# Number (multiplication and division): Beaver Dam

## The Problem

Barney the beaver dammed a stream so that he could build a lodge for his family. He used 11 branches to make his dam. The stream had a width of 2 m. (You can see a bird’s eye view of the stream, his dam and the family lodge in the picture opposite.) To build the dam, Barney used a mixture of branches of varying lengths. The shortest branch that he used was 40 cm. The longest branch was 70 cm. Other branches had lengths of either 50 cm or 60 cm.

How many branches of each length might Barney have used?

What might his dam look like?

Is there more than one solution to this problem? How do you know?

(Teacher’s note: Barney liked arranging his dam branches end to end with no gaps in between, and each row of branches spanned the exact width of the stream. See diagram below.)

Did you know?

Beavers are herbivores and do not eat fish as commonly thought. Their diet is made up of aquatic plants and grasses, as well as the bark, twigs and leaves of trees.

## Visualising the Problem and Getting Started

Drake said, “Barney’s dam must have more than one row of branches.”

Do you agree with Drake? How do you know?