Mathematical+Reflections,+p.+17+0910

4/13/10 TJ 7E

Big Idea: Negative numbers help us to model many real world situations. Essential Question: How do I put positive and negative numbers in order? Notes from class:
 * Whole numbers are always integers
 * Fractions and decimals are not integers

__Mathematical Reflection 1__ In terms of keeping score in MathMania, if a team begins at 0 points, if they answered a question correctly, the score would add up to be a positive number. If they answered a question incorrectly, they would lose points and their score would be a negative number.
 * 1.Describe what positive numbers, negative numbers and 0 (zero), mean in terms of:**
 * A) Keeping score in MathMania.**

In terms of temperature readings, if the temperature is above 0 degrees, it means that it is positive which says that the temperature is warmer. If the temperature is below 0 degrees, it means that it is negative which says that the temperature is colder.
 * B) Temperature Readings.**

A) Two positive numbers.** To decide the greater number between two positive numbers, the one that is higher is greater. For example: 6 is higher than 5, therefore it is the greater positive number.
 * 2.Describe how you can compare the following types of numbers to decide which is greater. Use examples to illustrate your thinking.

To decide the greater number between two negative numbers, the one that is lower is greater. This seems strange but it is true. For example: -1 is lower than -3, therefore it is the greater negative number.
 * B) Two negative numbers.**

To decide the greater number between a positive and a negative number, the positive number is always greater than the negative number. For example: between -4 and 5, 5 is the postive number therefore it is the greater number.
 * C) A positive and a negative number.**

On a number line, the numbers to the right of 0 are positive while the numbers to the left of 0 are negative. The greater negative numbers are closer to 0. Postive numbers are always in the same order. When locating a decimal on the number line, it's on the negative side between two numbers. For example, between -1 and -2, the decimal would be -1.5. Fractions are located on the positive side between two numbers. For example, 1 1/2 is between 1 and 2. This picture above is an example of a number line that has positive and negative numbers as well as fractions and decimals. It also shows how to locate numbers on a number line.
 * 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 in your examples.**

In this investigation we worked with positive and negative numbers on a number line. We also compared numbers and learned how to decide whether one number is less or greater than another. We even looked at temperature readings and analyzed sequences of events in the MathMania game.
 * Summary**