A Quick Test to check your mathematical thinking.
None of these questions require calculations beyond the simple math you can do in your head. Mathematical thinking is NOT about doing calculations. You should, however, write your responses and sometimes briefly explain your thinking.
1. Draw a line across your paper. On the left place a zero, on the right, place one billion (1,000,000,000). Now, without doing any math, write an M where you think one million should fit on this number line. After doing this, consider what you know about these numbers. If you want to change your estimate, write M-2 and explain why you made the change.
2. The King created a new metric unit of length. He stretches his arms out to his sides. The distance from one fingertip to another is now called a “King”. This is, of course divided into deciKings, centiKings, milliKings, etc. How many centiKings are in 1 King? How many square centiKings are in a Square King? How many cubic centiKings are in a Cubic King?
3. A room is 20 feet long, 10 feet wide, and 8 feet high. It has 2 doors 3 windows, 5 pictures on the wall and the temperature was 78 degrees. What is the area of the ceiling?
4. Joan sees some fabric she likes and buys three yards. Her friends like it too. She divided the cloth into eight equal parts, one for each of them. How what is the length of each piece? I promised no math, so I’ll do it for you. Three yards divided by 8 on a calculator gives you .3750 yards. If you changed 3 yards into 9 feet, 9 feet divided by 8 equals 1.2350 feet. How would you best describe the length of each piece?
5. A reporter did a survey of what kind of novels people prefer. He showed his results on a pie chart. It was labeled 55% romance, 40% mysteries or thrillers, 33% Adventure, and 20% other. Would you trust these numbers? Explain what the reporter might have done wrong.
6. A newspaper reported that 70% of females under 18 were sexually active in the past year. Do you trust this statistic? What would make better sense to you?
7. Mrs. Johnson has five children, all girls. What are the chances that her next child will be a boy?
8. Apply your answer in number 7 to gamblers who say that if Roulette machine has landed on seven odd numbers in a row that, by the “Law of Averages,” it is highly likely it will land on an even number.
9. You are interested in getting a job at a local factory. You have read that the average starting salary is $56,000 a year. This sounds like a really great salary for factory work. Would you agree? What questions would you have?
10. What are significant digits? When are they important?
11. Enrique measures hydrochloric acid in a graduated cylinder in chemistry class. The graduated cylinder is marked in milliliters. The acid comes somewhere between 24 and 25 milliliters. It seems to be just over halfway between the two marks. The best way to record this measurement is:
a. 24 ml b. 25 ml c. 24.5 ml d. 24.6 ml e. 24.65 mil f. 24.648 ml
12. 3.56 x 10³ is equal to
a. 3.56000 b. 356 c. 3560 d. 356000 e. 356.000 f. 3560000000000
13. What is 45.3769021 x 10° ?
14. What is 5x² + 6x² What is 5x² + 6x³ What is x² times x³
15. An artist claims she has no use for math in her field. Give several ways that, even an artist, needs to understand math.
The Answers are on the next page. You will understand Mathematical Thinking better if you read the answers and the explanations. Study your mistakes. Could you now avoid making these mistakes in similar problems?
If you have already read the answers and explanations, you might want to continue to the Nine Ways of Mathematical Thinking