List

Year 7 Conjecturing and generalising

More Less is More
problem

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.
Dicey Operations
game
Favourite

More Dicey operations

Age
7 to 14
Challenge level
filled star empty star empty star

In these multiplication and division games, you'll need to think strategically to get closest to the target.

Factors and Multiples Game
game
Favourite

Factors and multiples game

Age
7 to 16
Challenge level
filled star empty star empty star

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

The Remainders Game
game
Favourite

The remainders game

Age
7 to 14
Challenge level
filled star empty star empty star

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

Dicey Operations
game
Favourite

Dicey operations

Age
7 to 14
Challenge level
filled star empty star empty star

In these addition and subtraction games, you'll need to think strategically to get closest to the target.

Consecutive Numbers
problem

Consecutive numbers

Age
7 to 14
Challenge level
filled star empty star empty star

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Dozens
problem

Dozens

Age
7 to 14
Challenge level
filled star empty star empty star

Can you select the missing digit(s) to find the largest multiple?

Treasure Hunt
problem

Treasure hunt

Age
7 to 14
Challenge level
filled star empty star empty star

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Number Lines in Disguise
problem

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.
Odds, Evens and More Evens
problem

Odds, evens and more evens

Age
11 to 14
Challenge level
filled star empty star empty star

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Changing areas, changing perimeters
problem

Changing areas, changing perimeters

Age
11 to 14
Challenge level
filled star empty star empty star

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

Magic Letters
problem

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?
Perimeter Possibilities
problem

Perimeter possibilities

Age
11 to 14
Challenge level
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I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Strange Bank Account
problem

Strange bank account

Age
11 to 14
Challenge level
filled star empty star empty star

Imagine a very strange bank account where you are only allowed to do two things...

Beach Huts
problem

Beach huts

Age
11 to 14
Challenge level
filled star empty star empty star
Can you figure out how sequences of beach huts are generated?
Parallelogram It
problem

Parallelogram it

Age
11 to 16
Challenge level
filled star empty star empty star

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.

Climbing Complexity
problem

Climbing complexity

Age
11 to 14
Challenge level
filled star empty star empty star

In the 2020 Olympic Games, sport climbing was introduced for the first time, and something very interesting happened with the scoring system. Can you find out what was interesting about it?

Have you got it?
problem

Have you got it?

Age
11 to 14
Challenge level
filled star empty star empty star

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

Summing Consecutive Numbers
problem

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

Picturing square numbers

Age
11 to 14
Challenge level
filled star empty star empty star

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

Number pyramids

Age
11 to 14
Challenge level
filled star empty star empty star

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

Square It
problem

Square it

Age
11 to 16
Challenge level
filled star empty star empty star

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

Mirror, mirror...

Age
11 to 14
Challenge level
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Explore the effect of reflecting in two parallel mirror lines.

Searching for mean(ing)
problem

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?
More Number Pyramids
problem

More number pyramids

Age
11 to 14
Challenge level
filled star filled star empty star

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Shear Magic
problem

Shear magic

Age
11 to 14
Challenge level
filled star filled star empty star

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

...on the wall
problem

...on the wall

Age
11 to 14
Challenge level
filled star filled star empty star

Explore the effect of reflecting in two intersecting mirror lines.

Litov's Mean Value Theorem
problem

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...