Name: Date: Core: Rational Numbers. Opposite and Absolute Value of Integers. Comparing and Ordering Rational Numbers

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1 Name: Date: Core: Rational Numbers Comparing and Ordering Integers Opposite and Absolute Value of Integers Intro to Rational Numbers Comparing and Ordering Rational Numbers Rational Numbers on Coordinate Grids Rational

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3 Name: Date: Class: Rational Numbers Initial Warm-up. Write these numbers in order from least to greatest: -, 3, 0,, -, 4,-5,. What number is the opposite of 5? 3. What is the absolute value of Explain what integers are: 5. List two different situations in the real world (not just in math class!) in which we use negative numbers: Situation : Situation : Rational 3

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5 Name: Date: Class: Integer Introduction Notes / Exploration Introducing Mr. Number Line!!! Key things to remember about Mr. Number Line: He has a really wide head (but please don t tease him). He has lots and lots of teeth (people say they go on forever!). He is happy (positive) half of the time and unhappy (negative) half the time. He is incredibly useful in doing all kinds of math. He s always there for you when you need him! What s on Mr. Number Line?: INTEGERS = + + and go on in both directions! Are integers the only numbers on Mr. Number Line?, Mr. Number Line also has and, but we ll work with those later! Rational 5

6 Name: Date: Class: Comparing and Ordering Integers Notes / Exploration Using Mr. Number Line to Compare and Order Integers: Integer Poetry to live by: Can we put them all in order? Plot the and we just might. Cause the number that is greater is the number to the! Example : Write these numbers in order from least to greatest (increasing order): 4, -, 3, 0,, -, -5 Step : Plot the points on Mr. Number Line , -, 3, 0,, -, -5 Step : Write the points from left to right as you see them on Mr. Number Line: Example : Write these numbers in order from greatest to least (decreasing order): -3, 7, 3, -4, -6 Step : Plot the points on Mr. Number Line , 7, 3, -4, -6 Step : Write the points from right to left as you see them on Mr. Number Line: Rational 6

7 Name: Date: Class: Comparing and Ordering Integers Worksheet First, remember the first two lines of your integer poetry: Can we put them all in order? Plot the points and we just might. Cause the number that is greater is the number to the right! Next, follow the instructions below:. Plot each pair of numbers on Mr. Number Line. Then insert > or < signs between them. The first problem has been completed for you > a. 8 b c d Label all tick marks first! e f Insert > or < signs between the numbers below by simply looking at or thinking about where they are on Mr. Number Line: a. 0-7 b c. -3 d. 4-5 e. 4 9 f. -7 g h i j k. -36 l m n. - Rational 7 o. 4-76

8 Name: Date: Class: Comparing and Ordering Integers Worksheet (Continued) First, remember the first two lines of your integer poetry: Can we put them all in order? Plot the points and we just might. Cause the number that is greater is the number to the right! Next, follow the instructions below: 3. Plot each group of numbers on Mr. Number Line. Then write them in order from least to greatest: Label all tick marks first! Be careful plotting these points! a. 7, -4, -5,, -8, b. 0, -, 3, -, 3, Plot each group of numbers on Mr. Number Line. Then write them in order from greatest to least: a. -8,, 6, -6, -4, 3 Be careful plotting these points! Label all tick marks first! b. -8, 5, -,6,-6, 5. Which of the following groups of numbers is listed in proper increasing order? a. 0, -, 5, 6, -7 b. -7, 6, 5, -, 0 c. 6, 5, 0, -, -7 d. -7, -, 0, 5, 6 6. Which of the following groups of numbers is listed in proper decreasing order? a. 0,, -4, -5, -8 b., 0, -4, -5, -8 c. -8, -5, -4, 0, d. -8, -5, -4,, 0 7. Benji swims below sea level at an altitude of -3 feet (3 feet below the surface). Kenji swims at 7 feet. Which scuba diver is deeper? How do you know? Rational 8

9 Name: Date: Class: Integer Opposite and Absolute Value Warm-up.Plot these points on Mr. Number Line, then write the numbers in order from least to greatest: , 3, 0,, -, 4, -5. What is the opposite of -5? Why do you think so? 3. In what ways are the integer 4 and the integer -4 similar? 4. In what ways are the integer 4 and the integer -4 different? Rational 9

