In plain English: 7.NS.A.1 is the Common Core grade 7 math standard that asks students to add and subtract rational numbers, including negative fractions and decimals, and to show sums and differences on horizontal and vertical number lines. Students learn that a number plus its opposite is 0, that subtracting means adding the opposite, and that the distance between two numbers is the absolute value of their difference.
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a.Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
b.Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
c.Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
d.Apply properties of operations as strategies to add and subtract rational numbers.
Common Core State Standards for Mathematics · Domain: The Number System (NS) · Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Also written as 7.NS.1 · Official standard
Students add and subtract rational numbers: numbers that can be written as a fraction of two integers, such as 5, -3, 2.5, -1/4 and -4 3/5. (The integers are the whole numbers and their negatives: ..., -2, -1, 0, 1, 2, ...) In grade 6, students placed these numbers on a number line and met opposites and absolute value. Now they use the number line to add and subtract them. A number line diagram can be horizontal, with positive numbers to the right, or vertical, like a thermometer or an elevation scale, with positive numbers up.
The lesson follows the four parts of the standard. Part a: opposite amounts, such as a gain and a loss of the same size, combine to make 0. Part b: p + q is the number you reach by starting at p and moving the distance |q| (the absolute value of q, its distance from 0) right or up when q is positive, and left or down when q is negative. Part c: subtracting is the same as adding the opposite, and the distance between two numbers is the absolute value of their difference. Part d: properties of operations, such as changing the order of the numbers you add, make sums easier. Multiplying and dividing rational numbers comes next, in 7.NS.A.2.
Learning Objectives
By the end of this lesson, students will be able to:
Describe real situations in which opposite quantities combine to make 0, and show that a number and its opposite have a sum of 0
Show p + q on a horizontal or vertical number line as a move of |q| from p, and describe what a sum means in a real-world context
Rewrite any subtraction p - q as p + (-q) and use it to subtract integers, fractions and decimals
Find the distance between two rational numbers as the absolute value of their difference, and use it in real-world problems
Use properties of operations, such as the commutative property (adding in any order) and the associative property (grouping in any way), to add and subtract rational numbers in easier ways
Prior Knowledge Required
Students should already be comfortable with:
Using positive and negative numbers for opposite directions or values, such as above and below zero 6.NS.C.5
Placing rational numbers and their opposites on horizontal and vertical number lines 6.NS.C.6
Absolute value as the distance of a number from 0 6.NS.C.7
Adding and subtracting fractions with unlike denominators 5.NF.A.1
Show the prompt and give pairs 3 minutes to talk before sharing.
Warm-Up Prompt
"A football team gains 7 yards on one play and loses 7 yards on the next. Where is the ball now, compared with where it started? Describe two other situations in which two amounts cancel each other out."
The ball is back where it started: a gain of 7 is +7, a loss of 7 is -7, and 7 + (-7) = 0. Collect student examples on the board, such as earning $10 and spending $10, or walking 5 steps forward and 5 steps back. Tell students that 7 and -7 are opposites: numbers the same distance from 0 on opposite sides of it. Today they will see why opposites always add to 0 and how to add numbers that do not cancel.
Direct Instruction20 minutes
Part 1: Opposites make 0 (standards a and b). Two numbers whose sum is 0 are called additive inverses. Every number has one: its opposite. The official example comes from science. Atoms are made of tiny parts. A proton has an electric charge of +1, and an electron has a charge of -1 (charge is a property that can be positive or negative, like a temperature above or below zero).
Opposites make 0 (the official example)
A hydrogen atom is made of one proton, with a charge of +1, and one electron, with a charge of -1. What is the total charge of the atom?
Equation: (+1) + (-1) = 0. The atom has 0 charge because its two parts are oppositely charged: +1 and -1 are additive inverses.
p + q on a horizontal number line
Find -2.5 + 4 and 3 + (-4.5) by moving along a number line.
Equation: -2.5 + 4: start at -2.5 and move 4 units right, to 1.5. 3 + (-4.5): start at 3 and move 4.5 units left, to -1.5.
p + q on a vertical number line, in context
A diver is at -9.5 m (9.5 m below sea level) and swims 6 m straight up. Where is she now? What does the sum mean?
Equation: -9.5 + 6: start at -9.5 and move 6 units up, to -3.5. She is 3.5 m below the surface.
A pelican flies 6.5 m above the water. The diver from the third example is at -3.5 m. How far apart are they?
