Conjecturing and generalising
-
problemThese squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like? -
problemPebbles
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?
-
problemFavouriteRound and Round the Circle
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
-
problemMagic Constants
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square? -
problemFavouriteMaking Boxes
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
-
problemMagic Circles
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers? -
problemRope Mat
How many centimetres of rope will I need to make another mat just like the one I have here? -
problemFavouriteAmy's Dominoes
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
-
problemFavouriteReach 100
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
-
problemFavouriteTwo Primes Make One Square
Can you make square numbers by adding two prime numbers together?