6.NS.C.7: Ordering and Absolute Value of Rational Numbers
In plain English: 6.NS.C.7 is the Common Core grade 6 math standard that asks students to order positive and negative numbers and to understand absolute value. Students read inequalities such as -3 > -7 as positions on a number line, write and explain order in real contexts like temperatures, use absolute value as distance from 0, and tell a comparison of sizes apart from a statement of order.
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. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
b.Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 °C > -7 °C to express the fact that -3 °C is warmer than -7 °C.
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. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.
d.Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.
Common Core State Standards for Mathematics · Domain: The Number System (NS) · Cluster: Apply and extend previous understandings of numbers to the system of rational numbers. Also written as 6.NS.7 · Official standard
Students learn to put positive and negative numbers in order and to measure how far a number is from 0. A rational number is a number that can be written as a fraction of two whole numbers or their opposites, such as -3, 1/2, -2.75 and 0. On a number line oriented from left to right, numbers get greater as you move right. An inequality such as -3 > -7 (read "-3 is greater than -7") is a statement about position: -3 is to the right of -7. Students then write, read and explain statements of order (sentences that say which of two numbers is greater or less) in real situations, such as -3 °C > -7 °C, which means -3 °C is warmer.
Next, students study absolute value, the distance of a number from 0 on the number line, written with bars: |-30| = 30. Because a distance is never negative, the absolute value of a number is never negative. In real situations, absolute value gives the size, or magnitude, of a quantity: an account balance (the amount of money in a bank account) of -30 dollars is a debt (money owed) of 30 dollars. Finally, students learn to tell the two kinds of comparisons apart. A balance less than -30 dollars is lower on the number line, but it stands for a debt greater than 30 dollars. The lesson compares and orders numbers only; adding and subtracting negative numbers comes in grade 7.
Learning Objectives
By the end of this lesson, students will be able to:
Read an inequality such as -3 > -7 as a statement about where two numbers are on a horizontal or vertical number line
Order positive and negative fractions and decimals, and write, interpret and explain statements of order in real situations
Find the absolute value of a rational number as its distance from 0 on the number line
Use absolute value to describe the size of a debt, a depth or another quantity in a real situation
Tell a comparison of absolute values apart from a statement of order, such as a lower balance and a greater debt
Prior Knowledge Required
Students should already be comfortable with:
Comparing two fractions with the symbols >, = and < 4.NF.A.2
Using positive and negative numbers for temperatures, elevations (heights above or below sea level) and account balances 6.NS.C.5
Placing integers (whole numbers and their opposites), fractions and decimals and their opposites (the same distance from 0 on the other side) on a number line 6.NS.C.6
Show three morning temperatures from a winter weather report (invented for this lesson) and ask students to answer before any formal method:
Warm-Up Prompt
"At 7 a.m. it was -9 °C in Duluth, 2 °C in Denver and -4 °C in Detroit. Put the cities in order from coldest to warmest. Which temperature is the greatest number? Which is the least?"
Collect answers: coldest to warmest is Duluth (-9 °C), Detroit (-4 °C), Denver (2 °C). Some students may say -9 is greater than -4 "because 9 is bigger than 4". Draw a vertical number line like a thermometer: -9 is below -4, so it is colder and it is the lesser number. Introduce the words: numbers are in order when they go from least to greatest (or greatest to least), and on a number line oriented from left to right, the greater number is always to the right. The least temperature, -9 °C, is the coldest.
Direct Instruction20-25 minutes
Part 1: Inequalities as positions (standard a). The symbol > means "is greater than" and < means "is less than". On a horizontal number line, a > b means a is to the right of b. On a vertical number line, a > b means a is above b. Work through the official examples with Diagram 1, then the examples below.
Official example (a): reading an inequality
What does -3 > -7 say about the positions of -3 and -7 on a number line oriented from left to right?
Equation: -3 is located to the right of -7, so -3 is greater; the same fact can be written -7 < -3
Official example (b): writing order in context
Write a statement of order that says -3 °C is warmer than -7 °C.
Equation: -3 °C > -7 °C, because -3 °C is higher on the thermometer
Ordering fractions and decimals
Order from least to greatest: -1.5, 0.25, -2 1/4, -3/4.
Equation: -2 1/4 < -1.5 < -3/4 < 0.25, because -2 1/4 is farthest to the left
Official example (c): absolute value as the size of a debt
An account balance is -30 dollars. Write an absolute value statement for the size of the debt.