Equation: |6.5 - (-3.5)| = |6.5 + 3.5| = |10| = 10 m. In the other order, |-3.5 - 6.5| = |-10| = 10 m. The order does not change the distance.
Part 2: p + q as a move (standard b). Diagram 1 shows the rule on a horizontal number line: start at p, then move the distance |q|, to the right if q is positive and to the left if q is negative. On a vertical number line (Diagram 2), positive moves go up and negative moves go down. The number line also shows why p + (-p) = 0: from p, you move the distance |p| back toward 0 and land exactly on it.
Part 3: Subtraction (standard c). Subtracting q gives the same result as adding its opposite: p - q = p + (-q). Check it with numbers students trust: 9 - 4 = 5 and 9 + (-4) = 5. The difference p - q tells how far and in which direction you go from q to p, so the distance between p and q is |p - q|. Diagram 2 shows this for the pelican and the diver.
Part 4: Properties of operations (standard d). The commutative property says you can add in any order (a + b = b + a). The associative property says you can group the numbers you add in any way ((a + b) + c = a + (b + c)). The additive inverse property says a + (-a) = 0, and the additive identity property says a + 0 = a. Subtraction is not commutative, so rewrite it as addition before you reorder:
Pairs work five problems. For each sum, one partner draws the move on a number line and the other writes the numbers, then they switch.
Guided practice problems with answers
Problem
Answer
Find -6 + 2.5 on a horizontal number line.
Start at -6, move 2.5 right: -3.5
Rewrite 1/2 - 3/4 as an addition and find it.
1/2 + (-3/4) = 2/4 + (-3/4) = -1/4
Find the distance between -4 and 9.
|9 - (-4)| = |13| = 13
A rock climber is 3 m above a ledge and climbs down 5 m. Where is she, compared with the ledge? Use a vertical number line with the ledge at 0.
3 + (-5) = -2: she is 2 m below the ledge
Describe a situation for 25 + (-25) = 0.
Sample: you earn $25 raking leaves and spend $25 on a gift, so your money has not changed
Listen for these errors: moving the wrong way for a negative q, changing both signs when rewriting a subtraction, and giving a negative distance. Ask pairs: "Which way did you move, and how far?"
Independent Practice15 minutes
Students solve six problems on their own and check two of them with a number line sketch.
Independent practice problems with answers
Problem
Answer
-8.4 + 3.1
-5.3
-2/5 + (-1/2)
-9/10
6 - (-2.75)
6 + 2.75 = 8.75
-1 1/3 - 2/3
-1 1/3 + (-2/3) = -2
The distance between -7.2 and -1.5
|-1.5 - (-7.2)| = 5.7
12 + (-5.5) + (-12) + 0.5, using properties
[12 + (-12)] + [(-5.5) + 0.5] = 0 + (-5) = -5
Closure5 minutes
Exit ticket: (1) Draw -4.5 + 1.5 on a vertical number line and give the answer. (Answer: start at -4.5, move 1.5 up, to -3.) (2) Rewrite -2 - 6.5 as an addition and find it. (Answer: -2 + (-6.5) = -8.5.) (3) Name two opposite amounts from your own life that combine to make 0.
Differentiation Strategies
For Struggling Students
Give a printed number line from -10 to 10 with half-unit marks, and have students trace each move with a finger before writing the answer
Use two colors of counters for zero pairs (two opposite amounts that add to 0, such as +1 and -1): one color for positive and one for negative
Start with integers, then change one number to a decimal or fraction once the moves feel easy
For Advanced Students
Ask students to explain why |p - q| and |q - p| are always equal, using a number line
Give a sum with six rational numbers and ask for the fewest steps using properties, with each property named
Ask students to write a real-world story for a sum of three rational numbers whose answer is negative, and to explain what the answer means
Assessment Guidance
What to Look For
Check that students name the start point and the direction of each move before they write an answer: right or up for positive q, left or down for negative q. When students subtract, look for the rewrite p + (-q) with only the second number changed. Distances must be positive, and answers to word problems should say what the number means, for example "3.5 m below the surface". For properties, students should name the property they used at each step.
02
Classroom Activities
3 Activities
1
Zero Pair Stories
15 minPairs
A zero pair is two opposite amounts that add to 0. Pairs get 8 story cards. For each card, they write the story as a sum, find the sum, and sort the cards into two piles: "combines to 0" and "does not combine to 0".
