This document provides ideas for assessing students' understanding of handshakes problems of increasing difficulty: 1) Have students draw diagrams and look for patterns when solving problems with 2-5 people to find the minimum number of handshakes. 2) Challenge students to suggest placing the results in a table and identify that the minimum number increases by one each time. 3) For stronger students, have them explain the pattern between the number of people and number of handshakes to begin deriving the triangular number formula.

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?