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The Tree and the Greenhouse

Age 7 to 11
Challenge Level

The Tree and the Greenhouse

view from greenhouse

Mum, Dad and their two children, Emily and Isabel, moved into a new house. At the end of the lawn was a big tree which had a disease and was dying.

tree, greenhouse and house


Mum said she wanted to cut the tree down before it fell down.

Dad said, "How do we know we won't hit the greenhouse?"

Mum answered," We'll measure the lawn and find out how tall the tree is!"

"How?!!" Dad, Emily and Isabel all exclaimed.

Mum said,"I'll show you!"

Emily measured the distance from the tree to the greenhouse with her metre ruler.

"Thirty-one and fourteen centimetres," Emily said.

"Now measure the shadow of the tree, you two, and make it fairly accurate!"

Emily and Dad measured the tree's shadow. Mum and Isabel pushed the end of the bamboo cane into the ground so that exactly a metre stuck out.

"Now," said Mum, "we'll measure the shadow of this cane and then we will be able to work out the height of the tree."

The shadow of the tree was $36.3$ metres long and the shadow of the cane was $123$ centimetres.

"It's OK," Mum announced, "it won't reach the greenhouse!"

fallen tree, greenhouse and house


How tall was the tree?

Why do this problem?

This problem will encourage children to draw diagrams and mark measurements on them in the process of solving the problem.

Key questions

Would it be a good idea to draw a diagram of the tree and its shadow, and the stick and its shadow?
Would using a calculator help you?

Possible extension

Learners could try Hello Again which is a Stage 3 problem.

Possible support

Suggest starting by drawing a diagram of the tree and its shadow, and the stick and its shadow. Alternatively, learners could try Once upon a time which is a similar, but easier, problem.