Story Cards (answer key)
S1: Hike 12 m up a trail, then 12 m back down: 12 + (-12) = 0
S2: Put $40 in a savings account, then take out $25: 40 + (-25) = 15
S3: The temperature rises 6.5 degrees, then falls 6.5 degrees: 6.5 + (-6.5) = 0
S4: A team gains 3 yards, then loses 5 yards: 3 + (-5) = -2
S5: A drone rises 30 m, then drops 30 m: 30 + (-30) = 0
S6: You owe a friend $8 (-8), then pay the friend $8: -8 + 8 = 0
S7: A helium atom has 2 protons (+1 each), 2 electrons (-1 each) and 2 neutrons (0 each): 2 + (-2) + 0 = 0
S8: Walk 3/4 mile east, then 1/2 mile west: 3/4 + (-1/2) = 1/4, so 1/4 mile east of the start
Discussion Questions
Five of the eight cards combine to 0. What do their two amounts have in common?
Change one number on S2, S4 and S8 so that each card combines to 0.
Card S7 is like the official hydrogen atom example. Why do the neutrons not change the total charge?
Modification for Distance Learning
Put the 8 cards on a shared slide with two boxes, "combines to 0" and "does not combine to 0". Pairs drag each card into a box and type its sum next to it.
2
Floor Number Line Walk
20 minGroups of 3-4
Tape a horizontal number line from -10 to 10 on the floor, with a mark every half unit, about 20 cm apart. Each group gets 6 sum cards. One student walks each card while the others record the start, the move and the end.
Sum Cards (answer key)
C1: 3 + (-7): start at 3, walk 7 left, end at -4
C2: -5 + 8: start at -5, walk 8 right, end at 3
C3: -2 - 4 = -2 + (-4): start at -2, walk 4 left, end at -6
C4: 1 - (-6) = 1 + 6: start at 1, walk 6 right, end at 7
C5: -6.5 + 6.5: start at -6.5, walk 6.5 right, end at 0
C6: -1.5 - (-4) = -1.5 + 4: start at -1.5, walk 4 right, end at 2.5
Procedure
Stand on the start number, facing the positive end of the line
For a subtraction card, first rewrite it as adding the opposite, then walk
Walk forward (right) for a positive number and backward (left) for a negative number
Record the distance from the start to the end as the absolute value of their difference, and compare it with the size of the move
Discussion Questions
Only two cards ended to the left of their start. Which ones, and what do their moves have in common?
On every card, the distance from start to end equals the size of the move. Why must that always be true?
Why does C5 end exactly at 0?
Challenge Variation
Hang a vertical number line from -10 to 10 on the wall. Groups redo two cards on it, moving up for positive and down for negative, and write one elevation story for each.
3
Thermometer Log
15 minPairs
Pairs get a table of invented winter temperatures for a town in the northern United States. They draw a vertical number line from -20°F to 20°F on grid paper, like a thermometer, plot each day's low and high, and find each day's range (the distance from the low to the high).
Mark each low with an open dot and each high with a closed dot, and connect them with a bar
Write each range as the absolute value of a difference
Write the change from Thursday's high to Friday's low as a sum or difference and say what it means
Discussion Questions
Tuesday had the greatest range. How can you see that on your number line?
Friday is the only day whose high was below 0°F. What does its bar look like?
From Thursday's high of 18°F to Friday's low of -15°F, the temperature fell 33 degrees. Write this as a subtraction.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Adding on a Horizontal Number Line
Each sum starts at p and moves the distance |q|. For -2.5 + 4, q is positive, so the move is 4 units to the right and ends at 1.5. For 3 + (-4.5), q is negative, so the move is 4.5 units to the left and ends at -1.5. Drawn to scale, with a mark every half unit.
Diagram 2: Sums and Distance on a Vertical Number Line
On a vertical number line, positive moves go up. The diver starts at -9.5 m and swims up 6 m, so -9.5 + 6 = -3.5. The pelican at 6.5 m is |6.5 - (-3.5)| = 10 m above her. Drawn to scale.
04
Homework Assignment
~30 min
7.NS.A.1 Homework: Adding and Subtracting Rational Numbers
Directions: Show all work. Draw a number line for every problem that asks for one, mark the start point, and show each move with an arrow. Rewrite every subtraction as adding the opposite, and answer word problems in a sentence.
