“Jacob, you estimated too high. You will have too much carpet,” said Jackie. “I think a better estimate is 8 feet 7 feet = 56 square feet of carpet.”
“Jackie, you estimated too low. You won't have enough carpet,” said Jerome. “I think the best estimate is to round 8.5 feet down to 8 feet and 7.5 feet up to 8 feet.
“8 feet 8 feet = 64 square feet of carpet.”
“Those estimates are useful, but I need a more exact answer to buy carpet,” explained Mr. Moreno.
“I've got it,” said John. “I can use a rectangle model to find the answer.”
Paper-and-Pencil Methods
John drew the rectangle below and filled in most of it. “But I'm not sure how to solve 0.5 0.5,” he said.
“I just forget about the decimal points and multiply the whole numbers,” Shannon suggested. “To solve 8 0.5, I thought 8 5 = 40 and estimated that the answer should be less than 8, so I wrote 4.0. To solve 0.5 7, I thought 5 7 = 35 and estimated that the answer should be 3.5.”
“So to solve 0.5 0.5, I can think 5 5 = 25 and estimate that the answer should be 0.25,” reasoned John.
John added up the partial products. “You will need to order 56 + 4.0 + 3.5 + 0.25 square feet of carpet, Mr. Moreno!” John said proudly. “That's a total of 63.75 square feet.”