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11 Name: Date: Class: Opposite and Absolute Value Notes / Exploration Using Mr. Number Line to Find Opposites: More Integer Poetry to live by: Can we put them all in order? Plot the points and we just might. Cause the number that is greater is the number to the right! Opposites are easy, just switch the. Or go the same distance on the far side of! Example : What is the opposite of the integer 5? Step : So we start at the origin and move units in the other direction to find the opposite. Step : We note that 5 is 5 units from the origin So the opposite of 5 is. We write it like this -(5) = Example : What is the opposite of the integer -6? Step : So we start at the origin and move units in the other direction to find the opposite. Step : We note that -6 is 6 units from the origin So the opposite of -6 is We write it like this: (-6) = Now try these without Mr. Number Line: a. (4) = b. -(-4) = c. -(-7) = d. (46) = e. (-) = Other Key Points to Remember About Opposites:. The sum of a number and its opposite is always.. 3. There is only one integer whose opposite is equal to itself and that integer is. Finding the opposite of an integer should not be confused with flipping the integer over (the opposite of the integer 5 is NOT 5!). The flipped over version of the number is called the of the number. Rational

12 Name: Date: Class: Opposite and Absolute Value Notes / Exploration (continued) Using Mr. Number Line to Find Absolute More Integer Poetry to live by: Values: Can we put them all in order? Plot the points and we just might. Cause the number that is greater is the number to the right! Opposites are easy, just switch the sign. Or go the same distance on the far side of Mr. Number Line! An absolute value is happy. It feels like a hero! Cause it s the distance of the number from. Example : What is the absolute value of the integer 6? The distance of the integer 6 from the origin is So the absolute value of 6 is. We write it like this 6 = Absolute value sign! Example : What is the absolute value of the integer -6? The distance of the integer -6 from the origin is So the absolute value of -6 is. We write it like this -6 =. Now try these without Mr. Number Line The opposite of the absolute value of negative one. a. 3 = b. -3 = c. -7 = d. 46 = e. - - = Other key points to remember about absolute values.. Unlike opposites, which can be negative or positive, absolute values are always. For all negative integers, the absolute value equals the of the integer. 3. For all non-negative integers, the absolute value of the integer equals. Rational

13 Name: Date: Class: Opposites and Absolute Values Worksheet Remember the integer poetry to live by: Opposites are easy. Just switch the sign. Or go the same distance on the other side of Mr. Number Line. An absolute value is happy. It feels like a hero! Cause it s the positive distance of the number from zero!. Draw appropriate arrows and labels, and plot appropriate points to find: a. The opposite of 8: b. -(-3): Arrow, label, and point go here! Arrows, labels, and points go on both sides! c The absolute value of 7: Arrow, label, and point go here! d. -5 = Arrow, label, and point go here! Evaluate each phrase or expression below: a. The opposite of 9 = b. The opposite of -7 = d. The absolute value of -36 = f. -(6) = g. -(-39) = l = 3. e. The opposite of the absolute value of 36 = h. - (0) = m. - -(-4) = c. The absolute value of 7 = i. 9 = n. - -(7) = j. -3 = o. - -(-7) = k. 0 = p. - 0 = Insert >, <, or = signs between each pair of numbers below: a. - -(-) b. - (-) c. - -() d. -() e. - -(-3) f. - - g. - h. - i. j. -3 k. -7 -(8) l. 7 -(-3) p. -(-3) -(-6) p m. - -(3) n Rational 3 o

14 Name: Date: Class: Opposites and Absolute Values Worksheet (continued) Remember the integer poetry to live by: Opposites are easy. Just switch the sign. Or go the same distance on the other side of Mr. Number Line. An absolute value is happy. It feels like a hero! Cause it s the positive distance of the number from zero! 4. Put each group of values in order from least to greatest: a. -3, 7, -(-6), 0, -(7), 5, -(-4) b. -3, -(-),, -4, -, -(-6) c. - -4, -(-3), 5, -, -, 4 5. Midori decides to use the points T (), S (7), O (-3), and P (-6), to have some fun with opposites and absolute values. a. First, she plots and labels the points on Mr. Number Line and writes the letters in order. What word does she spell? Plot and label points like this! b. Next, she takes the opposite of each of the numbers, plots and labels the resulting points on Mr. Number Line, and writes the letters in order. What word does she spell? T c. Then she takes the absolute value of each of the original numbers, plots and labels the resulting points on Mr. Number Line, and writes the letters in order. What word does she spell? d. Finally, she takes the opposite of the absolute value of each of the original numbers, plots and labels the resulting points on Mr. Number Line, and writes the letters in order. What word does she spell? Rational 4

