6.NS.C.5: Positive and Negative Numbers in Real-World Situations
In plain English: 6.NS.C.5 is the Common Core grade 6 math standard that asks students to use positive and negative numbers together to describe quantities with opposite directions or values, such as temperatures above and below zero, elevations above and below sea level, deposits and withdrawals, and electric charge. Students also explain what 0 means in each situation.
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
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.5 · Official standard
Students learn that numbers can have a direction as well as a size. A positive number is greater than 0, such as 5 or +5. A negative number is less than 0 and is written with a minus sign, such as -5 (read "negative five"). Positive and negative numbers are used together when a situation has two opposite directions or values: above or below zero on a thermometer, above or below sea level for elevation (height compared with the average level of the ocean's surface), money added to or taken out of an account, and positive or negative electric charge.
Students write numbers for real situations, choose which direction is positive, and explain what 0 means each time. The meaning of 0 changes with the situation: 0 °C is the temperature at which water freezes, 0 meters of elevation is sea level, and a change of $0 means the account did not change. The lesson stays with writing and reading these numbers. Adding and subtracting positive and negative numbers comes in grade 7 (7.NS.A.1).
Learning Objectives
By the end of this lesson, students will be able to:
Explain that positive and negative numbers describe quantities with opposite directions or values
Write a positive or negative number for a quantity in a real situation, with its unit
Explain what 0 means in each situation, and why it is not always "nothing"
Choose which direction is positive in a new situation and describe the opposite quantity
Prior Knowledge Required
Students should already be comfortable with:
Placing whole numbers and fractions on a number line 3.NF.A.2
Reading and writing decimals to hundredths, as in money 4.NF.C.6
Using a number line as an axis, starting at 0 5.G.A.1
Reading a thermometer and a ruler with whole-number marks
Show a weather app screenshot, or draw one on the board, and ask:
Warm-Up Prompt
"In a town in Minnesota, the temperature at 7 a.m. was 3 degrees below zero on the Fahrenheit scale. Yesterday at 3 p.m. it was 5 degrees above zero. How could you write both temperatures with numbers so a reader knows which is which? Does 0 °F mean there is no temperature?"
Collect answers. Students often write "3 below" and "5". Show the math way: 5 degrees above zero is 5 (or +5), and 3 degrees below zero is -3. The minus sign tells the direction, and the 3 tells how far from 0. Then discuss 0 °F: it is just one mark on the thermometer. Air at 0 °F is very cold, but it still has a temperature, and it can get colder. Tell students that today they will see many situations where 0 is a starting mark that people chose, not "nothing".
Direct Instruction20 minutes
Opposite directions. Many quantities come in two directions: up or down, gain or loss, in or out. We pick one direction to be positive and use negative numbers for the other. Two numbers such as 12 and -12 are opposites: they are the same distance from 0, in opposite directions. Two words from the standard need a definition. A credit is money added to an account (a deposit), and a debit is money taken out (a withdrawal or a payment). In science, electric charge comes in two kinds. An atom is a tiny particle of matter. It is made of even smaller particles: each proton carries a charge of +1 and each electron carries a charge of -1. An atom that has gained or lost electrons is a charged particle, called an ion.
Opposite directions and the meaning of 0 in six situations
Situation
Positive means
Negative means
0 means
Temperature (°C)
above 0 °C
below 0 °C
the temperature at which water freezes
Elevation
above sea level
below sea level
sea level
Bank account change
credit (deposit)
debit (withdrawal)
no change to the balance
Electric charge
more protons than electrons
more electrons than protons
the charges balance (neutral)
Football play
yards gained
yards lost
no gain and no loss
Time around a rocket launch
seconds after launch
seconds before launch
the moment of launch
Temperature above and below zero
At 6 a.m. the thermometer outside a ski lodge reads 11 °F below zero. By noon it reads 4 °F above zero. Write both temperatures as numbers.
