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Counting Factors
Age 11 to 14
Challenge Level
Is there an efficient way to work out how many factors a large number has?
Nim-7 for Two
Age 5 to 14
Challenge Level
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Got it for Two
Age 7 to 14
Challenge Level
Got It game for an adult and child. How can you play so that you know you will always win?
Coordinate Patterns
Age 11 to 14
Challenge Level
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
What Numbers Can We Make Now?
Age 11 to 14
Challenge Level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Route to Infinity
Age 11 to 14
Challenge Level
Can you describe this route to infinity? Where will the arrows take you next?
Steps to the Podium
Age 7 to 14
Challenge Level
It starts quite simple but great opportunities for number discoveries and patterns!
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?
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?
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?
Multiplication Arithmagons
Age 14 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.