Mathematical+Reflections,+p.+17

Eva v. V.
Block B

Big Idea:
Negative numbers help us to model many real world situations.

Essential Question:
How do I put positive and negative numbers in order?

Mathematical Reflections 1, page 17
a. keeping score in MathMania. b. temperature readings.**
 * 1. Describe what positive numbers, negative numbers, and 0 mean in terms of


 * 1a.** In MathMania, a score below zero (a negative number) means that you're not doing too well in the game, because the goal is to get as many points as possible. A score above zero (a positive number) is good, because at least you're a positive number, which is more than a negative number. A zero just means you're in the middle, with no points at all.
 * b.** In temperature readings, a positive number means that the temperature is above zero, warmer than below zero, and if you're measuring in degrees celcius, above the freezing point. A negative number means that the temperature has dropped below zero, so has gotten colder, and in degrees celcius it means that it's below the freezing point. A zero means it's cold, and exactly on the freezing point, and in the middle of being above or below zero.

a. two positive numbers b. two negative numbers c. a positive and a negative number**
 * 2. Describe how you can compare the following types of numbers to decide which one is greater. Use examples to illustrate your thinking.


 * 2a.** If you're comparing two positive numbers, the bigger number, the one furthest away from zero, is always greater in value, because it's a number above zero. So if you had the numbers 4 and 53, 53 is the greater number because it is further away from zero.
 * b.** If you're comparing 2 negative numbers, the one closest to zero is always greater, because the numbers get smaller the further away from zero, because they're less than a whole. So if you have the numbers -10 and -28, -10 would be the greater number because it is closer to zero.
 * c.** If you're comparing a positive and negative number, the positive number will always be greater because it's above zero.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 **0** 1 2 3 4 5 6 7 8 9 10
 * 3. Describe how to locate numbers on a number line. Use examples to illustrate your thinking. Be sure to include positive and negative numbers as well as fractions and decimals.**

If you want to find numbers on a number line, you really just have to look for them. Look to the left of the zero to find negative numbers, and to the right of the zero to find positive numbers. Say you're looking for -5. You find the zero on the number line, and look to the left. You'll see -1, and you just go down the line till -5. If you need to find a decimal on one of these number lines, you'd just about always look to the left of (below) zero, and for a fraction as well; unless the fraction is 1 whole and 1/5 or something like that.


 * Summary:** In this investigation, positive and negative numbers got introduced to us, and we learned how to use them and times when they might come in handy; temperatures and games. Also, we learnt how to add and subtract them, how to find the greatest number, how to use a number line, what zero has to do with all of this, and what opposites are. The problems we did were sort of an introduction to the chapter about positive and negative numbers, something to help us get started.