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Resources tagged with Generalising similar to Matching Fractions, Decimals and Percentages:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

Other tags that relate to Matching Fractions, Decimals and Percentages
Calculating with fractions. Decimals. Fractions. Working systematically. Generalising. Games. Roadshow. Percentages. Visualising. Interactivities.

There are 143 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising

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Snake Coils

Stage: 2 Challenge Level: Challenge Level:1

This challenge asks you to imagine a snake coiling on itself.

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Nim-7

Stage: 1, 2 and 3 Challenge Level: Challenge Level:1

Can you work out how to win this game of Nim? Does it matter if you go first or second?

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Sum Equals Product

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Triangle Pin-down

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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Pentanim

Stage: 2, 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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More Magic Potting Sheds

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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Dotty Circle

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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Sliding Puzzle

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:1

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.

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Fault-free Rectangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find out what a "fault-free" rectangle is and try to make some of your own.

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Domino Numbers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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Number Differences

Stage: 2 Challenge Level: Challenge Level:1

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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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.

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Picturing Triangle Numbers

Stage: 3 Challenge Level: Challenge Level:1

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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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.

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Number Pyramids

Stage: 3 Challenge Level: Challenge Level:1

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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One, Three, Five, Seven

Stage: 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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More Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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All Tangled Up

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you tangle yourself up and reach any fraction?

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Egyptian Fractions

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

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Have You Got It?

Stage: 3 Challenge Level: Challenge Level:1

Can you explain the strategy for winning this game with any target?

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Nim-7 for Two

Stage: 1 and 2 Challenge Level: Challenge Level:1

Nim-7 game for an adult and child. Who will be the one to take the last counter?

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Got It

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Konigsberg Plus

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Got it for Two

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Got It game for an adult and child. How can you play so that you know you will always win?

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Nim-interactive

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Nim-like Games

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A collection of games on the NIM theme

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Sums and Differences 2

Stage: 2 Challenge Level: Challenge Level:1

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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Roll over the Dice

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

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Tilted Squares

Stage: 3 Challenge Level: Challenge Level:1

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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Strike it Out for Two

Stage: 1 and 2 Challenge Level: Challenge Level:1

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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Always, Sometimes or Never?

Stage: 1 and 2 Challenge Level: Challenge Level:1

Are these statements relating to odd and even numbers always true, sometimes true or never true?

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Walking the Squares

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

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Special Sums and Products

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Odd Squares

Stage: 2 Challenge Level: Challenge Level:1

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

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Up and Down Staircases

Stage: 2 Challenge Level: Challenge Level:1

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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Tourism

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Cuisenaire Rods

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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Shear Magic

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

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Sums and Differences 1

Stage: 2 Challenge Level: Challenge Level:1

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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Crossings

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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Sitting Round the Party Tables

Stage: 1 and 2 Challenge Level: Challenge Level:1

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Button-up Some More

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Circles, Circles

Stage: 1 and 2 Challenge Level: Challenge Level:1

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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Spirals, Spirals

Stage: 2 Challenge Level: Challenge Level:1

Here are two kinds of spirals for you to explore. What do you notice?

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Three Dice

Stage: 2 Challenge Level: Challenge Level:1

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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Keep it Simple

Stage: 3 Challenge Level: Challenge Level:1

Can all unit fractions be written as the sum of two unit fractions?

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Christmas Chocolates

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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Broken Toaster

Stage: 2 Short Challenge Level: Challenge Level:1

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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Build it Up

Stage: 2 Challenge Level: Challenge Level:1

Can you find all the ways to get 15 at the top of this triangle of numbers?

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Build it up More

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This task follows on from Build it Up and takes the ideas into three dimensions!