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Resources tagged with Generalising similar to Red Balloons, Blue Balloons:

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

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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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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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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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Number Tracks

Stage: 2 Challenge Level: Challenge Level:1

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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Play to 37

Stage: 2 Challenge Level: Challenge Level:1

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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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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Repeaters

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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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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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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Calendar Calculations

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

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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What Numbers Can We Make?

Stage: 3 Challenge Level: Challenge Level:1

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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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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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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GOT IT Now

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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Three Times Seven

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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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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Round and Round the Circle

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

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Adding in Rows

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

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?

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Division Rules

Stage: 2 Challenge Level: Challenge Level:1

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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Doplication

Stage: 2 Challenge Level: Challenge Level:1

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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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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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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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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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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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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Journeys in Numberland

Stage: 2 Challenge Level: Challenge Level:1

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Picturing Square Numbers

Stage: 3 Challenge Level: Challenge Level:1

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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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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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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Hidden Squares

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

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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Magic Letters

Stage: 3 Challenge Level: Challenge Level:1

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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Tiling

Stage: 2 Challenge Level: Challenge Level:1

An investigation that gives you the opportunity to make and justify predictions.

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Strike it Out

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

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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Handshakes

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

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

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Make 37

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

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.

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Lower Bound

Stage: 3 Challenge Level: Challenge Level:1

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

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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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Magic Vs

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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Oddly

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

Find the sum of all three-digit numbers each of whose digits is odd.

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One O Five

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

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. . . .

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Squares in Rectangles

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

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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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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Magic Constants

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

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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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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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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Cut it Out

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

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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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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Magic Circles

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

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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Nim-7

Stage: 1 and 2 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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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?