Equation: |-30| = 30, so the debt is 30 dollars
Official example (d): order compared with size
A balance of -45 dollars is less than -30 dollars. Is its debt greater or less than 30 dollars?
Equation: -45 < -30, but |-45| = 45 and 45 > 30, so the debt is greater than 30 dollars (Diagram 2)
Part 2: Order in real situations (standard b). Students write, interpret and explain statements of order. Write: a diver at -12 meters is deeper than a fish at -4 meters, so -12 < -4. Interpret: on a vertical number line, -12 < -4 means the diver is below the fish. Explain: "-12 is less than -4 because -12 is farther below sea level (0)." Remind students that the symbol and the words must agree.
Absolute value (standard c): |a| is the distance from a to 0, so |-6| = 6 and |6| = 6. A number and its opposite have the same absolute value, and |0| = 0.
Absolute value as magnitude: in a situation, the sign tells the direction (above or below, owed or saved) and the absolute value tells the size. An elevation (a height compared with sea level, which is 0) of -20 meters is 20 meters below sea level.
Order or size? (standard d): order asks "which is farther right (or higher)?" and absolute value asks "which is farther from 0?" For negative numbers the answers are opposite: -45 is less than -30, but its absolute value is greater, as Diagram 2 shows.
Guided Practice15 minutes
Pairs solve four problems on a number line handout. After each one, a pair explains its answer in words, not only with a symbol. (1) Place -2, 1.5, -3.5, 0.5 and -1 on a number line and order them from least to greatest. Write two inequalities and say what each one means about position. (-3.5 < -2 < -1 < 0.5 < 1.5; for example, -1 > -2 means -1 is to the right of -2.) (2) In golf, par is the usual number of strokes for a course. A score below par is negative, and a lower score is better. Ana scored -2, Ben +1, Cy -5 and Di 0. Order the scores from least to greatest and say who won. (-5 < -2 < 0 < 1, so Cy won.) (3) Find |-6.5|, |4| and |0|, and show each as a distance on the number line. (6.5, 4 and 0.) (4) A diver is at -16 meters and a pelican flies at 16 meters. Which is farther from sea level? (Neither: |-16| = |16| = 16.)
Independent Practice10-15 minutes
Students work alone on four problems. (1) Write an inequality that says -8 °F is colder than -1 °F. (-8 < -1, or -1 > -8.) (2) Order these balances from least to greatest: -12.50, 4.00, -20.00 and -3.75 dollars. (-20.00 < -12.50 < -3.75 < 4.00.) (3) Which is greater, |-9| or |5|? Which number is greater, -9 or 5? (|-9| = 9 is greater than 5, but 5 is greater than -9.) (4) One submarine is at -250 meters and another at -175 meters. Write an inequality and say which is deeper. (-250 < -175; the first is deeper, 250 meters below sea level.)
Closure5 minutes
Exit ticket: (1) Is -4 to the left or to the right of -6? Write the inequality. (To the right: -4 > -6.) (2) What is |-2.8|? (2.8.) (3) Jo's balance is -15 dollars. Does a balance of -22 dollars mean more debt or less debt? Explain with order and with absolute value. (More debt: -22 < -15, and |-22| = 22 is greater than 15.)
Differentiation Strategies
For Struggling Students
Give a printed number line from -10 to 10 with every whole number labeled, and have students place both numbers before they write any symbol
Use a thermometer drawing for order problems so students can say "higher is warmer, higher is greater"
Have students draw an arc from each number to 0 and count the units to find its absolute value
For Advanced Students
Ask for two numbers a and b with a < b but |a| > |b|, and then two numbers with a < b and |a| < |b|. When does each happen?
Ask students to order -7/8, -0.9, -5/6 and -0.85 and explain their method
Ask students to write a real situation where a lower number is better (golf, race times compared with a record) and one where a higher number is better
Assessment Guidance
What to Look For
Check that students read -3 > -7 as a position (to the right) and not as a size. When students order negative numbers, look for the error of ordering them as if they were positive (-2 before -5). In context problems, the symbol and the words must match: -3 °C > -7 °C goes with "warmer". For absolute value, students should say "distance from 0" and never give a negative answer. For standard d, ask each student to explain why a lower balance can mean a greater debt.
