article
Placing Our Trust in Learners
In this article Liz Woodham reflects on just how much we really listen to learners’ own questions to determine the mathematical path of lessons.
Conjecturing and generalising
problem
Finding 3D Stacks
Age
7 to 11
Challenge level
Can you find a way of counting the spheres in these arrangements?
problem
Summing Consecutive Numbers
Age
11 to 14
Challenge level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
problem
All Change
Age
5 to 7
Challenge level
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
problem
Poly Plug Rectangles
Age
5 to 11
Challenge level
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
problem
Attractive Tablecloths
Age
14 to 16
Challenge level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem
Few and far between?
Age
16 to 18
Challenge level
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
problem
Filling the gaps
Age
14 to 16
Challenge level
Which numbers can we write as a sum of square numbers?
problem
Can they be equal?
Age
11 to 14
Challenge level
Can you find rectangles where the value of the area is the same as the value of the perimeter?
problem
Generating Triples
Age
14 to 16
Challenge level
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?