15 Name: Date: Class: Rational Number Introduction Notes / Exploration Re-Introducing Mr. Number Line!!! Key things to remember about Mr. Number Line: He has a really wide head (but please don t tease him). He has lots and lots of teeth (people say they go on forever!). He is happy (positive) half of the time and unhappy (negative) half the time. He is incredibly useful in doing all kinds of math. He s always there for you when you need him! What kinds of numbers are 𝟑 𝟏 𝟑 on Mr. Number Line?: π 4.8 𝟔 𝟑 𝟓 = = = Integers = + + and go on in both directions! = = = Numbers = and include any number that can be made into a. π does not or, making it an Number. Numbers = + (everything on Mr. Number Line!) Rational 5

16 Name: Date: Class: Comparing and Ordering Rationals Notes / Exploration Using Mr. Number Line to Compare and Order Rationals: First, remember your Rational Number Poetry to live by! Can we put them all in order? Plot the and we just might. Cause the number that is greater is the number to the! Opposites are easy. Just switch the. Or go the same on the other side of Mr.. An is happy. It feels like a hero! Cause it s the distance of the number from! Next, use what you know to plot the points and write them in order: Example: Write these numbers in order from least to greatest (increasing order): 𝟏 𝟐 4., - (-), 𝟑, 0,, -.5, -5, -𝟏 𝟑 𝟓 Step : Evaluate all opposites and absolute values and convert fractions to decimals as necessary: 𝟏 𝟐 4., - (-), 𝟑, 0,, -.5, -5, -𝟏 𝟑 𝟓 3 5 = = Step : Plot the points on Mr. Number Line: Step 3: Write the plotted points from left to right as you see them on Mr. Number Line: Rational 6

17 Name: Date: Class: Comparing and Ordering Rationals Worksheet First, remember the first two lines of your rational number poetry: Can we put them all in order? Plot the points and we just might. Cause the number that is greater is the number to the right! Next, follow the instructions below:. Plot each pair of numbers on Mr. Number Line. Then insert > or < signs between them. The first problem has been completed for you > a. 8 b c d Label all tick marks first! e. -.5 f Insert >, <, or = signs between the numbers below by simply looking at or thinking about where they are on Mr. Number Line: a. 0-7 b c. 3 e f g i. m. 4 7 j k n..7 9 Rational 7 h. 3 d (- ) 8 l o. 4 7

18 Name: Date: Class: Comparing and Ordering Rationals Worksheet (Continued) First, remember the first two lines of your integer poetry: Can we put them all in order? Plot the points and we just might. Cause the number that is greater is the number to the right! Next, follow the instructions below: 3. Plot each group of numbers on Mr. Number Line. Then write them in order from least to greatest: a. -(-7.5), -., -5.4, -.4 b. 0, -4,, c. 3.5,, -.3, 3 3 Label all tick marks first! Label all tick marks first! d. -0.5, 9 0 3, 4, -(- 0.6) 4. Which of the following groups of numbers is listed in proper increasing order? 3 4 a. 0, -.6,,., 3 4 b.,., -.6,, c.,, -.6, 0,. 5. Which of the following groups of numbers is listed in proper decreasing order? a. -,, -4, , 4 b , -,, -4, 4 c. 4, -4,, -, Sadie the salmon swims below sea level at an altitude of -.6 feet (.6 feet 7 below the surface). Freddie the flounder swims at feet. Which fish is deeper? 0 How do you know? Rational 8

19 Name: Date: Class: Comparing and Ordering Rationals Worksheet (continued) 7. In the middle of a running race with his gym class, Tomiko looks forward and backward to see where her competitors are relative to her position. She is able to use her amazing powers of estimation to approximate where they are. a. Complete the table below by writing the distances from Tomiko as rational numbers: Classmate Name Pedro Kaitlyn Isabella Francois Deepah Distance from Tomiko 3.5 yds behind 5 yds ahead. yds behind 3 0 yds ahead yds behind Distance from Tomiko represented by a rational number b. Explain what positive and negative numbers mean in this table. c. Which of the classmates is closest to Tomiko? Explain why you think so. d. If two classmates are the same distance from Tomiko, are they at the same location? Explain why or why not. Use examples from the table to help in your explanation. Rational 9

