4.a 7.NS.A.1a Math.7.NS.1a 7.NS.A.1.A 7.NR.1.1 7.NS.1.a 7.NS.A.1.a 7.NS.1a 7.NS.1 7.NS.A.1.A 7.NS.1.a 7.NS.A.1.a 7.NS.A.1.a 4.b 7.NS.A.1b Math.7.NS.1b 7.NS.A.1.B 7.NR.1.2 7.NS.1.b 7.NS.1b 7.NS.1.b 7.NS.1.b 4.c 7.NS.A.1c Math.7.NS.1c 7.NS.A.1.C 7.NR.1.4 7.NS.1.c 7.NS.1c 7.NS.1.c 4.d 7.NS.A.1d Math.7.NS.1d 7.NS.A.1.D 7.NR.1.5 7.NS.1.d 7.NS.1d 7.NS.1.d CC.2.1.7.E.1 M07.A-N.1.1.1 M07.A-N.1.1.2 7.NR.1.1 7.NR.1.2 7.NR.1.3 7.NR.1.4 7.NR.1.5 7.NCC.1 7.NCC.2 7.NCC.3 7.NCC.6 7.NCC.7 7.NCC.9

Understanding Operations - Add/Subtract 7th Grade

Alabama Course of Study Standards: 4.a
Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.
Arizona Academic Standards: 7.NS.A.1a New York State Next Generation Learning Standards: 7.NS.1.a Tennessee Academic Standards: 7.NS.A.1.a
Describe situations in which opposite quantities combine to make 0.
Common Core State Standards: Math.7.NS.1a or 7.NS.A.1.A Kentucky Academic Standards (KAS): 7.NS.1.a Mississippi College- and Career-Readiness Standards: 7.NS.1a
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.
Georgia Standards of Excellence (GSE): 7.NR.1.1
Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.
Massachusetts Curriculum Frameworks: 7.NS.A.1.a
Describe situations in which opposite quantities combine to make zero. For example: A hydrogen atom has zero charge because its two constituents are oppositely charged; If you open a new bank account with a deposit of $30 and then withdraw $30, you are left with a $0 balance.
North Carolina - Standard Course of Study: 7.NS.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences.
New Jersey Student Learning Standards: 7.NS.A.1.A
Describe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20 points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round?
Wisconsin Academic Standards: 7.NS.A.1.a
Describe situations in which opposite quantities combine to make 0. For example, if you earn $10 and then spend $10, you are left with $0.
Alabama Course of Study Standards: 4.b
Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.
Arizona Academic Standards: 7.NS.A.1b Common Core State Standards: Math.7.NS.1b or 7.NS.A.1.B Kentucky Academic Standards (KAS): 7.NS.1.b Mississippi College- and Career-Readiness Standards: 7.NS.1b North Carolina - Standard Course of Study: 7.NS.1.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.
Georgia Standards of Excellence (GSE): 7.NR.1.2
Show and explain 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. Interpret sums of rational numbers by describing applicable situations.
New York State Next Generation Learning Standards: 7.NS.1.b
Understand addition of rational numbers; p + q is 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.
Alabama Course of Study Standards: 4.c
Explain subtraction of rational numbers as addition of additive inverses.
Arizona Academic Standards: 7.NS.A.1c Common Core State Standards: Math.7.NS.1c or 7.NS.A.1.C Kentucky Academic Standards (KAS): 7.NS.1.c Mississippi College- and Career-Readiness Standards: 7.NS.1c North Carolina - Standard Course of Study: 7.NS.1.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.
Georgia Standards of Excellence (GSE): 7.NR.1.4
Show and explain 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 contextual situations.
Alabama Course of Study Standards: 4.d
Use a number line to demonstrate 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.
Arizona Academic Standards: 7.NS.A.1d Common Core State Standards: Math.7.NS.1d or 7.NS.A.1.D Kentucky Academic Standards (KAS): 7.NS.1.d Mississippi College- and Career-Readiness Standards: 7.NS.1d North Carolina - Standard Course of Study: 7.NS.1.d
Apply properties of operations as strategies to add and subtract rational numbers.
Georgia Standards of Excellence (GSE): 7.NR.1.5
Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
Pennsylvania Core Standards: CC.2.1.7.E.1
Apply and extend previous understandings of operations with fractions to operations with rational numbers.
Pennsylvania Core Standards: M07.A-N.1.1.1
Apply properties of operations to add and subtract rational numbers, including real-world contexts.
Pennsylvania Core Standards: M07.A-N.1.1.2
Represent addition and subtraction on a horizontal or vertical number line.
Georgia Standards of Excellence (GSE): 7.NR.1.1
Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.
Georgia Standards of Excellence (GSE): 7.NR.1.2
Show and explain 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. Interpret sums of rational numbers by describing applicable situations.
Georgia Standards of Excellence (GSE): 7.NR.1.3
Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems.
Georgia Standards of Excellence (GSE): 7.NR.1.4
Show and explain 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 contextual situations.
Georgia Standards of Excellence (GSE): 7.NR.1.5
Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
Arkansas Academic Standards: 7.NCC.1
Represent addition and subtraction of rational numbers in real-world contexts using a variety of forms.
Arkansas Academic Standards: 7.NCC.2
Model and describe additive inverse in real-world situations to show opposite quantities combine to make 0.
Arkansas Academic Standards: 7.NCC.3
Demonstrate in real-world contexts the distance between two rational numbers on the number line as the absolute value of their differences.
Arkansas Academic Standards: 7.NCC.6
Apply properties of operations as strategies to fluently add, subtract, multiply, and divide rational numbers.
Arkansas Academic Standards: 7.NCC.7
Use addition and subtraction with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.
Arkansas Academic Standards: 7.NCC.9
Apply operations with rational numbers involving the order of operations, involving nested grouping symbols.

