Education
Age Range: 14-16
Duration: 0-29 mins
• Mathematics

# Model boat maths challenge for GCSE

## Calculate the distance a model boat will travel across water

Two friends are on opposite banks of a river which is 30m wide. One of them has a model boat and plans to send it across the river to the other. The boat has a small motor which moves it forward. Once the boat is in the water, it cannot be steered. Can you calculate the distance that the model boat will need to travel across the water?

This fun maths challenge will teach students about forces and motion and is perfect for GCSE students!

## Activity: Model boat maths challenge for GCSE

The students can work individually or in pairs. Download the teacher presentation below and allow the students some time to read the task on the first slide, then show them slide 2.

Students will need to find the distance downstream from the starting point. A generalised approach to such problems should be introduced along with slide 2.

Leave the students to work on the task and then compare approaches and answers. A GeoGebra file has been supplied to help with the discussion.

## Problem Solving

The students can tackle the problem in a number of ways. Some may choose to look at the path of the boat at 1 second intervals, possibly plotting the path on a graph. This is the way the GeoGebra file works. Others may use trigonometry to find the angle the boat travels and then use this with the 30m width of the river to find the distance downstream.

Another approach would be to use a scale drawing.

Pythagoras theorem or trigonometry can be used to find the displacement of the boat from its original position.

The GeoGebra file may be useful to students who wish to gather some results for the general approach or to check their answers.

## Discussion Points

This activity could provide an opportunity to introduce vectors and possible resultant force, making a connection with Physics.

Comparing the advantages and disadvantages of various approaches would provide students with the opportunity to consolidate their learning.

## Extending the problem

It could also be possible, with some students, to consider how to point the boat upstream, so that it ends up at the point directly opposite the start.

## Potential GCSE content covered

In this activity students will cover graphs, Pythagoras theorem and vectors.

## Download the free activity sheet below!

All activity sheets, worksheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs.

The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales.

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