CLASS NOTES. In the context of this story, what does a positive number mean? A negative number? Zero?

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1 CLASS NOTES NAME So far in this chapter, you have made connections between integer expressions and movement on a number line. Today you will use your understanding to compare expressions, to determine the values of signed numbers, and to find out which frog is farther from the starting place in a jumping contest even if the frogs hop in different directions. As you work today, keep these target questions in mind: What does it mean for a number to be greater? What are the ways in which I can compare two numbers? How can I determine the distance jumped? Lorena s bank will loan money to customers if they overdraw their accounts by less than $100. (To overdraw an account means to have the account balance fall below zero.) Lorena started out with a balance of $13.00 and made a withdrawal from her account of $ In the context of this story, what does a positive number mean? A negative number? Zero? Lorena's final balance is $ Will the bank loan her this amount? Write a numerical inequality to show why or why not Dr. Frog and Bumble Frog were in a jumping competition. Both frogs started at zero on a number line, but they had trouble jumping in the same direction consistently. Dr. Frog hopped 8 feet to the right and then 3 feet to the left. Bumble Frog hopped 9 feet to the left and then 1 foot to the right. Write expressions to represent the jumps for each frog. Which frog is ahead? (That is another way of asking which frog is sitting on a larger number on the number line.) Explain. Imagine now that the winner of the frog-jumping contest is the frog that lands farthest from zero and that the direction the frog jumps does not matter. In this case, which frog would win? Explain When you compare jumping frogs, sometimes you want to compare the values of where they land. Other times, you want to compare the distances between the ending spots and the starting spots. In the case of the frog problems, the distance between the ending and starting spots is the distance from zero. The numerical value of a number without regard to its sign is called the absolute value. Absolute value can represent the distance on a number line between a number and zero. Whether a frog is 3 feet to the left of zero on a number line ( 3), or if a frog is 3 feet to the right of zero on the number line (+3), either way, the frog is still just 3 feet away from zero! This is the idea of absolute value. Straight vertical bars around the expression or number are used to indicate the distance or absolute value of an expression or number. For example, to show that a frog s location is 3 feet right of zero, you would write. To show that a frog s location is 3 feet left of zero, you would write.

2 Mr. Wizzard started at 0 and jumped left 7 feet. Auntie Long Legs started at 0 and jumped right 5feet. Which frog was ahead? Write an inequality statement (using < or >) to compare the values of their landing points. For each frog in part (a), write an absolute value statement that shows the distance that each frog ended up from zero. Which frog was farther from zero? To find the absolute value of an expression, you put the expression into the absolute value bars. For example, in problem you could have written and. For the two jumping contests described below: Find the landing point of each frog. Then compare the value of the two landing points with an inequality statement. Write mathematical sentences using absolute value for the distance each frog landed from zero. Which frog was farther from zero? Write another inequality statement. Hopping Hannover: 7 5 GG: Bea Major: 3 6 Dee Minor: 7 3.5

You have worked with movement along a one-dimensional number line, but what if the movement is two-dimensional? This kind of movement can be represented on a coordinate graph like the one shown below.

3 You have worked with movement along a one-dimensional number line, but what if the movement is two-dimensional? This kind of movement can be represented on a coordinate graph like the one shown below. Imagine a grid overlaying the Calaveras County Frog Jumping Contest, with the center of the grid as the spot where the frogs begin jumping. The center of the grid is also called the origin, or (0, 0). A coordinate point on the grid could represent the landing point of each frog s jump. How can you use this information to find the distance that the frog jumped? Think about this as you work on today s problems Suzie has decided it is time to improve the recreation room in her house. She wants to estimate the cost of her improvement project. To help her visualize the room, she started by creating a scale drawing of the room, shown at right. The drawing is an accurately drawn smaller version of the room. Each unit represents 1 foot. Obtain the Lesson 3.2.4B Resource Page, Suzie s Recreation Room, from your teacher. You will use it to answer the questions below. Why do you think Suzie created her scale drawing on a coordinate graph instead of on plain paper? The flooring will cost $2 per square foot. How much will it cost Suzie to lay this flooring so it fully covers the floor of room? Now Suzie wants to install new baseboards along the bottom of all of the walls. The baseboard will cost $0.75 per foot. How much will this cost Suzie? Suzie s cousin, Antwon, was impressed with her scale drawing and cost estimate. He wanted her help to figure out a problem. a. Antwon lived in a different state, so he called Suzie and gave her the coordinates to the scale drawing he made for his room. The points were A( 4, 6), B(6, 6), C(6, 10), D(2, 10), E(2, 2), and F( 4, 2). Sketch Antwon s room on the bottom half of the Lesson 3.2.4B Resource Page. b. Is there a way to find the length of the sides using just the coordinates and without actually plotting the diagram? For example, can you determine the length of the side from point D to point E using the points (2, 10) and (2, 2)? c. Without looking at your graph, use your reasoning from part (b) to find the length of the remaining sides. Then, check your work using your graph.

4 Read the Math Notes box at the end of this lesson to refresh your memory about absolute value. Think about how you can use absolute value notation to express the distance between two points on a coordinate graph. For each pair of points below, find the distance between the given points and express your work using absolute value symbols. (4, 9) and ( 5, 9) (7, 1) and (7, 4) (0, 9) and (0, 7) (4, 8) and ( 10, 8) HOW DO THE LOCATIONS COMPARE? For each set of coordinates listed below, what do you notice? Plot each set of coordinates below on a coordinate graph. Explain what you noticed about the location of pairs of coordinates on the graph. (8, 1) and ( 8, 1) (5, 7) and (5, 7) ( 4, 3) and ( 4, 3) (3, 5) and ( 3, 5) Explain how what you noticed about the sets of ordered pairs relate to the locations of the pairs of points..

5 3.2.3/3.2.4 CLASSWORK NAME Simplify the following expressions. Show your work Solve the number puzzles below. If I add 9 to my number, I get 6. What is my number? If I start at 5 on a number line and end up at 8, what direction did I move? How many units did I move? If I moved up 8 and then moved down 8, what can you tell me about my ending position? Evaluate each absolute value expression below Name the endpoints of the segment shown on the graph below. What is the length of the segment? Write an absolute value expression to show how to calculate the length of the segment.

6 Bellringer Compute each sum or difference. Simplify if possible.

Fair Game Review. Chapter 2. Name Date. Write the decimal as a fraction Write the fraction as a decimal. 7.

$Fair Game Review. Chapter 2. Name Date. Write the decimal as a fraction Write the fraction as a decimal. 7.$ Name Date Chapter Fair Game Review Write the decimal as a fraction.. 0.6. 0.79. 0.7. 0.86 Write the fraction as a decimal.. 8 6. 7. 6 8. 7 0 9. A quarterback completed 0.6 of his passes during a game.