Adding or subtracting a rational number can be represented by moving left (in the negative direction) or right (in the positive direction) on a horizontal number line.

The expression p + q represents the number located |q| units from p in the
positive or negative direction if q is positive or negative, respectively.

ADDITION

Adding a positive number indicates moving that many units to the right on a number line.

Adding a negative number indicates moving that many units to the left on a number line.

SUBTRACTION

Subtracting a positive number indicates moving that many units to the left on a number line.

First, draw an arrow to represent

1 \frac{1}{2}

.
Start at 0 and extend the arrow

1 \frac{1}{2}

units in the positive direction, which is to the right.

Next, draw an arrow to represent subtracting

3 \frac{1}{4}

from

1 \frac{1}{2}

.
Start at

1 \frac{1}{2}

and extend the arrow

3 \frac{1}{4}

units in the negative direction, which is to the left.

The second line ends at

- 1 \frac{3}{4}

. So,

1 \frac{1}{2} - 3 \frac{1}{4} = - 1 \frac{3}{4}

Understanding Operations - Add/Subtract

Alabama Course of Study Standards: 4.a

Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.

Arizona Academic Standards: 7.NS.A.1a

New York State Next Generation Learning Standards: 7.NS.1.a

Tennessee Academic Standards: 7.NS.A.1.a

Describe situations in which opposite quantities combine to make 0.

Common Core State Standards: Math.7.NS.1a or 7.NS.A.1.A

Kentucky Academic Standards (KAS): 7.NS.1.a

Mississippi College- and Career-Readiness Standards: 7.NS.1a

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.

Georgia Standards of Excellence (GSE): 7.NR.1.1

Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.

Massachusetts Curriculum Frameworks: 7.NS.A.1.a

Describe situations in which opposite quantities combine to make zero. For example: A hydrogen atom has zero charge because its two constituents are oppositely charged; If you open a new bank account with a deposit of $30 and then withdraw $30, you are left with a $0 balance.

North Carolina - Standard Course of Study: 7.NS.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences.

New Jersey Student Learning Standards: 7.NS.A.1.A

Describe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20 points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round?

Wisconsin Academic Standards: 7.NS.A.1.a

Describe situations in which opposite quantities combine to make 0.For example, if you earn $10 and then spend $10, you are left with $0.

Alabama Course of Study Standards: 4.b

Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

Arizona Academic Standards: 7.NS.A.1b

Common Core State Standards: Math.7.NS.1b or 7.NS.A.1.B

Kentucky Academic Standards (KAS): 7.NS.1.b

Mississippi College- and Career-Readiness Standards: 7.NS.1b

North Carolina - Standard Course of Study: 7.NS.1.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.

Georgia Standards of Excellence (GSE): 7.NR.1.2

Show and explain 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. Interpret sums of rational numbers by describing applicable situations.

New York State Next Generation Learning Standards: 7.NS.1.b

Alabama Course of Study Standards: 4.c

Explain subtraction of rational numbers as addition of additive inverses.

Arizona Academic Standards: 7.NS.A.1c

Common Core State Standards: Math.7.NS.1c or 7.NS.A.1.C

Kentucky Academic Standards (KAS): 7.NS.1.c

Mississippi College- and Career-Readiness Standards: 7.NS.1c

North Carolina - Standard Course of Study: 7.NS.1.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.

Georgia Standards of Excellence (GSE): 7.NR.1.4

Show and explain 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 contextual situations.

Alabama Course of Study Standards: 4.d

Use a number line to demonstrate 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.

Arizona Academic Standards: 7.NS.A.1d

Common Core State Standards: Math.7.NS.1d or 7.NS.A.1.D

Kentucky Academic Standards (KAS): 7.NS.1.d

Mississippi College- and Career-Readiness Standards: 7.NS.1d

North Carolina - Standard Course of Study: 7.NS.1.d

Apply properties of operations as strategies to add and subtract rational numbers.

Georgia Standards of Excellence (GSE): 7.NR.1.5

Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.

Pennsylvania Core Standards: CC.2.1.7.E.1

Apply and extend previous understandings of operations with fractions to operations with rational numbers.

Pennsylvania Core Standards: M07.A-N.1.1.1

Apply properties of operations to add and subtract rational numbers, including real-world contexts.

Pennsylvania Core Standards: M07.A-N.1.1.2

Represent addition and subtraction on a horizontal or vertical number line.

Georgia Standards of Excellence (GSE): 7.NR.1.1

Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.

Georgia Standards of Excellence (GSE): 7.NR.1.2

Show and explain 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. Interpret sums of rational numbers by describing applicable situations.

Georgia Standards of Excellence (GSE): 7.NR.1.3

Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems.

Georgia Standards of Excellence (GSE): 7.NR.1.4

Show and explain 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 contextual situations.

Georgia Standards of Excellence (GSE): 7.NR.1.5

Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.

Arkansas Academic Standards: 7.NCC.1

Represent addition and subtraction of rational numbers in real-world contexts using a variety of forms.

Arkansas Academic Standards: 7.NCC.2

Model and describe additive inverse in real-world situations to show opposite quantities combine to make 0.

Arkansas Academic Standards: 7.NCC.3

Demonstrate in real-world contexts the distance between two rational numbers on the number line as the absolute value of their differences.

Arkansas Academic Standards: 7.NCC.6

Apply properties of operations as strategies to fluently add, subtract, multiply, and divide rational numbers.

Arkansas Academic Standards: 7.NCC.7

Use addition and subtraction with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.

Arkansas Academic Standards: 7.NCC.9

Apply operations with rational numbers involving the order of operations, involving nested grouping symbols.

Describe situations in which opposite quantities combine to make 0.
For example, if you earn $10 and then spend $10, you are left with $0.