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21 Name: Date: Class: Comparing and Ordering Rational Numbers Round Warmup. Explain what the term absolute value means:. Classify each of the phrases below as positive or negative? Put the letters of the answers in the correct boxes below. a. You owe $5 b. A helicopter flies 500 feet above sea level c. You have $4 in your bank account d. Your football team loses five yards on a running play e. You have a debt of $000 on your student loan f. A shark swims 3 feet below sea level g. You owe -$4 h. A company loses money in a particular year i. You are feet behind Jimmy in a race j. The temperature is 5 degrees below zero k. You have a debt of -$ l. A company makes $3000 profit in a given quarter Positive Negative Rational

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23 Name: Date: Class: Comparing and Ordering Rationals Worksheet (Round ) First, remember the first two lines of your rational number poetry: Can we put them all in order? Plot the points and we just might. Cause the number that is greater is the number to the right! Next, follow the instructions below:. Plot each pair of numbers. Then insert > or < signs between them. The first problem has been completed for you a. 6 > 3 b c. 4 d Label all tick marks first! e g f h. -(0.5) Insert >, <, or = signs between the numbers below by simply looking at or thinking about where they are on the number line: a b c. 5 e f g i. 4 5 m. j. 4 -(- ) k. -.5 n Rational h. 3 d (- ) 6 l o. 5

24 Name: Date: Class: Comparing and Ordering Rationals Worksheet (Round - cntd) 3. Plot each group of numbers on the number line. Then write them in order from least to greatest: a. -(-5.5), -4., -5.5, - 4. b. 0, -, 3, c..5, 3, -3.3, d. -.5, 9,, -(- 0.) e. -0.4, -, -(- ), 7 f. - (- 0.73), -, - ( ), Georgina and Frankie are comparing the freezing points of different elements for their chemistry class. They put these elements into the table below: Element Hydrogen Lithium Mercury Freezing Point ( o C) Georgina thinks this inequality represents the relationship between the freezing points: Frankie thinks this inequality is correct: -59. < 80.5 < < < 80.5 a. Is either student correct? Explain. b. For their element project, Georgina and Frankie need to report on elements that have a freezing point lower than -38 o C. On which of these elements could they do their project? Why? Rational 4

25 Name: Date: Class: Comparing and Ordering Rationals Worksheet (Round - cntd) 5. Nigel sits down one day to try to figure out his finances. He now has six different accounts he has to monitor. This is what he finds: - He owes $7. on his purchases with Amazon.com. - He has $4.7 in his Paypal account. - His credit card company says he owes them $ His savings account now has $86.07 in it. - He does not owe and is not owed any money in his Ebay account. - He is overdrawn by $6 in his checking account a. Write a rational number that represents the amount of money (balance) Nigel has in each account: Amazon Savings Account Paypal Ebay Credit Card Checking Account b. Explain what positive and negative numbers tell Nigel about his accounts: c. In the chart below: I. Order the balances from least to greatest. II. State the absolute values of each balance next to the balances Balance ($) Absolute Value of Balance ($) d. Explain what the row with zeroes means in this table: Rational 5

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27 Name: Date: Class: Coordinate Grid Warm-up. Complete the following: Plot the integer -7 on the number line below. Label it A. Label point T: the opposite of A. Label point H: a number greater than T. Label point M: a number less than A. What is the opposite of the opposite of point H?. Plot the following on the number line below: A. -9 B. 8 C D. E. the opposite of 4 3. Write the numbers in the problem above in order from least to greatest. Remember to write the numbers in the original form:,,,, Rational 7

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29 Name: Date: Class: Coordinate Grid - Notes Coordinate grids can be useful in many cases such as creating plans, mapping out areas, and finding distances between locations.. Use the coordinate grid to label the terms below. (, -4) a. Highlight the x-axis (horizontal) and the y-axis (vertical). b. Label the origin where the x-axis and y-axis meet. c. Label the quadrants (I, II, III, and IV).. An ordered pair has an x-coordinate followed by a y-coordinate. Look along the x-axis for the x-coordinate and along the y-axis for the y-coordinate. Example: (, -4) Plot the following ordered pairs: a. (-7, 3) b. (-8, -6) c. (4, 7) x-coordinate y-coordinate d. (-3, 0) e. (8.5, -) f. (0, ) Rational 9

30 Name: Date: Class: Coordinate Grid Notes (continued) When you look in the mirror you see your. It is your exact image, just flipped! We can create reflections on a coordinate grid as well. We can reflect a single point or an image (one point at a time) over a. We will use either the x-axis or the y-axis as the line of reflection. When reflecting a point over an axis, the point must be the from the axis you are reflecting over. Follow these steps to create a reflection in the coordinate grid:. Highlight the line of reflection.. Count the number of jumps to touch the line of reflection. 3. Count the same number of jumps on the opposite side of the line of reflection. To check your answer, imagine folding the paper along the line of reflection. The points should touch. On the grid, the point (, -4) has been plotted. Which shape shows a reflection over the x-axis? Identify the ordered pair. (, ) Which shape demonstrates a reflection over the y-axis? Identify the ordered pair. (, ) (, -4) Rational 30

