Conjecturing and generalising

  • Which Scripts?
    problem
    Favourite

    Which Scripts?

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

    There are six numbers written in five different scripts. Can you sort out which is which?

  • Broken Toaster
    problem

    Broken Toaster

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
  • Zios and Zepts
    problem
    Favourite

    Zios and Zepts

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

    On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

  • problem
    Favourite

    Abundant Numbers

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

    48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

  • problem
    Favourite

    Flashing Lights

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

    Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

  • Square Corners
    problem
    Favourite

    Square Corners

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

    What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

  • problem
    Favourite

    Which is Quicker?

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

    Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

  • Odd Squares
    problem
    Favourite

    Odd Squares

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

    Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

  • problem
    Favourite

    Up and Down Staircases

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

    One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

  • Number Tracks
    problem

    Number TRACKS

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

    Ben's class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?