# The tomato and the bean

At the beginning of May, Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Tom's Dad sowed some tomato seed in February. He gave Tom one of the tomato plants in a pot.

At the beginning of May, Tom put his tomato plant outside. On the same day he sowed a bean in another pot.

Ten days later the bean plant was just $1$ cm (centimetre) above the soil surface. Tom measured his tomato plant which was already $38$ cm tall.

Each evening Tom measured his two plants.

On the evening of the next day the little bean plant had grown another $2$ cm so it was $3$ cm high. Each day it continued to grow double the amount it had grown the day before.

The tomato plant grew at a steady $5$ cm a day.

After how many days were the two plants the same height when Tom measured them in the evening? How high were they?

How tall will the bean plant be the next day?

How tall will the tomato plant be on that day?

How about the day after that?

The solutions we had in, varied in the ways they were expressed.

We had many contributions from Crudgington Primary School in Shropshire, U.K.

Firstly, I drew two pictures one of a tomato plant and one of the bean plant. Then I made myself a little chart like this ...

... and so on. As you can see that on the section where I worked out the bean plant's results the first number I wrote was how much the plant would need to increase in size. I found that this helped me a lot. Then I wrote the height of the plant and finally how many days it took for the plant to reach that height. I did this same method for the tomato plant until the height was the same. So the answer is: the height is $63$cm after $15$ days of growing.

Tom

First I looked at the information and saw that the bean plant grew only $1$cm after $10$ days! So I started from $10$ days. And after the bean plant grew $1$cm the tomato plant had already grown $38$cm. And then after each day the bean plant doubled its current size and the tomato plant grew $5$cm. So after $15$ days both plants are $63$cm.

From Curl Curl North School in New South Wales we had two answers that at first looked different but were just being expressed from a different point of view. Christopher, Ashton, Grace, Charlotte, Kaden, Ben, Kate, Charlie, Dylan, Josh, Matthew and Mitchell's team, said;

$6$ days from the time the bean was first measured.

And from Sean, Emma, Emily, Amelia, Ed and Stacey's team we had:

$5$ days because you count from when the bean was $3$ cm tall.

I wonder if they thought the other team had the wrong answer?

**Why do this problem?**

This problem can help to give learners an understanding of the difference between a steady and an increasing rate of growth. It could be used when looking at number patterns, especially doubling. It puts patterns in a real context, and can be used to demonstrate the use of tables in problem solving. It will also be fascinating for you, as the teacher, to see how children represent the problem while they work on it.

### Possible approach

### Key questions

### Possible extensions

Learners can be encouraged to open out this activity further by considering plants that increase their rate of growing by trebling/quadrupling the growth each year. Each year's height could be calculated and learners can see what happens.

### Possible support

Suggest using this sheet and filling in first the days ($1$-$8$) and the heights on the first day. The bean's growth is easier to work out than the tomato's so this can be tackled next.