Start Thinking… When playing the Integer Game, give two ways you can increase the value of your hand. Give two ways you can decrease the value of your.

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Presentation transcript:

Start Thinking… When playing the Integer Game, give two ways you can increase the value of your hand. Give two ways you can decrease the value of your hand.

Lesson 6: The Distance Between Two Rational Numbers Objective: I can show that the distance between two rational numbers on a number line is the absolute value of their difference. I can solve word problems involving changes in distance or temperature.

Exercise 1 Partner up with the person sitting next to you Exercise 1 Partner up with the person sitting next to you. Draw a number line on your desk. One person be A, the other person is B. Using your number line, QUIETLY solve your designated 3 problems.

Deep Thoughts…. 1. In life, at any given moment, will we always be able to use a number line to find the distance between two rational numbers? Is it the most efficient way to calculate the distance between two points? 3. If the distance between 5 and 0 can be represented as 5−0 = 5 = 5, can we use this to find the distance between -4 and 5? 2. What represents the distance between a number and zero on the number line?

Distance Formula For any two rational numbers p and q, the distance between p and q is │p - q│. The distance between -3 and 8 is 11. │-3 - 8│= │-3 + (-8)│= │-11│=11 or │8 – (-3)│= │8 + 3│= │11│=11

Exercise 2 Use the formula to find the distance between each of the two given end points. Use a number line to verify. What is the distance between 0 and -8? What is the distance between -2 and −1 1 2 ? What is the distance between -6 and -10?

Example 1 Change in Elevation vs. Distance

Distance is always _______________________. Change can _____________ or ______________.

Example 2

Example 3 & 4

Exit Ticket

Closing Reflection 1. How can we use a number line to find the distance between two rational numbers? What does it mean to find the absolute value of a number? Is it possible to use absolute value to find the distance between a number p, and another number, q, that is not zero? If so, how? Is distance always positive? Is change always positive?