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Lesson Plan: A problem-solving activity involving students recognising the relationships of direct proportions.

Subject: Mathematics.
Age of students: 11-14 years.
Hardware: Tablets (iPad 1 per class or student).
Software: Socrative or Classflow + Apple airserver,
OR Showme and Reflector,
OR Plickers.
Functionalities of Technology: Sending and displaying,
Processing and analysing.
Time needed: 2-3 hours.
FaSMEd partner: University of Newcastle Upon Tyne.

This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who:

  • Use inappropriate additive strategies in scaling problems, which have a multiplicative structure.
  • Rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems.
  • See multiplication as making numbers bigger and division as making numbers smaller.


This tool describes ways in which digital technology can be used to support formative assessment. The original materials (pen-and-paper) were designed by the Mathematics Assessment Project and can be found under the link above.

Formative assessment in Science and
Mathematics Education (FaSMEd)
The Research Centre for Learning and Teaching
Newcastle University