02
Classroom Activities
3 Activities
1
Human Number Line
15 minWhole class
A masking tape number line on the floor runs from -10 to 10 with a mark at each whole number. Eight students each hold a card with a rational number and stand where it belongs. The class then tests inequality statements by looking at who stands to the left or right (standard a).
Number Cards (8 cards)
-7.5, -4, -2 1/2, -1/2, 0, 1.25, 3 and 6 3/4
Statement Cards (6 cards)
-4 > -7.5 (true: -4 stands to the right)
-1/2 < 0 (true)
-2 1/2 < -4 (false: -2 1/2 stands to the right of -4)
1.25 > -2 1/2 (true)
-7.5 > 3 (false)
6 3/4 > 3 (true)
Procedure
Card holders place themselves on the tape without talking, then the class checks the order
The teacher reads a statement card; students who agree stand up, and a volunteer explains using left and right
For each false statement, a student rewrites it so it is true
Card holders then each take one step toward 0 and say their distance from 0 before the step
Discussion Questions
Who is standing farthest from 0? (The student with -7.5: |-7.5| = 7.5)
Which two card holders are the same distance from 0? (None: all eight distances are different)
Name a card holder who is to the left of -2 1/2 but closer to 0 than 6 3/4 is. (-4)
Modification for Distance Learning
Use a shared slide with a number line and eight movable number labels. Students drag the labels into place and vote on each statement card in the chat.
2
Weather Station Order Cards
20 minPairs
Pairs get 8 temperature cards from winter mornings (invented but realistic), order them, and write statements of order with explanations in words (standard b).
Temperature Cards (8 cards)
Station A: -14 °C
Station B: -6.5 °C
Station C: -2 °C
Station D: 0 °C
Station E: 3.5 °C
Station F: -9 °C
Station G: 1 °C
Station H: -11.5 °C
Procedure
Order the cards from coldest to warmest and tape them next to a vertical number line
Write three statements of order with > or <, each with a sentence, for example "-6.5 °C > -9 °C, so Station B was warmer than Station F"
Swap statements with another pair; the other pair checks that each symbol matches its sentence
Discussion Questions
Which station was coldest, and which was warmest? (Station A at -14 °C; Station E at 3.5 °C)
How many stations were colder than -5 °C? (Four: A, B, F and H)
Is "-14 °C > -11.5 °C" true? Explain with the thermometer. (No: -14 °C is lower, so it is colder)
Challenge Variation
Pairs write the temperatures in a new order, from farthest to closest to 0 °C, using absolute value, and explain why this order is not the same as coldest to warmest.
3
Order or Size? Balance Statement Sort
20 minGroups of 3-4
Groups get four account balances and 8 statement cards. They sort each statement into "order" or "absolute value (size)", then decide whether it is true or false (standards c and d).
Balances
Rita: -35 dollars. Sam: -20 dollars. Tess: 15 dollars. Uri: -5 dollars. A negative balance is a debt, money the person owes the bank.
Statement Cards (8 cards)
-35 < -20 (order, true)
|-35| > |-20| (size, true)
Rita owes more than Sam (size, true)
-5 > -20 (order, true)
|15| > |-20| (size, false)
-35 > -20 (order, false)
Uri owes 5 dollars, because |-5| = 5 (size, true)
Tess has the greatest balance (order, true)
Procedure
Place the four balances on a number line from -40 to 20
Sort the 8 cards into two columns, "order" and "size", then mark each true or false
Rewrite each false card so it is true
Discussion Questions
Whose balance is lowest, and who owes the most? (Rita for both: -35 is the least balance and 35 is the greatest debt)
Who is farthest from 0 on the number line: Tess or Sam? (Sam: |-20| = 20 and |15| = 15)
Finish the sentence: "A balance less than -20 dollars means a debt ____ than 20 dollars." (greater)
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Reading -3 > -7 on a Number Line and a Thermometer
Left: on a number line oriented from left to right, -3 is located to the right of -7, so -3 > -7 (official example a). Right: on a thermometer, a vertical number line, -3 °C is above -7 °C, so -3 °C > -7 °C: -3 °C is warmer (official example b). Tick marks are equally spaced on both lines.
Diagram 2: Lower Balance, Greater Debt
Balances of -30 and -45 dollars on a number line drawn to scale. The brackets show absolute value as distance from 0: |-30| = 30 and |-45| = 45, the sizes of the debts (official example c). The balance -45 is less than -30, yet it is the greater debt, so a balance less than -30 dollars represents a debt greater than 30 dollars (official example d).