31 Name: Date: Class: Coordinate Grid Notes (continued) Reflecting an image over an axis is done in the same way, there are just more points to reflect. We reflect one point at a time. The triangle in the grid has 3 points. Write the ordered pairs: A (, ) B (, ) C (, ) To reflect the image over the x-axis, reflect each point over the x-axis. Connect the points and write the new ordered pairs: A (, ) B (, ) C (, ) Notation: We read the new points as A prime, B Prime and C Prime but when we write them we use an apostrophe after the letter. If we reflect the new image, we would use TWO apostrophes and say A double prime etc. A B C Rational 3

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33 Name: Date: Class: Coordinate Grid Worksheet Prior to completing the questions below, a. Label the origin where the x-axis and y-axis meet. b. Label the quadrants (I, II, III, and IV).. Name the letter at each ordered pair: (6, 9): (-4, -5): (-7, 6): (-5, 0): (, 5): (7, ):. Name the quadrant or axis on which each point lies: B: (7, ): (-7, 6): E: (8, -3): (-9, -9): 3. Find the coordinates of the indicated point: A: (, ) I: (, ) G: (, ) C: (, ) J: (, ) N: (, ) 4. Plot the points and complete the chart below: Rational 33 Plot Original Reflect over x-axis Reflect the new image over y-axis S: (-5, ) S :(, ) S :(, ) U: (-, -7) U :(, ) U :(, ) Z: (7, 8) Z :(, ) Z :(, ) Y: (8, -) Y :(, ) Y :(, ) A: (0, 5) A :(, ) A :(, )

34 Name: Date: Class: Coordinate Grid Worksheet (continued) 5. Use the table to: * identify the ordered pairs for A, B, and C * plot and identify the ordered pairs when the original is reflected over the y-axis * plot and identify the ordered pairs when the new image is reflected over the x-axis Original Reflect over y-axis Reflect the new image over x-axis A: (, ) A : (, ) A : (, ) B: (, ) B : (, ) B : (, ) C: (, ) C : (, ) C : (, ) 6. Complete the following on the coordinate grid on the right. a. Plot the point (-4, 7) and label it R. b. Label point O: the reflection of point R across the y-axis. The ordered pair is (, ) c. Label point K: the reflection of point R across the x-axis. The ordered pair is (, ) d. Label point C: the reflection of point K across the y-axis. The ordered pair is (, ) Rational 34

35 Name: Date: Class: Coordinate Grid Worksheet (continued) 7. Use the coordinate grid below to follow the directions. a. Plot the point (8, 5) and label it point R. b. What ordered pair would represent a reflection of point R over the y-axis? (, ) c. Plot the ordered pair from (b) on the graph and label it point Q. d. What ordered pair would represent a reflection of point R over the x-axis? (, ) e. Plot the ordered pair from (d) on the graph and label it point S. f. What reflection(s) from point R are required to get to (-8,-5)? Rational 35

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37 Name: Date: Class: Coordinate Grid: Distances Warm-up. Match the word with the correct definition: Positive Number Absolute Value Negative Number Opposite a. The set of numbers less than zero b. These numbers are equidistant from zero on the number line such as 5 and -5. c. The positive distance from a number to zero d. The set of numbers greater than zero. Plot the integers on the number line below: A. The opposite of -9 B. 6 C D. 7.5 E. -3 Rational Follow the instructions below: a. Plot and label the following points: L: (, -3 ) I: (7, -3 ) S: (7, -6) b. Plot one more point to create a rectangle. Label it A and write the coordinates: (, ) c. Reflect the image over the y-axis and write the new coordinates: L : (, ) I (, ) S (, ) A (, ) d. What is the distance from point L to point A?