Equation: 6 a.m.: -11 °F; noon: 4 °F (or +4 °F). The sign shows the side of 0, and 0 °F is a mark on the scale, not "no temperature"
Elevation above and below sea level
Badwater Basin in Death Valley, California, is about 282 feet below sea level. Mount Whitney, in the same state, is about 14,505 feet above sea level. Write both elevations as numbers.
Equation: Badwater Basin: about -282 feet; Mount Whitney: about +14,505 feet; 0 feet is sea level
Credits and debits
Maya's savings account shows a credit of $40 for dog-walking money and a debit of $15.75 for a book she bought online. Write each change as a number.
Equation: Credit: +40 dollars; debit: -15.75 dollars; a change of 0 dollars would mean the balance stayed the same
Positive and negative electric charge
An oxygen atom has 8 protons. When it gains 2 electrons, it has 8 protons and 10 electrons. A sodium atom with 11 protons can lose 1 electron and keep 10. What is the charge of each?
Equation: Oxygen: 8 protons cancel 8 electrons, 2 electrons are left over, so the charge is -2. Sodium: 1 proton is left over, so the charge is +1. A charge of 0 would mean the protons and electrons balance
After each example, ask the same two questions: "Which direction did we call positive?" and "What does 0 mean here?" Use Diagram 1, a vertical number line of elevation drawn to scale, to show that 0 is sea level and that the pier (+4 m) and the snorkeler (-3 m) are on opposite sides of it. Use Diagram 2 to show that temperatures left of 0 °C are colder and are written as negative numbers.
Guided Practice15 minutes
Pairs answer three short sets on whiteboards. For each, they write the numbers and one sentence about 0. After each set, one pair explains.
Elevator buttons: a hotel's lobby is floor 0. The parking levels below it are P1, P2 and P3, and the rooftop pool is 12 floors above the lobby. Write the parking levels and the pool floor as numbers. (P1 = -1, P2 = -2, P3 = -3; pool = +12. 0 is the lobby, the street level.)
Golf scores:par is the number of strokes a good golfer is expected to need. Scores are written compared with par. Write "2 under par" and "3 over par" as numbers. (-2 and +3. A score of 0, called "even", means exactly par.)
Rocket countdown: a model rocket club writes times in seconds from launch. Write "10 seconds before launch" and "30 seconds after launch" as numbers. (-10 and +30. 0 is the moment the rocket lifts off.)
Listen for students who drop the sign ("3" for P3) or who think a golf score of 0 means the golfer did not play. Ask them to say the full sentence: "0 means ...".
Independent Practice10-15 minutes
Students work alone. For each situation they write a number with its unit and say what 0 means. (1) A humpback whale feeds 60 meters below sea level. (-60 m; 0 is sea level.) (2) Ava gets a deposit of $12 of allowance. (+12 dollars; 0 is no change.) (3) A kitchen freezer keeps food at 18 °C below zero. (-18 °C; 0 °C is where water freezes.) (4) A football team loses 4 yards on a play. (-4 yards; 0 is no gain and no loss.) (5) Write your own situation for -6, and say what 0 means in it. (Sample: a video game's price drops by $6; 0 means the price did not change.)
Closure5 minutes
Exit ticket: (1) Write "a withdrawal of $30" as a number. (-30 dollars.) (2) A vet records a dog's weight change each month. The dog gained 3 pounds in March and lost 2 pounds in April. Write both changes as numbers and say what 0 would mean. (+3 pounds and -2 pounds; 0 means the weight stayed the same.) (3) A golfer's score is +1. What does it mean, and what would a score of 0 mean? (1 stroke more than par; 0 means exactly par.)
Differentiation Strategies
For Struggling Students
Give a two-column card for each situation, "positive means" and "negative means", and have students fill it in before writing any number
Use a vertical number line (a paper thermometer or elevation strip) for every problem, so students point to 0 first and then count up or down
Provide a word bank of direction words: above, below, gain, loss, deposit, withdrawal, before, after
For Advanced Students
Ask students to find a situation where people usually call the "down" direction positive, such as a diver's depth, and to explain how the numbers change if up is positive instead
Ask why a person's height or the number of pages in a book has no negative values, and to name two more quantities like that
Have students write a short story with at least four quantities, two positive and two negative, and a sentence explaining 0 for each
Assessment Guidance
What to Look For
Check that students write the sign whenever a quantity is in the negative direction, and that they include the unit (degrees, feet, dollars, yards). Ask every student to finish the sentence "0 means ..." for at least two different situations: listen for answers such as "sea level" or "no change", not "nothing". Students should be able to explain which direction they chose as positive. Watch for students who think that negative numbers are only for "bad" things: a debit of $5 for a book is negative, but it is not a mistake.