04
Homework Assignment
~30 min
6.NS.C.7 Homework: Order and Absolute Value
Directions: Draw a number line for every problem. When you write an inequality, also write a sentence that says what it means. For absolute value, say what distance or size it describes.
Part 1: Order on the Number Line (Problems 1-2)
Plot -4.5, 3, -1 3/4, 0.5 and -3 on a number line. List them from least to greatest. Then write two inequalities with these numbers and say what each one means about their positions.
(a) Explain what -2 < -1/2 means about the positions of the two numbers on a horizontal number line. (b) Explain what 0.75 > -1.25 means on a vertical number line.
Part 2: Order in Real Situations (Problems 3-4)
The low temperatures in a northern town one week (invented) were Monday -6 °F, Tuesday 4 °F, Wednesday -11 °F and Thursday -2.5 °F. Order the days from coldest to warmest. Write an inequality that compares Wednesday and Monday, and explain it in words.
A scuba diver is at an elevation of -14.5 meters, a snorkeler is at -1.5 meters and a seagull is at 6 meters, where 0 is sea level. Write two statements of order that compare them. Who is lowest? Explain using a vertical number line.
Part 3: Absolute Value (Problems 5-6)
(a) Find |-17|, |2.25|, |-3/8| and |-0.4|, and explain each as a distance. (b) A bank account has a balance of -65 dollars. Write an absolute value statement that describes the size of the debt.
Jay's balance is -48 dollars, Kim's is -19 dollars and Lu's is 12 dollars. Who has the lowest balance? Who owes the most money? Is Jay's balance less than -25 dollars, and what does that tell you about his debt? Explain how your answers use order and how they use absolute value.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Number Lines and Order
All numbers placed correctly and listed in the right order
One number misplaced or out of order
Order incorrect or no number line
Statements of Order
Inequalities correct and each matches a sentence about position or the situation
Correct symbols but a sentence that does not match
Symbols reversed or missing
Absolute Value
All absolute values correct and explained as distance or size
Correct values without explanation
Negative answers or missing
Order or Size
Problem 6 clearly separates the lowest balance from the greatest debt
A partly correct explanation
No explanation
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
On a number line oriented from left to right, what does -6 < -1 mean?
Answer: A
The lesser number is always to the left, so -6 < -1 means -6 is to the left of -1. Choice B reverses the meaning of the symbol. Choice C is false: -6 is 6 units from 0 and -1 is only 1 unit away. Choice D is false because both numbers are negative, so both are to the left of 0.
Question 2 of 20 · Multiple Choice
Which statement means that 1.5 is located to the right of -2.5 on a number line?
Answer: C
To the right means greater, so 1.5 > -2.5. Choices A and B both say that -2.5 is the greater number, which would put it on the right. Choice D compares distances from 0, not positions, and it is also false: |1.5| = 1.5 is less than |-2.5| = 2.5.
Question 3 of 20 · Multiple Choice
Which list is in order from least to greatest?
Answer: B
On the number line, -2.4 is farthest to the left, then -1.8, then -0.6, and 0.3 is the only positive number, so B is correct. Choice A orders the negative numbers as if they were positive (0.6, 1.8, 2.4). Choice C is from greatest to least. Choice D puts the positive number first.
Question 4 of 20 · Multiple Choice
At 7 a.m. it was -12 °C in Bismarck and -5 °C in Chicago. Which statement is true?
Answer: D
On a thermometer, -5 °C is above -12 °C, so -5 °C > -12 °C and Chicago was warmer. Choices A and B reverse the order because 12 is greater than 5. Choice C compares absolute values: -12 °C is farther from 0 °C, which makes it colder, not warmer.
Question 5 of 20 · Multiple Choice
In golf, par is the usual number of strokes for a course. A score below par is negative, and a lower score is better. Mo's score is -3 and Pat's score is -6. Which statement is true?
Answer: A
-6 is to the left of -3, so -6 < -3, and the lower score is better, so Pat wins. Choice B has the right winner but a false inequality. Choice C has a false inequality. Choice D has a true inequality, but it picks the higher score, which is the worse score in golf.
Question 6 of 20 · Multiple Choice
Maya says -8 > -5 because 8 is greater than 5. Which explanation corrects her?
