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A Day with Grandpa

Age 7 to 11 Challenge Level:

William went to spend the day with Grandpa. Grandpa was busy measuring a rug to put on the hall floor. He was using yards, feet and inches to measure with. Grandpa always did.

William was learning about area at school. "I wonder what the area is?" he pondered.

Grandpa wrote down his measurements and drew this sketch.

"It's two yards and one foot by one yard and one foot. There's three feet in a yard, so that's seven foot by four foot. Let me see, that's twenty-eight square feet and that's .... hmm ..... three square yards and one square foot."

Was his calculation correct?

"Let's measure the doormat," he said, "You do it." William used Grandpa's measuring tape.
"The doormat's two feet and six inches by one foot three inches," he announced.
Grandpa did another sketch.


He thought for a while.
"There's twelve inches in a foot, so it's three square feet and eighteen square inches," he announced at last.

Was this calculation correct?

Grandpa was getting into his stride. "Let's measure the rug in front of the fire, too," he said excitedly.

It was two yards, one foot and five inches long and one yard, two feet and seven inches wide.

"How do you work it out?" inquired William. "You multiply them together, of course," said Grandpa airily.

He wrote some figures on his paper.

"Wow! How do you do that?" asked William peering at it.
Grandpa looked at his paper for a long time.
"I can't remember," he hesitated, "Can you think of a way to do it?"

Can you think of a way to do it?