02
Classroom Activities
3 Activities
1
Opposites Card Sort
15 minPairs
Each pair gets 12 cards that form 6 pairs of opposite situations. Pairs match each card with its opposite, write a signed number on every card, and write what 0 means for each pair.
Situation Cards (12 cards)
Card 1: the temperature is 6 °F above zero. Card 2: the temperature is 6 °F below zero. (+6 °F and -6 °F)
Card 3: a deposit of $25. Card 4: a withdrawal of $25. (+25 and -25 dollars)
Card 5: a kite flies 30 feet above sea level at the beach. Card 6: a diver swims 30 feet below sea level. (+30 feet and -30 feet)
Card 7: a gain of 9 yards. Card 8: a loss of 9 yards. (+9 and -9 yards)
Card 9: an office 4 floors above the lobby. Card 10: a parking level 4 floors below the lobby. (+4 and -4)
Card 11: a particle with 3 more protons than electrons. Card 12: a particle with 3 more electrons than protons. (+3 and -3)
Procedure
Spread out all 12 cards face up and match each card with its opposite
Write the signed number on a sticky note on each card, with its unit
For each pair, write one sentence that begins "0 means ..."
Check your pairs with another pair and discuss any card you placed differently
Discussion Questions
In every pair, the two numbers are the same distance from 0. What is different about them?
In which pairs is 0 a mark that people chose, rather than "none of something"? (Temperature, elevation and floors: 0 °F, sea level and the lobby. For money and yards, 0 means no change, and for charge, 0 means the charges balance.)
Could you call the diver's direction positive instead? What would change?
Modification for Distance Learning
Share the cards on a slide as movable boxes. Pairs drag each card next to its opposite and type the numbers in the boxes. Collect one screenshot per pair.
2
Where Is Zero? Stations
20 minGroups of 3-4
Four posters hang around the room, one for each situation the standard names. Groups spend 4-5 minutes at each station, write numbers for the quantities on the poster, and explain what 0 means there.
Station Posters (4 stations)
Station A, thermometer (°C): a drawing of a thermometer with marks at -15, -5, 0, 10 and 25. Question: write the temperature of a snowy morning, 5 degrees below zero, and a warm afternoon, 25 degrees above zero. (-5 °C and +25 °C)
Station B, elevation: a side view of a coast with a lighthouse top 40 m above sea level and a cave floor 15 m below sea level. (+40 m and -15 m)
Station C, bank statement (invented): a birthday deposit of $50, a debit of $8.49 for a phone case, and a debit of $2.00 for a bus fare. (+50, -8.49 and -2 dollars)
Station D, electric charge: a drawing of a particle with 6 protons and 6 electrons, and one with 6 protons and 7 electrons. (0 and -1)
Procedure
At each station, one student reads the poster aloud, one writes the numbers on the group's recording sheet, and one writes "0 means ..."; rotate roles at every station
Before leaving a station, the group writes one new quantity for the same situation, and its opposite
After all four stations, each group shares its best "0 means ..." sentence
Discussion Questions
At which station does 0 mean that two amounts balance? (Station D: equal numbers of protons and electrons)
At Station C, why are the phone case and the bus fare both negative?
Which stations use 0 as a mark people chose, and which use 0 as "no change"?
Challenge Variation
Add a fifth poster with no labels: a picture of a hiking trail that goes over a hill and into a canyon. Groups must choose a 0 themselves (for example, the trailhead), label it, and write three numbers for points on the trail.