Answer: B
Order is about position: -8 is to the left of -5, so -8 is less. Choice A mixes up absolute value with order: -8 is farther from 0, but that makes |-8| greater, not -8. Choice C gets the symbol right, but -8 is to the left, not the right. Choice D is false because different numbers are never equal in order.
Question 7 of 20 · Multiple Choice
What is |-7.25|?
Answer: C
Absolute value is the distance from 0, and -7.25 is 7.25 units from 0, so |-7.25| = 7.25. Choice A keeps the negative sign, but a distance cannot be negative. Choice B is the absolute value of 0 only. Choice D doubles the number, which is the distance from -7.25 to 7.25, not to 0.
Question 8 of 20 · Multiple Choice
Which two numbers have an absolute value of 4 1/2?
Answer: D
Both 4 1/2 and its opposite, -4 1/2, are 4 1/2 units from 0. Choice A is wrong because |0| = 0. Choice B doubles 4 1/2. Choice C splits the mixed number into two separate numbers.
Question 9 of 20 · Multiple Choice
A diver's elevation is -26 meters, where 0 is sea level. What does |-26| = 26 describe?
Answer: C
The absolute value gives the size of the elevation, 26 meters, and the negative sign says the direction is below sea level. Choice A ignores the sign of -26. Choice B gives a negative distance, which is not possible. Choice D doubles 26.
Question 10 of 20 · Multiple Choice
Owen's account balance is -55 dollars. Which statement describes the size of his debt?
Answer: A
The absolute value of the balance, |-55| = 55, is the size of the debt: Owen owes 55 dollars. Choice B keeps the negative sign, but an absolute value is never negative. Choice C uses order, which does not give a size. Choice D has the right absolute value but reads the debt as money he has.
Question 11 of 20 · Multiple Choice
Which statement compares absolute values instead of order?
Answer: B
Only choice B uses absolute value bars: it says -12 is farther from 0 than -3 is. Choices A, C and D all describe order, the positions of the two numbers on the number line, and all three say the same true thing.
Question 12 of 20 · Multiple Choice
An account balance is less than -40 dollars. What does that tell you about the debt?
Answer: D
A balance less than -40 is to the left of -40, so it is farther from 0, and its absolute value is greater than 40. For example, -50 < -40 and |-50| = 50. Choice A carries the word "less" from the order over to the size, which is the error this standard warns about. Choice B would need a balance of exactly -40. Choice C reads a negative balance as money in the account.
Question 13 of 20 · Multiple Choice
Which statement is true?
Answer: C
-15 is to the left of -2, so -15 < -2, and -15 is farther from 0, so |-15| = 15 is greater than |-2| = 2. Choice A uses the absolute values to decide the order. Choice B has the correct order but the wrong comparison of absolute values. Choice D reverses both comparisons.
Question 14 of 20 · Multiple Choice
A freezer is set to -20 °C and a refrigerator to 4 °C. Which inequality says that the freezer is colder than the refrigerator?
Answer: A
Colder means lower on the thermometer, so the freezer temperature is less: -20 < 4. Choices B and D both say that -20 is the greater number. Choice C compares absolute values, and it is false: |-20| = 20 is greater than 4.
Question 15 of 20 · Short Answer
The low temperature on Saturday was -1.5 °C and on Sunday it was -8 °C. Write a statement of order with > or <, and explain what it means about the weather.
-1.5 °C > -8 °C (or -8 °C < -1.5 °C). It means Saturday was warmer than Sunday: on a thermometer, -1.5 °C is above -8 °C. A sentence such as "-8 °C < -1.5 °C, so Sunday was colder" is also correct.
Question 16 of 20 · Short Answer
Order -5/8, -1 1/8, 3/8 and -1/8 from least to greatest. Then write one inequality for the two numbers that are farthest to the left, and explain it with a number line.
-1 1/8 < -5/8 < -1/8 < 3/8. The two numbers farthest to the left are -1 1/8 and -5/8, so -1 1/8 < -5/8: -1 1/8 is located to the left of -5/8 on a number line oriented from left to right.
Question 17 of 20 · Short Answer
Find |-9.6|, |3/5| and |-1 1/4|. Explain what absolute value means using a number line.
|-9.6| = 9.6, |3/5| = 3/5 and |-1 1/4| = 1 1/4. Absolute value is the distance from a number to 0 on the number line: -9.6 is 9.6 units from 0, 3/5 is 3/5 of a unit from 0, and -1 1/4 is 1 1/4 units from 0. Distances are never negative.
