Can you solve this 11+ Maths Question from St Olave’s School?

Hey, everyone! Welcome back to another St. Olave’s video. Today, we’re delving into a fascinating 11+ Maths question. This blog post stems from our experience working with students on this exact problem. Let’s jump right in as we explore how to solve this with the bar model approach.

The Problem Statement

Ben plants a seed, and each morning, the plant grows to one and a third times its height from the previous day. On Tuesday morning, the plant is 18 centimetres tall. Here’s the full question:

How tall will the plant be on Thursday?

Let’s break it down step-by-step using the bar model method, a strategy we’re quite well-known for, but still relatively new to many teachers in England.

Understanding the Growth Rate

Every morning, Ben finds that the plant is one and a third times taller than the previous morning. Here’s the breakdown:

Tuesday: The plant is 18 cm tall.

Our task is to determine the plant’s height on Thursday. To do this, we need to understand the plant’s growth over two subsequent days: Wednesday and Thursday.

Visualising the Growth

First, we need to grasp what it means for the plant to grow “one and a third” times taller each day.

Tuesday: 18 cm

------|------|------18 cm        (whole)

This bar represents Tuesday’s height of 18 cm.

Wednesday’s Growth

On Wednesday, the plant is one and a third times Tuesday’s height:

------|------|------18 cm + (1/3 of 18 cm) 18 cm / 3 = 6 cm

So, Wednesday’s height is:

18 cm (whole) + 6 cm (1/3 of 18 cm) = 24 cm

------|------|------18 cm |  6 cm (1/3) |  24 cm

Therefore, the plant’s height on Wednesday is 24 cm.

Thursday’s Growth

Now, applying the same logic to find Thursday’s height:

Wednesday: 24 cm24 cm (whole) + 8 cm (1/3 of 24 cm)

------|------|------24 cm + (1/3 of 24 cm)24 cm / 3 = 8 cm24 cm + 8 cm = 32 cm

So, on Thursday:

------|------|------24 cm | 8 cm (1/3) |  32 cm

Thus, the plant will be 32 cm tall on Thursday.

Reverse Calculation: Finding Monday’s Height

Now, let’s tackle a slightly trickier part of the question:

How tall was the plant on Monday morning?

Given Tuesday’s height of 18 cm (including the one and a third growth from Monday), we need to backtrack to Monday.

Bar Model for Reverse Calculation

We know Tuesday’s height includes an additional third of Monday’s height.

Tuesday: 18 cm (whole)18 cm = Monday’s 3 parts + 1 additional part.

This means Tuesday’s height (18 cm) is equivalent to four parts (three parts being Monday’s height, and one part the additional third of Monday).

Let’s divide 18 cm into four equal parts to find one part:

18 cm / 4 = 4.5 cm

Each part is 4.5 cm. So, Monday’s height (three parts) is:

4.5 cm * 3 = 13.5 cm

Therefore, on Monday, the plant was:

------|------|------4.5 cm | 4.5 cm | 4.5 cm = 13.5 cm

The plant was 13.5 cm tall on Monday.

Conclusion: Utilising Bar Models

By using the bar model approach, we’ve visually and analytically broken down a relatively complex word problem into simpler, manageable parts. This methodology is not only effective for understanding growth patterns but also reversing calculations to determine prior measurements.

The power of bar modeling lies in its simplicity and effectiveness in visualizing problems:

“It opens up the question for you, allows you to see what the next steps are, and then enables you to solve challenging word problems with a lot more ease.”

We hope this detailed breakdown has clarified how to tackle such problems. Let us know if you found this question easier with the bar model or prefer another method.

Thank you for reading, and see you in the next blog post!