Year 7 Conjecturing and generalising

  • The Remainders Game
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    The Remainders Game

    Age
    7 to 14
    Challenge level
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    Play this game and see if you can figure out the computer's chosen number.

  • Dicey Operations
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    Dicey Operations

    Age
    7 to 14
    Challenge level
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    In these addition and subtraction games, you'll need to think strategically to get closest to the target.

  • Consecutive Numbers
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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
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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?

  • Got It
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    Got It

    Age
    7 to 14
    Challenge level
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    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.

  • A rolled up old-fashioned treasure map.
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    Treasure Hunt

    Age
    7 to 14
    Challenge level
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    Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

  • More Less is More
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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.

  • Dicey Operations
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    More Dicey Operations

    Age
    7 to 14
    Challenge level
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    In these multiplication and division games, you'll need to think strategically to get closest to the target.

  • Number Lines in Disguise
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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?

  • Factors and Multiples Game
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    Factors and Multiples Game

    Age
    7 to 16
    Challenge level
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    A game in which players take it in turns to choose a number. Can you block your opponent?

  • Summing Consecutive Numbers
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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
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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
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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?

  • Mirror, mirror...
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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
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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...

  • Changing areas, changing perimeters
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    Changing Areas, Changing Perimeters

    Age
    11 to 14
    Challenge level
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    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
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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?

  • Perimeter Possibilities
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    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
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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...

  • About Average
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    About Average

    Age
    11 to 14
    Challenge level
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    Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?

  • Beach Huts
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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?

  • Climbing Complexity
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    Climbing Complexity

    Age
    11 to 14
    Challenge level
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    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?

  • More Number Pyramids
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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
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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
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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.

  • Litov's Mean Value Theorem
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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...

  • 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.

  • Square It
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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.

  • Parallelogram It
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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.

  • Searching for mean(ing)
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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?