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Solve mathematical problems, including those in real-world contexts, involving the four operations with positive and negative rational numbers. (7.NS.3)

Concepts and Skills

* Power Standard Content

* Add and subtract rational numbers

Represent on a number line model

Describe how opposites combine to make 0

Understand subtraction as being the same as adding the additive inverse

Apply properties of operations as strategies

* Multiply and divide rational numbers

Understand rules for multiplying and dividing integers

Convert fractions to decimals using long division

Apply properties of operations as strategies

* Apply operations in real-world problem solving situations

Use positive and negative numbers to graph in four quadrants

Solve problems following appropriate order of operations

Critical Language

Language Usage

A student in 7th grade can demonstrate the ability to apply and comprehend critical language by developing and explaining systematic ways to add, subtract, multiply, and divide positive and negative numbers, developing algorithms for computation and using the order of operations to solve problems.

Content-Specific Vocabulary

Add

Subtract

Multiply

Divide

Sum

Difference

Product

Quotient

Rational numbers

Integers

Number line

Quadrants

Opposite

Additive inverse

Fractions

Decimals

Algorithm

Order of operations

Long division

Positive

Negative

Process-Specific Vocabulary

Convert

Apply

Model

Graph

Concept-Based Connections

Essential Understandings

Integers allow us to describe values relative to a fixed point (e.g., the origin, 0°).

Rules for operating on signed integers result from extending patterns and applying properties of operations.

A standard order of operations exists to solve problems with consistent results.

Factual Guiding Questions

How do you add and subtract integers?

How do you multiply and divide integers?

How do you determine the opposite of an integer?

What is the order of operations?

How do you locate a point given its coordinates?

What is a number’s absolute value?

Conceptual Guiding Questions

How can you decide whether a sum/difference will be positive or negative?

What patterns exist when multiplying/dividing positive and negative numbers?

How can you apply the order of operations to solve a problem?

What does absolute value represent?

How would you represent addition and subtraction using a number line? Using chips?

Engaging/Debatable Guiding Questions

How are positive and negative numbers used in the real world?

What is the purpose of the order of operations and why is it important?

How does the meaning of an absolute value help solve a problem?

How are the patterns affected if you multiply or divide more than two numbers?