3
Tabletop Sea Level: Measure Above and Below
15 minPairs
Pairs treat the top of their desk as "sea level", the 0 mark. They tape a meter stick upright against the desk and measure heights above and below the desktop in centimeters, writing heights above as positive and heights below as negative.
Procedure
Stand a meter stick on the floor next to the desk and tape it in place. Put a strip of tape at the desktop height and label it 0
Measure and record, as signed numbers: the top of a water bottle standing on the desk, the top of a stack of 3 textbooks, the seat of a chair, and the floor
Typical results: a classroom desk is about 70-76 cm tall and a chair seat about 43-46 cm, so the floor is about -70 to -76 cm and the chair seat about -24 to -33 cm. A water bottle is about +20 to +25 cm
Now use the floor as 0 instead and measure again. Record the new numbers next to the old ones
Discussion Questions
When the floor is 0, which of your numbers are negative? (None: every object is above the floor)
Why do maps use sea level as 0 instead of the ground under each town?
Your chair seat was about -30 cm. What does the minus sign tell a reader who cannot see your desk?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: A Vertical Number Line of Elevation
A vertical number line drawn to scale, with 1 small tick for each meter. Sea level is 0. Places above sea level, such as the pelican (+12 m) and the pier deck (+4 m), have positive elevations. Places below sea level, such as the snorkeler (-3 m), the top of the coral reef (-8 m) and the shipwreck (-22 m), have negative elevations. The harbor is invented.
Diagram 2: Temperatures Above and Below 0 °C
A horizontal number line of invented morning temperatures, drawn to scale. Temperatures below 0 °C, the temperature at which water freezes, are to the left and are negative: -8 °C on Friday, -6 °C on Monday and -2 °C on Tuesday. Wednesday was exactly 0 °C, and Thursday was 3 °C, above freezing.
04
Homework Assignment
~30 min
6.NS.C.5 Homework: Positive and Negative Numbers
Directions: Write every quantity as a positive or negative number with its unit. For each situation, say which direction you called positive and what 0 means.
Part 1: Opposite Quantities (Problems 1-2)
Write each pair as two numbers: (a) a trail 250 feet above sea level and a mine tunnel 250 feet below sea level; (b) a team that gains 12 points and a team that loses 12 points in a quiz game; (c) 5 minutes before sunrise and 5 minutes after sunrise. What makes each pair opposite?
Each proton has a charge of +1 and each electron a charge of -1. Find the charge of each particle: (a) a calcium particle with 20 protons and 18 electrons; (b) a chlorine particle with 17 protons and 18 electrons; (c) a neon atom with 10 protons and 10 electrons. Explain what the charge of 0 in part (c) means.
Part 2: Representing Quantities (Problems 3-4)
In Fargo, North Dakota, a January morning was 14 °F below zero, the afternoon was 9 °F above zero, and at midnight the thermometer read exactly zero. Write each temperature as a number. Then draw a vertical number line from -20 to 20 (like a thermometer) and mark all three.
Jonah's savings account statement (invented) shows: a deposit of $18 for mowing a lawn, a withdrawal of $7.50 for a movie ticket, and $0.25 of interest (money the bank pays for saving). Write each change as a number. Which changes are credits and which are debits? What would a change of $0 mean?
Part 3: What Does 0 Mean? (Problems 5-6)
Write a number for each situation and explain what 0 means: (a) a scuba diver 18 meters below the surface of the ocean; (b) a team that loses 10 points for a wrong answer in a spelling game; (c) a runner who finishes a race 8 seconds faster than her best time, when race times are written compared with her best time and slower is positive.
Choose one situation (temperature, elevation, money or another of your own). Write a sentence that uses -40, a sentence that uses +40 and a sentence that uses 0, all in that same situation. Explain why -40 and +40 are opposites and what 0 means in your situation.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Signs and Units
Every quantity has the correct sign and unit
One or two missing signs or units
Signs missing or reversed throughout
Opposites
Opposite pairs and charges are correct and explained
Correct numbers but no explanation
Pairs or charges incorrect
Meaning of 0
0 is explained correctly in every situation
0 is explained in some situations, or as "nothing" once
0 is not explained
Own Situation
Problem 6 uses one situation with -40, +40 and 0 correctly
The situation works but one number is unclear
Problem 6 is missing or does not use opposites
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
Which pair of situations can be written as a number and its opposite?
