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#### Resources tagged with Generalising similar to Advent Calendar 2011 - Secondary:

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### There are 123 results ### Janine's Conjecture

##### Age 14 to 16 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. . . . ### Multiplication Square

##### Age 14 to 16 Challenge Level:

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice? ### Magic Squares II

##### Age 14 to 18

An article which gives an account of some properties of magic squares. ### AMGM

##### Age 14 to 16 Challenge Level:

Can you use the diagram to prove the AM-GM inequality? ### All Tangled Up

##### Age 14 to 18 Challenge Level:

Can you tangle yourself up and reach any fraction? ### 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. ### 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? ### Mystic Rose

##### Age 14 to 16 Challenge Level:

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes. ### 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. ### One, Three, Five, Seven

##### Age 11 to 16 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. ### Pentanim

##### Age 7 to 16 Challenge Level:

A game for 2 players with similarities 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. ### 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? ### Jam

##### Age 14 to 16 Challenge Level:

To avoid losing think of another very well known game where the patterns of play are similar. ### Lower Bound

##### Age 14 to 16 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 = ### 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? ##### Age 7 to 14 Challenge Level:

I added together some of my neighbours house numbers. Can you explain the patterns I noticed? ### What's Possible?

##### Age 14 to 16 Challenge Level:

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make? ### 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. ### 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?” ### Problem Solving, Using and Applying and Functional Mathematics

##### Age 5 to 18 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. ### Square Pizza

##### Age 14 to 16 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? ### Winning Lines

##### Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games. ### Jam

##### Age 14 to 16 Challenge Level:

A game for 2 players ### More Twisting and Turning

##### Age 11 to 16 Challenge Level:

It would be nice to have a strategy for disentangling any tangled ropes... ### Building Gnomons

##### Age 14 to 16 Challenge Level:

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible. ### 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? ### 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? ### 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? ### Odd Differences

##### Age 14 to 16 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. ### 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? ### Cuboid Challenge

##### Age 11 to 16 Challenge Level:

What's the largest volume of box you can make from a square of paper? ### Attractive Tablecloths

##### Age 14 to 16 Challenge Level:

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs? ### Dotty Triangles

##### Age 11 to 14 Challenge Level:

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw? ### Harmonic Triangle

##### Age 14 to 16 Challenge Level:

Can you see how to build a harmonic triangle? Can you work out the next two rows? ### Nim-like Games

##### Age 7 to 16 Challenge Level:

A collection of games on the NIM theme ### 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? ### 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. ### Pick's Theorem

##### Age 14 to 16 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. ### Arithmagons

##### Age 14 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges? ### 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? ### 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. ### Converging Means

##### Age 14 to 16 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. . . . ### Pareq Calc

##### Age 14 to 16 Challenge Level:

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . . ### 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? ### 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? ### Regular Hexagon Loops

##### Age 11 to 14 Challenge Level:

Make some loops out of regular hexagons. What rules can you discover? ### Take Three from Five

##### Age 14 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? ### Route to Infinity

##### Age 11 to 14 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next? ### Pinned Squares

##### Age 14 to 16 Challenge Level:

What is the total number of squares that can be made on a 5 by 5 geoboard?