Exploring and noticing

  • Special 24
    problem

    Special 24

    Age
    7 to 11
    Challenge level
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    Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
  • Thinking Mathematically - Short Problems
    problem

    What two ...?

    Age
    7 to 11
    Challenge level
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    56 406 is the product of two consecutive numbers. What are these two numbers?

  • Arranging the Tables
    problem

    Arranging the tables

    Age
    7 to 11
    Challenge level
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    There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
  • Egyptian Rope
    problem
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    Egyptian rope

    Age
    7 to 11
    Challenge level
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    The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

  • Pizza Cut
    problem

    Pizza cut

    Age
    7 to 11
    Challenge level
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    Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).
  • problem
    Favourite

    Wonky watches

    Age
    7 to 11
    Challenge level
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    Mandeep's watch loses two minutes every hour. Adam's watch gains one minute every hour. Can you work out what time they arrived at the airport?

  • Make 100
    problem
    Favourite

    Make 100

    Age
    7 to 11
    Challenge level
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    Find at least one way to put in some operation signs to make these digits come to 100.

  • Forgot the Numbers
    problem
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    Forgot the numbers

    Age
    7 to 11
    Challenge level
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    On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

  • Pumpkin Pie Problem
    problem
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    Pumpkin pie problem

    Age
    7 to 11
    Challenge level
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    Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

  • Amy's Dominoes
    problem
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    Amy's dominoes

    Age
    7 to 11
    Challenge level
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    Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?