Answer: C
A deposit of $20 is +20 and a withdrawal of $20 is -20: the same distance from 0, in opposite directions, so they are opposites. Choice B has opposite directions but different sizes: +20 and -5 are not opposites. Choice A is two positive numbers, +20 and +5. Choice D is -20 twice, which is the same number, not a number and its opposite.
Question 2 of 20 · Multiple Choice
Which situation could be represented by the number -48?
Answer: A
Below sea level is the negative direction for elevation, so 48 meters below sea level is -48 meters. Choice B is the opposite direction, above sea level, so it is +48. Choice C adds money, which is positive. Choice D is above zero, which is positive too.
Question 3 of 20 · Multiple Choice
Lena's savings account shows a deposit of $45 and a withdrawal of $16. Which pair of numbers represents these two changes?
Answer: D
A deposit adds money, so it is +45. A withdrawal takes money out, so it is -16. Choice A reverses both signs. Choice B drops the sign of the withdrawal and treats both changes as money added. Choice C makes both changes negative, as if the deposit were taken out too.
Question 4 of 20 · Multiple Choice
A store records its monthly profit as a positive number and a loss as a negative number. (Profit is the money a store takes in minus the money it spends.) In March, the store's result was $0. What does this mean?
Answer: C
A result of $0 means there was no profit and no loss: the money taken in equals the money spent. Choice A reads 0 as "nothing": the store may have sold a lot, but it spent the same amount. Choice B describes a positive result. Choice D is not what 0 means here, because the result compares the money in with the money out during March only.
Question 5 of 20 · Multiple Choice
A school writes arrival times in minutes compared with the first bell: times before the bell are negative and times after it are positive. Ari's arrival time is -6. What do 0 and -6 mean?
Answer: B
The times are measured from the first bell, so 0 is the moment it rings. Negative means before the bell, so -6 means Ari arrives 6 minutes early. Choice A reverses the direction: after the bell would be +6. Choice C uses the wrong 0 mark. Choice D treats 0 as the start of the day instead of the first bell.
Question 6 of 20 · Multiple Choice
Which pair of words describes opposite directions in the same situation?
Answer: B
A gain and a loss go in opposite directions, so one is positive and the other negative, for example +7 yards and -7 yards. Choice A names two ways to add money, and both are positive. Choice D names two ways to take money out, and both are negative. Choice C describes the same direction on a thermometer.
Question 7 of 20 · Multiple Choice
A vertical number line shows elevation, with 0 at sea level. Each tick mark stands for 5 meters. A sea turtle is swimming at the fourth tick mark below 0. What is its elevation?
Answer: C
Four ticks of 5 meters each is 20 meters, and the turtle is below sea level, so its elevation is -20 meters. Choice A drops the sign, which would put the turtle 20 meters above sea level. Choice B counts ticks instead of meters. Choice D adds 4 and 5 instead of multiplying 4 × 5.
Question 8 of 20 · Multiple Choice
Each proton has a charge of +1 and each electron has a charge of -1. A particle has 5 more electrons than protons. What is its overall charge?
Answer: B
Each proton balances one electron. After the pairs balance, 5 electrons are left over, and each has a charge of -1, so the charge is -5. Choice A gives the extra electrons a positive charge. Choice C assumes the charges balance, which happens only when the numbers are equal. Choice D counts the extra electrons as a single charge of -1.
Question 9 of 20 · Multiple Choice
A magnesium atom has 12 protons and 12 electrons. Which statement describes its charge?
Answer: D
The 12 positive charges and the 12 negative charges balance, so the overall charge is 0. Here 0 means balanced, not empty. Choice A has the right number but the wrong reason: the atom has 24 charged particles. Choice B counts only the protons, and choice C counts only the electrons.