Part 1: Opposites and Sums on a Number Line (Problems 1-2)
A nitrogen atom has 7 protons, each with a charge of +1, 7 electrons, each with a charge of -1, and some neutrons, each with a charge of 0. (a) Write a sum for the atom's total charge and find it. (b) The atom gains 3 extra electrons. What is its total charge now? (c) Describe one other situation in which opposite quantities combine to make 0.
Draw a horizontal number line from -6 to 6. Show each sum with a start point and an arrow, and give the answer: (a) -3 + 5.5 (b) 4.5 + (-7) (c) -1 1/2 + (-2 1/2). For each sum, say which way you moved and how far.
Part 2: Subtraction and Distance (Problems 3-4)
Rewrite each subtraction as adding the opposite, then find the answer: (a) -9 - 4 (b) 2.3 - (-1.7) (c) -5/8 - (-1/4) (d) 1/3 - 5/6
A hiker starts at a trailhead in a desert valley, 45.5 m below sea level (-45.5 m), and climbs to a lookout 135 m above sea level. Draw a vertical number line with sea level at 0. How many meters did she climb? Write your answer as the absolute value of a difference.
Part 3: Real-World Sums and Properties (Problems 5-6)
At 6 a.m. the temperature was -7.5°C. At 3 p.m. it was 4°C. (a) How many degrees did the temperature rise? (b) That night the temperature fell 9.5°C from 4°C. Write a sum for the new temperature, find it, and say what it means.
Use properties of operations to find each answer the easy way. Name the property you used at each step. (a) -6.25 + 13 + 6.25 (b) 3/5 + (-7) + (-3/5) + 3 (c) 18 - 4.6 - 8
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Number Line Models
Start point, direction and length of each move are correct and to scale
Correct direction but a length or start point is off
Number line missing or moves in the wrong direction
Subtraction and Distance
Every subtraction rewritten as p + (-q); distances positive and correct
One rewrite or distance error
Several errors, or negative distances
Properties
Properties used correctly and named at each step
Correct answers but properties not named
Properties misused or missing
Meaning in Context
Each word problem answered in a sentence that explains the sign
Correct number but no explanation
Answer missing or does not fit the story
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Sketch a number line whenever it helps. 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 situation combines opposite quantities to make 0?
Answer: C
Diving 30 m is -30 and rising 30 m is +30, and -30 + 30 = 0, so the submarine is back where it started. Choice A combines two gains: 6 + 6 = 12. Choice B combines amounts of different sizes: 20 + (-12) = 8. Choice D combines two drops: -5 + (-5) = -10.
Question 2 of 20 · Multiple Choice
What is the sum of -4 3/5 and its opposite?
Answer: B
The opposite of -4 3/5 is 4 3/5, and a number plus its opposite is 0: -4 3/5 + 4 3/5 = 0. Choice A adds -4 3/5 to itself. Choice C adds the two absolute values. Choice D is the opposite itself, not the sum.
Question 3 of 20 · Multiple Choice
How can you find 2.5 + (-6) on a horizontal number line?
Answer: A
Start at p = 2.5. Since q = -6 is negative, move |-6| = 6 units to the left, which ends at -3.5. Choice B moves the wrong way and ends at 8.5. Choice C starts at 6 instead of 2.5, ends at 3.5, and never uses the negative sign. Choice D moves the difference of 6 and 2.5 instead of 6 and ends at -1.
Question 4 of 20 · Multiple Choice
Find -7 + 3.25.
Answer: D
Start at -7 and move 3.25 units right: -7 + 3.25 = -3.75. Choice A moves left, as if 3.25 were negative. Choice B finds 7 - 3.25 but drops the negative sign. Choice C adds the absolute values, 7 + 3.25.
Question 5 of 20 · Multiple Choice
A thermometer reads -3°F. Then the temperature rises 8°F. Moving on the thermometer as a vertical number line, where do you end?
Answer: A
Start at -3 and move 8 units up: -3 + 8 = 5, so it is 5°F. Choice B moves down instead of up. Choice C adds the absolute values, 3 + 8. Choice D gets the size of the answer right but gives it the wrong sign.
Question 6 of 20 · Multiple Choice
Which expression has the same value as -6 - (-10)?
Answer: C
Subtracting -10 is the same as adding its opposite, 10: -6 - (-10) = -6 + 10 = 4. Choice A changes the subtraction to addition but keeps -10 instead of its opposite, which gives -16. Choice B also changes the sign of the first number, which gives 16. Choice D changes the first number instead of the second, which gives -4.
