Exploring and noticing

  • Tiles on a Patio
    problem

    Tiles on a Patio

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    How many ways can you find of tiling the square patio, using square tiles of different sizes?
  • A stack of open magazines on colourful pages.
    problem

    Magazines

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

    Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

  • Pebbles
    problem

    Pebbles

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

    Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

  • My New Patio
    problem

    My New Patio

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

    What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

  • Presents
    problem

    Presents

    Age
    7 to 11
    Challenge level
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    We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
  • Different coloured hula hoops.
    problem

    Bean Bags for Bernard's Bag

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

    How could you put eight bean bags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

  • Special 24
    problem

    Special 24

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

    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
    filled star filled star empty star
    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.
  • Pizza Cut
    problem

    Pizza Cut

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    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).