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STANDARDS THE NUMBER SYSTEM TEACHER GUIDE 6.NS.5 Understand that positive and negative numbers are used together to describe quantites having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.7. Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. b. Write, interpret, and explain statements of order for rational numbers in real world contexts. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real world situation. d. Distinguish comparisons of absolute value from statements about order. VOCABULARY & KEYWORDS absolute value: integer: magnitude: opposite: rational number: the distance a number is away from zero a positive or negative whole number the distance a number is away from zero; typically used in a problem situation two integers can be opposites if they are equal distance away from zero on the number line but on different sides of zero a number that can be written as a fraction, as a terminating decimal or as a repeating decimal whole number: a positive counting number starting with 0 COMMON MISTAKES & MISCONCEPTIONS Students may order numbers the wrong way, ex: least to greatest rather than greatest to least. Students may struggle to place rational numbers on the number line in the correct position.

THE NUMBER SYSTEM WARM -UP 1. Place the following numbers in the appropriate section below. Name Date Pd 2. Simplify the following expressions. A. - -9 2 3-1.5 0.8 8 4 B. 3 C. -( 8 ) -2-1 0 1 2 D. 2 THE NUMBER SYSTEM WARM -UP 1. Place the following numbers in the appropriate section below. Name Date Pd 2. Simplify the following expressions. 2 3-1.5 0.8 8 4 A. - -9 B. 3-2 -1 0 1 2 C. -( 8 ) D. 2

THE NUMBER SYSTEM CHEAT SHEET - A Integer vocabulary NEGATIVE ZERO POSTITIVE debit decrease withdrawal loss expense below neutral neutron increase gain rise credit deposit proton above Name Date Pd The ABSOLUTE VALUE of a number is its DISTANCE AWAY FROM ZERO on the number line. -6 D A -4-2 0 2 4 POINT NUMBER OPPOSITE B C ABSOLUTE VALUE A -1 1 1 B 3-3 3 C 5-5 5 D -3 3 3 ABSOLUTE VALUE ORDERING RATIONALs & integers PUT THE NUMBERS IN THE SAME FORM FIRST! For example, convert all numbers to decimals before ordering. EXAMPLE 1: Order from greatest to least scientific -4 notation 4, 3, 1, 7, 4-8 -6-2 0 2 4 6 EXAMPLE 2: Order from least to greatest 5.2, 5 1, 555%, 5.07 4 5 6 REAL WORLD SITUATIONS An INEQUATLITY can be interpreted to represent REAL WORLD SIATIONS. INEQUALITY -6 < -2 7 > -1 -$320 > -$500-432 < 200 INTERPRETATION -6 degrees is colder than -2 degrees 7 is located to the right of -1 on a number line Owing $320 is better than owing $500 A town that is 432 feet below sea level is lower than a town that is 200 feet above sea level

THE NUMBER SYSTEM CHEAT SHEET - B Integer vocabulary Name Date Pd The of a number is its on the number line. D A B C NEGATIVE ZERO POSTITIVE -6-4 -2 0 2 4 POINT NUMBER OPPOSITE A ABSOLUTE VALUE B C D ABSOLUTE VALUE ORDERING RATIONALs & integers PUT THE NUMBERS IN THE SAME FORM FIRST! For example, convert all numbers to decimals before ordering. EXAMPLE 1: Order from greatest to least scientific notation 4, 3, 1, 7, 4 EXAMPLE 2: Order from least to greatest 5.2, 5 1, 555%, 5.07 4 REAL WORLD SITUATIONS An can be interpreted to represent. INEQUALITY INTERPRETATION -6 < -2 7 > -1 -$320 > -$500-432 < 200

THE NUMBER SYSTEM CHEAT SHEET - C Name Date Pd Integer vocabulary ABSOLUTE VALUE ORDERING RATIONALs & integers scientific notation REAL WORLD SITUATIONS

THE NUMBER SYSTEM STATIONS INSTRUCTIONS TO PREP Print station cards on cardstock and set up desks into groups of 3-4. Print and copy a recording sheet for each student. TO USE Students should work through all stations, showing their work and solutions on their recording sheet. OTHER TIPS Laminate station cards to protect the cards for future use. This activity works well when students are in groups of 3-4.

THE NUMBER SYSTEM STATIONS STATION 1: RECORDING SHEET Name Date Pd STATION 2: SET A: SET B: 1. 2. 3. 4. 5. STATION 3: A: B: STATION 4: 1. C: D: E: F: G: H: 2. I: J:

STATION 5: 1. 2. 3. 4. STATION 6: 1. 2. 3. 4. 5. 6. 7. 8. 9. 5. 6. STATION 7: 1. 2. 3. 4. STATION 8: 1. 2. 3. 4.