Question 18 of 20 · Short Answer
A submarine is at an elevation of -310 meters, and the top of a lighthouse is at 12 meters, where 0 is sea level. Use absolute value to say how far each is from sea level. Which one is farther from sea level?
|-310| = 310, so the submarine is 310 meters below sea level, and |12| = 12, so the top of the lighthouse is 12 meters above sea level. The submarine is farther from sea level, because 310 > 12, even though -310 is the lower elevation.
Question 19 of 20 · Short Answer
Rae's balance is -36 dollars and Sol's balance is -27 dollars. Who has the lower balance? Who owes more money? Explain how order answers one question and absolute value answers the other.
Rae has the lower balance, because -36 < -27 (order: -36 is to the left). Rae also owes more, because |-36| = 36 is greater than |-27| = 27 (absolute value: the size of the debt). The lower balance is the greater debt.
Question 20 of 20 · Short Answer
The bottom of a well is at -14 feet and the bottom of a pond is at -9 feet, where 0 is ground level. Interpret -14 < -9 in words, and explain it with a vertical number line.
-14 < -9 means the bottom of the well is lower (deeper) than the bottom of the pond. On a vertical number line with 0 at ground level, -14 is below -9, and a number below another is the lesser number. The well bottom is 14 feet below ground and the pond bottom is 9 feet below ground.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.NS.C.7 mean?
6.NS.C.7 means students understand how to order positive and negative numbers and what absolute value is. It has four parts: (a) read inequalities as positions on a number line, (b) write and explain order in real situations, (c) find absolute value as distance from 0 and use it as the size of a quantity, and (d) tell comparisons of absolute value apart from statements of order.
Why is -10 less than -1?
Because -10 is to the left of -1 on the number line. Numbers get smaller as you move left, even though 10 is greater than 1. On a thermometer, -10 degrees is colder than -1 degree, which is another way to see that it is the lesser number.
What is absolute value in simple terms?
Absolute value is how far a number is from 0, no matter which side it is on. For example, |-4| = 4 and |4| = 4, because both are 4 units from 0. It is written with two straight bars, and it is never negative.
Can an absolute value be negative?
No. An absolute value is a distance, and a distance is never negative. The smallest possible absolute value is |0| = 0. A statement like |-5| = -5 is always false.
What is the difference between order and absolute value?
Order tells which number is greater, that is, farther to the right. Absolute value tells which number is farther from 0. For positive numbers the two agree, but for negative numbers they are opposite: -60 is less than -10, yet |-60| is greater than |-10|. Part d of 6.NS.C.7 asks students to keep these apart.
How does absolute value describe a debt?
A negative account balance means money is owed, and its absolute value is the amount owed. A balance of -80 dollars is a debt of |-80| = 80 dollars. So the lower the balance goes, the greater the debt becomes.
What are common mistakes with 6.NS.C.7?
A common mistake is ordering negative numbers as if they were positive, for example saying -7 is greater than -2. Another is giving a negative absolute value. Students also mix up the two kinds of comparisons, for example saying a balance of -50 dollars is a smaller debt than -20 dollars. Drawing a number line for each problem prevents most of these errors.
Is 6.NS.C.7 taught in grade 6 or grade 7?
It is a grade 6 standard. In grade 6, students compare and order rational numbers and find absolute values. In grade 7, they add, subtract, multiply and divide positive and negative numbers, and they find the distance between two numbers as the absolute value of their difference (7.NS.A.1).
How do vertical number lines help with order?
Many real quantities are vertical: temperatures on a thermometer, elevations above and below sea level, and floors above and below ground. On a vertical number line, greater numbers are higher, so "a > b" means a is above b. This makes statements like "-2 meters is higher than -8 meters" easy to picture.
How can parents help with ordering and absolute value at home?
Use the weather forecast in winter: ask which day will be coldest and write the order with < or >. Ask how far a temperature is from 0 degrees. If your child follows golf or a game with negative scores, ask who is winning and why. Always ask for a sentence that goes with each symbol.
07
Related Standards
6 standards
These standards connect to 6.NS.C.7: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.NS.C.5Prerequisite
Use positive and negative numbers for quantities with opposite directions or values
