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Solve These International Test Math Problems

Here are a few samples for readers whose appetite for math was whetted by my Monday column on international test comparisons:

From the Programme for International Student Assessment (PISA): for 15 year olds

1. Mark (from Sydney, Australia) and Hans (from Berlin, Germany) often communicate with each other using "chat" on the Internet. They have to log on to the Internet at the same time to be able to chat. To find a suitable time to chat, Mark looked up a chart of world times and found the following: Greenwich 12 Midnight is the same time as Berlin 1 a.m. and Sydney 10 a.m.

Mark and Hans are not able to chat between 9 a.m. and 4:30 p.m. their local time, as they have to go to school. Also, from 11 p.m till 7 a.m. their local time they won't be able to chat because they will be sleeping. When would be a good time for Mark and Hans to chat?

Trends in International Mathematics and Science Study (TIMSS): For eighth graders

2. Katy made a table to keep track of how long it took water in a beaker to cool from 95 degrees C to 70 degrees C. She measured the time it took the water to cool in 5 degree C intervals.

95 to 90 degrees C--Cooling time: 2 minutes, 10 seconds
90 to 85--2 min., 19 sec.
85-80--4 min., 48 sec.
80-75--6 min., 55 sec.
75-70--9 min., 43 sec.

Estimate to the nearest minute the total time taken for the temperature of the water in the beaker to cool from 95 degrees C to 70 degrees C, and explain how your estimate was made.

3. A car salesman placed this advertisement in the newspaper: "Old and new cars for sale, different prices, average price 5,000 zeds." From the advertisement, which of the following must be true?
a. Most of the cars would cost between 4,000 zeds and 6,000 zeds.
b. Half of the cars would cost less than 5,000 zeds, and half would cost more than 5,000 zeds.
c. At least one of the cars would cost 5,000 zeds.
d. Some of the cars would cost less than 5,000 zeds.

Answers: 1. 7:30 to 9 am in Berlin, which is 4:30 to 6 pm in Sydney, or 10 to 11 pm in Berlin, which is 7 to 8 am in Sydney. (Tom Loveless said the scoring guidelines appear to give full credit for either interval, and full credit if a test taker identifies just part of one of those intervals.) 2. 27 minutes; 3. d.

By Jay Mathews  | October 19, 2009; 5:55 AM ET
Categories:  Jay on the Web  
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