SET A: Order the integers on the cards below on a number line. 1-2 SET B: Order the rational numbers below on a number line. 23% 5 8

POSITIVE NEUTRAL NEGATIVE Sort the following real life situations based on whether the situation is referring to a positive number, a negative number, or a neutral number. 1. A quarterback runs a play, but it results in a sack for a loss of 13 yards. 2. The weather man is predicting a cold front and a drop in temperature of 20 o on Sunday. 3. Mrs. Payne credits her account with a $75 deposit. 4. Death Valley is 279 ft below sea level. 5. In a golf game, the leader was at par.

READ EACH PROBLEM. DETERMINE THE OPPOSITE AND ABSOLUTE VALUE OF EACH PROBLEM SITUATION. PROBLEM OPPOSITE ABSOLUTE VALUE Jericho, West Bank is 846 ft below sea level The temperature on the thermometer reads 32 o F. 5 10 A board game card states to move back 15 spaces. -15-14 A. B. C. D. E. F. G. H. I. J.

SOLVE THE PROBLEMS BELOW. 1. An eye doctor keeps his contact lenses ordered from greatest to least in prescription strength. He has prescriptions for -2.5, +0.25, -1.25, -1.5, +1.25, +0.5, -2.25. In what order should the lenses be? 2. The table below shows the height of five children in inches. Order the children from shortest to tallest. CHILD JONAH ELISE AVERY MIGUEL AMOS HEIGHT (IN) 35 5 6 35 3 8 35 1 4 35.1 35.7

Match each inequality statement in column A to the correct interpretation in column B. 1. 2. 3. 4. 5. 6. COLUMN A 9 > 6 80 < 50 80 > 50 1 > 2 9 < -6 2 > 1 COLUMN B A. A deposit of 80 is greater than a deposit of 50 B. Negative six is located to the right of negative nine C. Owing $50 is better than owing $80 D. Negative 1 o C is less than 2 o C E. Negative 2 o C is less than negative 1 o C F. Nine is located to the to right of six

A B C D E F -10-9 -8-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 8 9 10 Use the number line above to determine the point that correctly matches each description 1. the opposite of point B 4. C 7. the absolute value of point E 2. F 5. the opposite of point C 8. the opposite of point F 3. the absolute value of point D 6. the opposite of point E 9. B

READ THE NUMBER LINES BELOW. WRITE AN INEQUALITY COMPARING THE TWO POINTS. 1. 2. -1 0 1-3 0 3 3. 4. -2 0 2-9 0 9

Each of the lists below is in order from least to greatest and has one number missing. List an example of a value that could correctly complete the blank in each list. 1. -0.65,, -0.6, -0.5, -0.4 2., 1 4, 2 5, 1 2, 3 2 3. 1.2%, 10%,, 16.7%, 40% 4. 1 20, 6.2%,, 1 3, 0.45

THE NUMBER SYSTEM QUICK CHECK Name Date Pd 1. Meredith must order the cards from greatest to least. Which list is correct? 1.5 1.05 1.55 1.0 A. -1.55, -1.5, -1.05, -1.0 B. -1.0, -1.05, -1.55, -1.5 C. -1.0, -1.05, -1.5, -1.55 D. -1.5, -1.55, -1.0, -1.05 2. The following numbers are placed on a number line. Which of the following best represents point A? C A B D -2-1 0 1 2 F. 2 1 G. 1 7 H. 2 1 J. 8 8 8 1 7 8 1. A B C D 2. F G H J 3. A B C D 4. F G H J 5. A B C D 6. F G H J 7. A B C D 8. F G H J 9. A B C D 10. F G H J 3. The table below shows the number of miles run each day of the week. Which list shows the number of miles run in order from least to greatest? MONDAY TUESDAY WEDNESDAY THURSDAY 3 1 3 3 2 5 3 3 8 3 1 2 A. Monday, Thursday, Wednesday, Tuesday B. Thursday, Tuesday, Wednesday, Monday C. Monday, Wednesday, Tuesday, Thursday D. Tuesday, Monday, Wednesday, Thursday 4. Jillian tracks her progress on her spelling tests over a period of four weeks. Which list shows her scores from greatest to least? WEEK 1 WEEK 2 WEEK 3 WEEK 4 25 30 F. Weeks 1, 3, 2, 4 G. Weeks 3, 1, 2, 4 H. Weeks 3, 1, 4, 2 J. Weeks 1, 3, 4, 2 11 15 82% 0.78 5. Which of the following situations does not represent the number -14? A. The temperature drops 14 o F. B. An account is credited $14. C. A football player runs for a loss of 14 yards. D. The element Silicon has 14 electrons.