Question 10 of 20 · Multiple Choice
A thermometer shows 7 °C in the afternoon and -7 °C at night. Which statement is true?
Answer: A
7 and -7 are opposites: each is 7 degrees from 0 °C, one above freezing and one below. Choice B ignores the sign, which tells the direction. Choice C ignores the minus sign on the night temperature. Choice D is false for the afternoon temperature, which is 7 degrees above 0 °C.
Question 11 of 20 · Multiple Choice
A lookout at the top of a sea cliff is 120 meters above sea level, and the bottom of the bay below it is 35 meters below sea level (invented). Which pair of numbers gives the two elevations?
Answer: C
The lookout is above sea level, so it is +120 m. The bottom of the bay is below sea level, so it is -35 m. Choice A drops the sign of the bottom of the bay. Choice B reverses both signs. Choice D writes both places as negative, as if every distance from sea level were negative.
Question 12 of 20 · Multiple Choice
Why do we need negative numbers to describe temperatures?
Answer: A
0 is only one mark on a thermometer, and the air can get colder than that, so temperatures below the mark need negative numbers. Choice B is false: 2 °C is cold but positive. Choice C is false: 0 degrees is a real temperature. Choice D is false: positive temperatures are usually written without a plus sign.
Question 13 of 20 · Multiple Choice
Which quantity is NOT a good fit for a negative number?
Answer: C
A count of students has no opposite direction: a class can have 0 students or more, but never fewer than 0. Choices A, B and D each have an opposite direction (above zero, a deposit, a floor above the ground floor), so they can be written as -4, -30 and -1.
Question 14 of 20 · Multiple Choice
A submarine's elevation is -150 meters. Which statement describes where it is?
Answer: B
Elevation is measured from sea level, and negative means below, so -150 meters is 150 meters below sea level. Choice A reverses the direction. Choice C uses the wrong 0: elevation starts at sea level, not at the sea floor. Choice D reads the number as a distance along the surface instead of up or down.
Question 15 of 20 · Short Answer
A hot-air balloon rises to 300 meters above the field where it took off, and a farmer's well goes 20 meters below the field. Using the field as 0, write both heights as numbers. What does 0 mean here?
Balloon: +300 meters. Bottom of the well: -20 meters. Here 0 is the ground level of the field, the mark from which both heights are measured. Up is positive and down is negative.
Question 16 of 20 · Short Answer
Dev's bank account has a balance of $0. What does that mean? Later the bank shows a balance of -$10. What does a negative balance mean?
A balance of $0 means Dev has no money in the account and owes the bank nothing. A balance of -$10 means he took out $10 more than he had, so he owes the bank $10. Positive balances are money he has, and negative balances are money he owes.
Question 17 of 20 · Short Answer
Write a real-world situation for -9 and a situation for its opposite, 9, in the same context. Then say what 0 means in your context.
Sample: in a board game, moving 9 spaces backward is -9 and moving 9 spaces forward is +9; 0 means staying on the same space. Any context works if both situations use the same unit, point in opposite directions, and 0 is explained (for example, 9 feet above and 9 feet below sea level, with 0 as sea level).
Question 18 of 20 · Short Answer
A weather station records 3.5 °C below zero at 5 a.m., exactly 0 °C at 9 a.m. and 6 °C above zero at 2 p.m. Write each temperature as a number, and say what 0 °C means.
5 a.m.: -3.5 °C; 9 a.m.: 0 °C; 2 p.m.: +6 °C (or 6 °C). On the Celsius scale, 0 °C is the temperature at which water freezes, so the station was below freezing at 5 a.m. and above freezing at 2 p.m. Negative numbers can be decimals, just like positive ones.
Question 19 of 20 · Short Answer
Each proton has a charge of +1 and each electron a charge of -1. A sulfur particle has 16 protons and 18 electrons. A potassium particle has 19 protons and 18 electrons. Write the charge of each and explain how you know.
Sulfur: 16 protons balance 16 electrons, and 2 electrons are left over, so the charge is -2. Potassium: 18 protons balance the 18 electrons, and 1 proton is left over, so the charge is +1. More electrons than protons gives a negative charge, and more protons than electrons gives a positive charge.
