Conjecturing and generalising

  • Pareq Calc
    problem

    Pareq Calc

    Age
    14 to 16
    Challenge level
    Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.
  • Pinned Squares
    problem

    Pinned Squares

    Age
    14 to 16
    Challenge level
    What is the total number of squares that can be made on a 5 by 5 geoboard?
  • Special Sums and Products
    problem

    Special Sums and Products

    Age
    11 to 14
    Challenge level
    Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
  • 2001 Spatial Oddity
    problem

    2001 Spatial Oddity

    Age
    11 to 14
    Challenge level
    With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
  • Square pizza
    problem

    Square Pizza

    Age
    14 to 16
    Challenge level
    Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
  • Semi-Square
    problem

    Semi-Square

    Age
    14 to 16
    Challenge level
    What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
  • In a Spin
    problem

    In a Spin

    Age
    14 to 16
    Challenge level
    What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
  • Three times Seven
    problem

    Three Times Seven

    Age
    11 to 14
    Challenge level
    A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
  • Next-door Numbers
    problem

    Next-Door Numbers

    Age
    5 to 7
    Challenge level

    Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

  • Logic Block Collections
    problem

    Logic Block Collections

    Age
    5 to 7
    Challenge level
    What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
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