Thinking For Ourselves

These activities, from the Association of Teachers of Mathematics (ATM) publication ‘Thinking for Ourselves’, provide a variety of contexts in which students are encouraged to think for themselves.

Activity 1: In the bag – More or less requires students to record how many more or less cubes in total there are in a bag as the teacher repeatedly adds or takes cubes from the bag. Students should record what they see carefully so they can check how many cubes there may have been in the bag at any stage.

Activity 2: No remainders begins with twelve of the front of the class stood in pairs to make six groups of two. Ask students to determine what other groupings could be made. What happens if the students are asked to stand in groups of eight? This introduces the idea of a remainder when dividing. Students are then given sets of cubes and asked to make different sized groups and record whether that group size produces a remainder. This activity could lead to practice of multiplication, division and the concept of factors.

Activity 3: Who was Sam? – Breaking the code! Students are given a problem to which there are many solutions. All of the satisfactory solutions are written on the board. Further conditions are introduced to reduce the number of solutions. The concept of the digital root is introduced in which the digits of a number are added to find the digital root.