6. The following integers are placed on a number line. Which of the following best represents their location on the number line? A. 6 B. 4 C. 7 D. 1 F. G. A B C D A B D C -6-3 0 3 6-6 -3 0 3 6 H. J. C A B D -6-3 0 3 6 A B D C -6-3 0 3 6 7. Which of the following statements correctly matches its description? 8. Lydia owes her parents $8.50. Maria owes her parents $9.25. Which of the following inequality shows the relationship between what Lydia and Maria owe their parents? A. -7 > - 9, -7 is located to the left of -9 B. -8 < -2.5, -2.5 is located to the right of -8 F. -8.50 > -9.25 G. 9.25 > 8.50 H. -8.50 < -9.25 C. 2 2 3 > 5, -5 is located to the right of 2 2 3 D. -10 < -9, -9 is located to the left of -10 J. 9.25 < 8.50 9. The table below includes information about a number. Which of the following best represents the missing information? 10. Which of the following statements best represents the expression below? 5 NUMBER OPPOSITE ABSOLUTE VALUE 6-6? -4 4 4-13 13 13 F. the opposite of negative five is 5 G. the absolute value of negative 5 is 5 H. the opposite of the absolute value of negative 5 is negative 5 A. 6 B. -6 J. the absolute value of 5 is negative 5 C. 0 D. -4

THE NUMBER SYSTEM ANSWER KEYS

THE NUMBER SYSTEM WARM -UP 1. Place the following numbers in the appropriate section below. Name Answer Key Date Pd 2. Simplify the following expressions. 2 3-1.5 0.8 8 4 A. - -9-9 B. 3 3 8 4 2 3-1.5 0.8-2 -1 0 1 2 C. -( 8 ) -8 D. 2 2 THE NUMBER SYSTEM WARM -UP 1. Place the following numbers in the appropriate section below. Name Date Pd 2. Simplify the following expressions. 2 3-1.5 0.8 8 4 A. - -9 B. 3-2 -1 0 1 2 C. -( 8 ) D. 2

THE NUMBER SYSTEM STATIONS STATION 1: SET A: -11, -9, -8, -2, 1, 16 SET B: RECORDING SHEET Name Date Pd STATION 2: Answer Key 1. neg 2. neg 3. pos 4. neg 5. neutral 4 3, 1, 23%, 5 8, 2 3, 3 STATION 3: A: 846 B: 846 STATION 4: 1. 1.25, 0.5, 0.25, -1.25, -1.5, -2.25, -2.5 C: -32 D: 32 E: -7.5 F: 7.5 G: 15 H: 15 I: 14.5 J: 14.5 2. Miguel, Avery, Elise, Amos, Jonah

STATION 5: F 1. 2. C 3. A 4. E STATION 6: 1. 5 2. 9 3. 2 4. 1 5. 1 6. -7 7. 7 8. -9 9. 5 5. B 6. D STATION 7: 1 1. 3 <1 or 1> 1 3 2. -2 < 1 or 1 > -2 3. -1.5 < 1 or 1> -1.5 4. -6 < 9 or 9 > -6 STATION 8: 1. 2. 3. 4. answers vary

THE NUMBER SYSTEM QUICK CHECK Name Answer Key Date Pd 1. Meredith must order the cards from greatest to least. Which list is correct? 1.5 1.05 1.55 1.0 A. -1.55, -1.5, -1.05, -1.0 B. -1.0, -1.05, -1.55, -1.5 C. -1.0, -1.05, -1.5, -1.55 D. -1.5, -1.55, -1.0, -1.05 2. The following numbers are placed on a number line. Which of the following best represents point A? C A B D -2-1 0 1 2 F. 2 1 G. 1 7 H. 2 1 J. 8 8 8 1 7 8 1. A B C D 2. F G H J 3. A B C D 4. F G H J 5. A B C D 6. F G H J 7. A B C D 8. F G H J 9. A B C D 10. F G H J 3. The table below shows the number of miles run each day of the week. Which list shows the number of miles run in order from least to greatest? MONDAY TUESDAY WEDNESDAY THURSDAY 3 1 3 3 2 5 3 3 8 3 1 2 A. Monday, Thursday, Wednesday, Tuesday B. Thursday, Tuesday, Wednesday, Monday C. Monday, Wednesday, Tuesday, Thursday D. Tuesday, Monday, Wednesday, Thursday 4. Jillian tracks her progress on her spelling tests over a period of four weeks. Which list shows her scores from greatest to least? WEEK 1 WEEK 2 WEEK 3 WEEK 4 25 30 F. Weeks 1, 3, 2, 4 G. Weeks 3, 1, 2, 4 H. Weeks 3, 1, 4, 2 J. Weeks 1, 3, 4, 2 11 15 82% 0.78 5. Which of the following situations does not represent the number -14? A. The temperature drops 14 o F. B. An account is credited $14. C. A football player runs for a loss of 14 yards. D. The element Silicon has 14 electrons.