Question 20 of 20 · Short Answer
A class records the water level of a pond compared with its level on June 1, which they call 0. In July the pond is 14 cm below that level, and after a storm in August it is 6 cm above it. Write both levels as numbers. Why would it be wrong to write the July level as 14?
July: -14 cm; August: +6 cm. 0 is the pond's level on June 1. Writing 14 would say the pond was 14 cm above the June 1 level, which is the opposite direction. The sign carries the direction, and the 14 tells how far from 0.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.NS.C.5 mean?
6.NS.C.5 means students use positive and negative numbers to describe quantities that go in opposite directions, and explain what 0 means each time. The standard names four examples: temperature above and below zero, elevation above and below sea level, credits and debits, and positive and negative electric charge. Students write numbers for real situations and explain the meaning of 0, such as sea level or no change.
Is 6.NS.C.5 taught in grade 6 or grade 7?
It is a grade 6 standard, and it is usually one of the first lessons on negative numbers. In grade 6, students write, read, place and compare these numbers (6.NS.C.6 and 6.NS.C.7). Adding, subtracting, multiplying and dividing positive and negative numbers comes in grade 7 (7.NS.A.1 to 7.NS.A.3).
What is a negative number, in simple words?
A negative number is a number less than 0. It is written with a minus sign, such as -4, and it shows a quantity in the opposite direction from the positive one. If up is positive, then 4 steps down is -4. The number 4 tells the size, and the sign tells the direction.
Why does the meaning of 0 matter?
Because 0 is not always "nothing". In many situations it is a starting mark that people chose: the lobby of a building, the moment a rocket launches, or par on a golf course. In others, it means no change or a balance. Asking "what does 0 mean here?" helps students choose the right sign and makes their answers easy to check.
Does 6.NS.C.5 include adding and subtracting negative numbers?
No. This standard is about using positive and negative numbers to represent quantities and explaining 0. Computing with them, such as finding a new temperature after a drop, belongs to grade 7 (7.NS.A.1). A grade 6 lesson can preview this idea, but tests of 6.NS.C.5 ask students to write, read and explain the numbers.
Is positive always "up" or "more"?
Not always. People choose the positive direction, and the usual choices are up, above, gained, deposited and after. Some fields choose differently: divers often record depth as a positive number going down. The important thing is to say which direction is positive and to use the opposite sign for the other direction.
What are common mistakes with positive and negative numbers in grade 6?
A common mistake is dropping the minus sign, for example writing 12 for a debit of $12. Another is thinking 0 always means "nothing", so that 0 °F sounds like no temperature at all. Some students also think negative numbers only describe bad things. A debit is negative even when it pays for something useful, and a temperature below 0 °C can be a good snow day.
How does 6.NS.C.5 connect to the number line?
It leads straight into 6.NS.C.6, where students place positive and negative numbers on horizontal and vertical number lines and on the coordinate plane. A thermometer and an elevation chart are vertical number lines, so they make a natural bridge. Opposites sit on opposite sides of 0, the same distance away.
How can parents help with 6.NS.C.5 at home?
Point out positive and negative numbers in everyday life: winter temperatures in a weather app, basement buttons in an elevator, and money going into and out of an account. Ask two questions each time: "Which direction is positive?" and "What does 0 mean here?" Short conversations like these build the idea better than drills.
Why is electric charge part of a grade 6 math standard?
Because it is a clear case of two opposite values that cancel. Each proton carries a charge of +1 and each electron a charge of -1. Students find a charge by pairing protons with electrons and counting what is left over, so they need only simple counting here, not science formulas.
07
Related Standards
6 standards
These standards connect to 6.NS.C.5: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
3.NF.A.2Prerequisite
Understand a fraction as a number on the number line
Lesson coming soon
5.G.A.1Prerequisite
Use perpendicular number lines (axes) with an origin at 0 to locate points
Lesson coming soon
Alongside
6.NS.C.6Parallel
Understand a rational number as a point on the number line, including negatives
