List

Year 7 Conjecturing and Generalising

Factors and Multiples Game
game
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Factors and Multiples Game

A game in which players take it in turns to choose a number. Can you block your opponent?

The Remainders Game
game
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The Remainders Game

Play this game and see if you can figure out the computer's chosen number.

Consecutive Numbers
problem
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Consecutive Numbers

Age
7 to 14
Challenge level
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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Dozens
problem
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Dozens

Age
7 to 14
Challenge level
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Can you select the missing digit(s) to find the largest multiple?
Nice or Nasty
problem
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Nice or Nasty

Age
7 to 14
Challenge level
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There are nasty versions of this dice game but we'll start with the nice ones...
More Less is More
problem
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More Less is More

Age
7 to 14
Challenge level
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In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.
Remainders
problem
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Remainders

Age
7 to 14
Challenge level
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I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Number Lines in Disguise
problem
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Number Lines in Disguise

Age
7 to 14
Challenge level
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Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
Train Spotters' Paradise
article

Train Spotters' Paradise

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
Parallelogram It
problem
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Parallelogram It

Age
11 to 16
Challenge level
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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

Dicey Operations
game
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Dicey Operations

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Have you got it?
problem
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Have you got it?

Age
11 to 14
Challenge level
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Can you explain the strategy for winning this game with any target?
Summing Consecutive Numbers
problem
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Summing Consecutive Numbers

Age
11 to 14
Challenge level
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15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Picturing Square Numbers
problem
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Picturing Square Numbers

Age
11 to 14
Challenge level
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Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Number Pyramids
problem
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Number Pyramids

Age
11 to 14
Challenge level
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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Square It
problem
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Square It

Age
11 to 16
Challenge level
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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Mirror, mirror...
problem
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Mirror, mirror...

Age
11 to 14
Challenge level
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Explore the effect of reflecting in two parallel mirror lines.
Odds, Evens and More Evens
problem
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Odds, Evens and More Evens

Age
11 to 14
Challenge level
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Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Magic Letters
problem
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Magic Letters

Age
11 to 14
Challenge level
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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Strange Bank Account
problem
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Strange Bank Account

Age
11 to 14
Challenge level
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Imagine a very strange bank account where you are only allowed to do two things...

Beach Huts
problem
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Beach Huts

Age
11 to 14
Challenge level
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Can you figure out how sequences of beach huts are generated?
More Number Pyramids
problem
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More Number Pyramids

Age
11 to 14
Challenge level
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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Shear Magic
problem
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Shear Magic

Age
11 to 14
Challenge level
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Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
...on the wall
problem
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...on the wall

Age
11 to 14
Challenge level
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Explore the effect of reflecting in two intersecting mirror lines.
Searching for mean(ing)
problem
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Searching for mean(ing)

Age
11 to 16
Challenge level
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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?
Litov's Mean Value Theorem
problem
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Litov's Mean Value Theorem

Age
11 to 14
Challenge level
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Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...