Question 7 of 20 · Multiple Choice
Find -2/3 - 1/4.
Answer: B
Rewrite as adding the opposite: -2/3 + (-1/4) = -8/12 + (-3/12) = -11/12. Choice A adds 1/4 instead of subtracting it: -8/12 + 3/12 = -5/12. Choice C drops the negative sign of -2/3: 8/12 - 3/12 = 5/12. Choice D adds the numerators and the denominators, which is not how fractions add.
Question 8 of 20 · Multiple Choice
What is the distance between -8.5 and 3 on a number line?
Answer: D
The distance is |3 - (-8.5)| = |3 + 8.5| = 11.5. Choice A subtracts 3 from 8.5 as if both numbers were on the same side of 0. Choice B finds -8.5 - 3 but does not take the absolute value, and a distance cannot be negative. Choice C adds -8.5 and 3 instead of subtracting.
Question 9 of 20 · Multiple Choice
A submarine is 180 m below sea level (-180 m). A helicopter hovers 75 m above sea level, right above it. How far apart are they?
Answer: A
The distance is |75 - (-180)| = |75 + 180| = 255 m. Choice B subtracts 75 from 180 as if both were below the water. Choice C finds -180 - 75 but forgets that a distance is an absolute value. Choice D is only the submarine's distance from sea level.
Question 10 of 20 · Multiple Choice
Which situation does the sum -12 + 12.5 describe?
Answer: C
The sum starts at -12 and adds a positive 12.5, which is a rise: -12 + 12.5 = 0.5, so it ends at 0.5°F. Choice A calls the change a fall, but a fall of 12.5 would be -12 + (-12.5) = -24.5. Choice B starts at 12 instead of -12. Choice D describes the rise but gives -24.5, the result of a fall.
Question 11 of 20 · Multiple Choice
Which property lets you rewrite -5.2 + 9 + 5.2 as -5.2 + 5.2 + 9?
Answer: D
The numbers 9 and 5.2 changed places, so this is the commutative property: a + b = b + a. Choice A, the associative property, changes how numbers are grouped, not their order. Choice B, the additive inverse property, is the next step, -5.2 + 5.2 = 0. Choice C, the additive identity property, is the last step, 0 + 9 = 9.
Question 12 of 20 · Multiple Choice
Use properties of operations to find 4.8 + (-13) + (-4.8) + 6.
Answer: B
Group the opposites: [4.8 + (-4.8)] + [(-13) + 6] = 0 + (-7) = -7. Choice A adds 4.8 twice instead of 4.8 and -4.8: 4.8 + 4.8 - 13 + 6 = 2.6. Choice C treats the +6 as -6: -13 + (-6) = -19. Choice D finds the right size but the wrong sign.
Question 13 of 20 · Multiple Choice
Point A is at -3/4 and point B is at 2 1/2 on a number line. What is the distance between them?
Answer: A
The distance is |2 1/2 - (-3/4)| = |10/4 + 3/4| = 13/4, or 3 1/4. Choice B adds -3/4 and 2 1/2 instead of subtracting. Choice C finds -3/4 - 2 1/2 but does not take the absolute value. Choice D is only the distance from point A to 0.
Question 14 of 20 · Multiple Choice
A drone is 4 m above the rim of a canyon. It drops 6 m, then rises 3 m. Using the rim as 0 on a vertical number line, where is the drone now?
Answer: C
4 + (-6) + 3 = -2 + 3 = 1, so the drone is 1 m above the rim. Choice A stops after the drop. Choice B moves down 3 m instead of up: 4 + (-6) + (-3) = -5. Choice D moves up 6 m instead of down: 4 + 6 + (-3) = 7.
Question 15 of 20 · Short Answer
Find -1.8 + (-2.9). Describe the moves on a horizontal number line.
Start at -1.8. Since -2.9 is negative, move 2.9 units left. You end at -4.7.
Question 16 of 20 · Short Answer
Rewrite 5.5 - 8.75 as an addition, then find the answer.
5.5 - 8.75 = 5.5 + (-8.75) = -3.25. On a number line: start at 5.5 and move 8.75 units left.
Question 17 of 20 · Short Answer
At dawn the temperature on a mountain was -9°C. By the afternoon it was 6.5°C. Draw a vertical number line and find how many degrees the temperature rose, as the absolute value of a difference.
