1. Handshakes – Assessment Ideas
Solving the problem
• Starting with a small number of people – 2 (Level 3)
• Increasing to 3,4,5, drawing a diagram for each number of people (Level 3)
• Diagram can be children’s own ideas, as this will be more relevant to them
(Level 3/4)
• Do the children suggest placing results in a table? (Level 4)
• Can the children see a pattern in the minimum number of handshakes?
(difference in numbers is plus one each time) (Level 4)
• This activity may need to be continued for some children. If they do not see
the pattern, continue using the next consecutive number – 6,7,8 etc (Level 3)
Reviewing and continuing
• If the children can see the pattern in the minimum number of handshakes can
they choose a larger (sensible) number of people, predict the answer and then
try it out, using their method of recording (probably diagrams) to prove their
hypothesis? (Level 4)
• Do the children see any mistakes in their working? If so do they correct them?
(Level 4)
Solutions
• Can the children explain the pattern to a partner? (Level 3)
• Can the children write the pattern down in their books? (Level 4)
• If triangle numbers have already been covered in previous work, do the
children see the connection? (Level 4)
• If not, an explanation could be given here – e.g. the numbers make a
triangle/difference increases by 1 each time
Extension work (Level 5)
• Can the children explain the pattern between the number of people and the
number of handshakes? (e.g. How can we get from 2 to 1, 3 to 3, 4 to 6, 5 to
10 etc, the same rule must be applied to all) This work can be linked to any
previous work on function machines.
• Can the children choose a larger (sensible) number of people, predict the
answer and then try it out, using their method of recording (probably diagrams)
to prove their hypothesis?
• This work will begin to work towards the formula for triangular numbers.
• Can the children explain the pattern to a partner?
• Can the children write the pattern down in their books?