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39 Name: Date: Class: Coordinate Grid: Distances Notes Coordinate grids can be helpful when finding distances between places on a map or grid. L A Did you have units as your answer for number 3d on the warm-up? If so, you are correct! You probably counted the jumps to obtain the result of units. This is an appropriate method if you just need to know the distance.. Plot points I (7, -3 ) and S (7, -6) on the grid above.. Show how to find the distance between points L and I. Distance = 3. Show how to find the distance between points A and S. Distance = 4. Show how to find the distance between points I and S. Distance = Rational 39

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41 Name: Date: Class: Coordinate Grid: Distances Worksheet. Use the coordinate grid below to complete the chart. Original Reflect over y-axis Reflect new symbol over x-axis : (, ) : (, ) : (, ) : (, ) : (, ) : (, ) : (, ) : (, ) : (, ). Use the coordinate grid to answer the questions below. a. Find the distance between and. (, ) (, ) b. Find the distance between and. (, ) (, ) c. Find the distance between and. (, ) (, ) d. Find the distance between and. (, ) (, ) e. Find the distance between and. (, ) (, ) Rational 4

42 Name: Date: Class: Coordinate Grid: Distances Worksheet (continued) 3. Einstein's great-granddaughter, Miss Einstein, loves math so much she had a coordinate grid printed on her gameroom wall. She is hanging a poster of her favorite band, BTS, on the wall. She hangs the poster and finds that the corners are at the following coordinate points (each block is one foot). Graph the points on the coordinate grid below. BTS Poster Point C: ( -4, 4) Point U: ( 3, 4) Point T: ( 3, -) Point E: ( -4, -) a. Miss Einstein wants to see how long the poster is from point C to point U. How long is the poster? b. Now she wants to see how wide the poster is from point E to point C. How wide is the poster? Rational 4

43 Name: Date: Class: Assessment Review. Fill in the blank with <, >, =. a b c Place the following on the number line, then write them in order from least to greatest: - 7, - 8 3, -5, -0.5, -5, 3.5 Order: 3. Complete the chart below by writing a rational number to represent each phrase. Word Representation Jordan is mile behind Tommy received $9 John travels 36.5 miles Flynn owes $76 Jessie is ahead 4 miles Mark has a debt of $67.50 Ben's balance is $34.5 The submarine is ft below sea level The plane is 3,000 feet above sea level A bird flies past its nest by blocks Katie stops at her friend's house which is 7 blocks before her final destination You are at sea level Ursela spent $36 more than she has Rational Number Representation Rational 43

44 Name: Date: Class: Assessment Review (continued) 4. Complete the following: Plot the integer -3 on the number line below. Label it U. Label point S: the opposite of U. Label point H: a number greater than S. Label point R: a number less than U. What is the opposite of the opposite of point H? 5. Plot the point (6, -3) and label it T. a. Label point I: the reflection of point T across the y-axis. The ordered pair is (, ) b. Label point S: the reflection of point T across the x-axis. The ordered pair is (, ) c. Label point P: the reflection of point S across the y-axis. The ordered pair is (, ) 6. Ryan and Kayla were absent yesterday. Today's warm-up says to put the measures of temperature ( C) in order as an inequality statement. The numbers are: -3., 4., and -.4. Ryan wrote the following: -.4 < -3. < 4. Kayla wrote the following: -3. < -.4 < 4. Is either student correct? Explain. Rational 44

45 Name: Date: Class: Assessment Review (continued) 7. You and five friends are going on a treasure hunt. You all start by facing the same direction. Only one person will find the treasure. Each person randomly draws directions that tell you how many steps to take from the starting point. Here are the cards that were drawn. YOU,46 steps forward SAMMY 39 steps back HORATIO 963 steps forward TOMIKO 498 steps forward FRANCOIS 5 steps back FREDA,004 steps back a. Write an integer that represents each location in relationship to the starting point. You Tomiko Sammy Francois Horatio Freda b. Explain what positive and negative numbers mean in this situation. c. In the chart below, order the integers from least to greatest then state their absolute value. Integer Person Steps from start Absolute Value d. Who is the farthest from the starting point? e. Who is the closest? f. If two treasure hunters are the same distance from the starting point, are they in the same location? Explain. Rational 45

46 Name: Date: Class: Assessment Review (continued) 6. Einstein's great-grandson, Mr. Einstein, is an architect and is designing a house for his daughter, Suzy. Mr. Einstein uses a coordinate grid to help him plan his design. The four corners of the kitchen are listed below (each block represents one foot). Graph and label the points on the coordinate grid below. Suzy s House Point S: ( -7, -5) Point U: ( 4, -5) Point Z: ( 4, 6) Point Y: ( -7, 6) a. Suzy Einstein wants to find the length of the kitchen from point Z to point U. Length: b. Now she wants to find the width of the kitchen is from point Y to point Z. Width: Rational 46