4.a 7.NS.A.1.A 7.NS.A.1a Math.7.NS.1a 7.NS.A.1.A MGSE7.NS.1a 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.1.B 7.NS.A.1b Math.7.NS.1b 7.NS.A.1.B MGSE7.NS.1b 7.NS.1.b 7.NS.1b 7.NS.1.b 7.NS.1.b 4.c 7.NS.A.1.C 7.NS.A.1c Math.7.NS.1c 7.NS.A.1.C MGSE7.NS.1c 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 MGSE7.NS.1d 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

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.
Arkansas Academic Standards: 7.NS.A.1.A
Describe situations in which opposite quantities combine to make 0 and show that a number and its opposite have a sum of 0 (additive inverses) (e.g., A hydrogen atom has 0 charge because its two constituents are oppositely charged.)
Arizona - K-12 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): MGSE7.NS.1a
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. For example, your bank account balance is -$25.00. You deposit $25.00 into your account. The net balance is $0.00.
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.
Arkansas Academic Standards: 7.NS.A.1.B
Understand p + q as a number where p is the starting point and q represents a distance from p in the positive or negative direction depending on whether q is positive or negative Interpret sums of rational numbers by describing real-world contexts (e.g., 3 + 2 means beginning at 3, move 2 units to the right and end at the sum of 5; 3 + (-2) means beginning at 3, move 2 units to the left and end at the sum of 1; 70 + (-30) = 40 could mean after earning $70, $30 was spent on a new video game, leaving a balance of $40)
Arizona - K-12 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): MGSE7.NS.1b
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. Interpret sums of rational numbers by describing real world contexts.
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.
Arkansas Academic Standards: 7.NS.A.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 (e.g., the distance between -5 and 6 is 11. -5 and 6 are 11 units apart on the number line)
Arizona - K-12 Academic Standards: 7.NS.A.1c Common Core State Standards: Math.7.NS.1c or 7.NS.A.1.C Georgia Standards of Excellence (GSE): MGSE7.NS.1c 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.
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 - K-12 Academic Standards: 7.NS.A.1d Common Core State Standards: Math.7.NS.1d or 7.NS.A.1.D Georgia Standards of Excellence (GSE): MGSE7.NS.1d 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.
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.

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.

Arkansas Academic Standards: 7.NS.A.1.A

Describe situations in which opposite quantities combine to make 0 and show that a number and its opposite have a sum of 0 (additive inverses) (e.g., A hydrogen atom has 0 charge because its two constituents are oppositely charged.)

Arizona - K-12 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): MGSE7.NS.1a

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.For example, your bank account balance is -$25.00. You deposit $25.00 into your account. The net balance is $0.00.

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.

Arkansas Academic Standards: 7.NS.A.1.B

Arizona - K-12 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): MGSE7.NS.1b

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. Interpret sums of rational numbers by describing real world contexts.

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.

Arkansas Academic Standards: 7.NS.A.1.C

Arizona - K-12 Academic Standards: 7.NS.A.1c

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

Georgia Standards of Excellence (GSE): MGSE7.NS.1c

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.

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 - K-12 Academic Standards: 7.NS.A.1d

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

Georgia Standards of Excellence (GSE): MGSE7.NS.1d

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.

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.

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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.
For example, your bank account balance is -$25.00. You deposit $25.00 into your account. The net balance is $0.00.

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.