The rise is |6.5 - (-9)| = |6.5 + 9| = 15.5°C. On the vertical number line, the bar from -9 up to 6.5 is 15.5 units long.
Question 18 of 20 · Short Answer
A lithium atom has 3 protons, each with a charge of +1, and 3 electrons, each with a charge of -1. Its neutrons have 0 charge. What is its total charge? Explain your answer using the word opposite or additive inverse.
3 + (-3) + 0 = 0. The protons give +3 and the electrons give -3. These are opposites (additive inverses), so they combine to make 0, and the neutrons add nothing.
Question 19 of 20 · Short Answer
Use properties of operations to find 2/7 + (-3.5) + 5/7 + 1.5. Show each step.
Reorder and group (commutative and associative properties): (2/7 + 5/7) + [(-3.5) + 1.5] = 1 + (-2) = -1.
Question 20 of 20 · Short Answer
Write a real-world situation for the sum -20 + 35. Find the sum and say what it means in your situation.
Sample: a school club owes $20 for T-shirts (-20) and then raises $35 at a bake sale (+35). The sum is -20 + 35 = 15, so after paying the debt the club has $15 left. Any story with a starting value of -20 and a gain of 35 is correct if the answer is explained.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 7.NS.A.1 mean?
7.NS.A.1 means students can add and subtract rational numbers, including negative fractions and decimals, and show the operations on a number line. The four parts cover opposites that make 0, sums as moves on a number line, subtraction as adding the opposite with distance as an absolute value, and properties of operations.
What grade is 7.NS.A.1, and what comes after it?
It is a grade 7 standard in The Number System domain. Next, students multiply and divide rational numbers (7.NS.A.2) and solve word problems with all four operations (7.NS.A.3). In grade 7 algebra, they use the same properties to simplify expressions such as 3x + (-5) + (-x) (7.EE.A.1).
Why is subtracting a negative number the same as adding?
Subtracting any number is the same as adding its opposite, and the opposite of a negative number is positive. So 3 - (-2) = 3 + 2 = 5. On a number line, 3 - (-2) asks how far and in which direction you go from -2 to 3: 5 units to the right, which is +5.
What is an additive inverse?
An additive inverse is the number you add to another number to get 0, and it is always that number's opposite. The additive inverse of 2.4 is -2.4, because 2.4 + (-2.4) = 0. The official example for 7.NS.A.1 is a hydrogen atom: the +1 charge of its proton and the -1 charge of its electron are additive inverses, so the atom has 0 charge.
Why is the distance between two numbers the absolute value of their difference?
The difference tells you how far you go from one number to the other and in which direction, and the absolute value keeps only how far. From -2 to 5 you go 7 units right, and 5 - (-2) = 7. From 5 to -2 you go 7 units left, and -2 - 5 = -7. Both distances are 7, because |7| = |-7| = 7.
When should students use a vertical number line instead of a horizontal one?
Use a vertical number line when the situation goes up and down, such as temperature on a thermometer, elevation above and below sea level, or floors of a mine. The rule is the same: positive moves go up and negative moves go down. The standard asks students to use both kinds.
Do students need to draw a number line for every problem?
No: the number line builds understanding, and students should move to working with the numbers once the moves make sense. A good sign is when a student can say, without drawing, "start at -6, move 2 left, so -8". Keep number lines for checking answers and for word problems about direction.
Which properties of operations does 7.NS.A.1 use?
It uses the commutative property (add in any order), the associative property (group in any way), the additive inverse property (a + (-a) = 0) and the additive identity property (a + 0 = a). Together they let students pair opposites or friendly numbers first. Subtraction is not commutative, so students rewrite it as addition before they reorder.
How can parents help with 7.NS.A.1 at home?
Look for positive and negative amounts in daily life, such as weather reports below zero, money earned and spent, or yards gained and lost in a football game. Ask your child to write the change as a sum, such as -4 + 10, and to say what the answer means. A thermometer drawn on paper is a quick vertical number line.
What mistakes should teachers watch for?
A common mistake is moving the wrong way for a negative number, for example treating 5 + (-3) as 8. Other frequent errors are changing both signs when rewriting subtraction, giving a negative answer for a distance, and adding numerators and denominators when adding fractions with different signs.
07
Related Standards
6 standards
These standards connect to 7.NS.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.NS.C.6Prerequisite
Understand a rational number as a point on the number line, including opposites
