St Olave’s 11+ Ratio Growth with Bar Model

In this video, Singapore Maths Academy uses the bar model approach to solve a creative and challenging ratio growth problem taken from a St Olave’s Grammar School 11+ maths past paper. The question tracks the height of a growing plant, where each day the plant increases to 1⅓ times its previous height.

Students are told the plant is 18 cm tall on Tuesday morning. The tasks are:

• (a) How tall will it be on Thursday morning?
• (b) How tall was it on Monday morning?

We solve part (a) by multiplying successively by 1⅓ (or 4/3) to move forward in time, and part (b) by dividing by 1⅓ to work backwards — all visualised through a clear bar model. This approach is ideal for students who benefit from visual learning and helps make abstract multiplicative reasoning more concrete.

This type of question is typical of St Olave’s 11+ exams, where logical reasoning and ratio skills are tested in creative contexts. A great problem for boosting confidence in both algebra-free reasoning and mathematical modelling.