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G.7 - Number System

This text resource illustrates the Standards Map for the Grade 7 Number System domain in the Common Core State Standards.

Standards

  1. Common Core Mathematics: G.7

    In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

  2. Common Core Mathematics: G.7 > NS

    The Number System (NS)

  3. Common Core Mathematics: G.7 > NS > C.1

    Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

  4. Common Core Mathematics: G.7 > NS > C.1 > S.1

    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.

    1. 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.
    2. 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.
    3. 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.
    4. Apply properties of operations as strategies to add and subtract rational numbers.
    Content Skills Learning Targets Big Ideas Essential Questions
    Previous understandings
    Rational numbers
    Number line
    a. Situations
    b. Quantity p + q
    c. Quantity p – q
    c. Distance between rational numbers
    d. Properties of Operations
    3 - Apply (Previous understanding)
    2 - Extend (Previous understanding)
    2 - Add/Subtract (Rational numbers)
    3 - Represent (Addition/Subtraction on a number line)
    2 - Describe (Situations of Additive Inverse[a])
    2 - Understand (Definition of addition[b])
    3 - Show (Additive Inverse Property[b])
    3 - Interpret (Sums of rational numbers[b])
    2 - Describe (Real World Contexts of sums[b])
    2 - Understand (Addition [b])
    3 - Show (Additive inverses have a sum of zero[c])
    3 - Interpret (Sums [b])
    2 - Describe (Real world contexts [b])
    1 - Understand (Subtraction of rational numbers [c])
    2 - Show (Distance on a number line [c])
    3 - Apply (Absolute value[c])
    3 - Apply (Properties of operations [d])
    2 - Add/Subtract (Rational numbers [d])
    3 - I can apply previous understandings of adding and subtracting.
    2 - I can extend previous understandings of adding and subtracting.
    2 - I can add and subtract rational numbers.
    3 - I can represent addition and subtraction on a number line.
    2 - I can describe situations involving the additive inverse property.[a]
    2 - I understand that p + q is the number that is |q| from p in the positive or negative direction depending on the sign of q.[b]
    3 - I can show the Additive inverse property on the number line.[b]
    3 - I can interpret sums of rational numbers.[b]
    2 - I can describe finding sums in real world context.[b]
    2 - I understand that subtraction is the process of adding the additive inverse.[c]
    3 - I can show that the distance on a number line is the absolute value of their difference.[c]
    3 - I can apply the principle of distance to real-world situations.[c]
    3 - I can apply the properties of operations.[d]
    2 - I can add and subtract rational numbers.[d]
    A. One can add and subtract rational numbers and can represent these processes on the number line.
    B. When opposite quantities combine, the result is zero.
    C. One understands the process of addition and can interpret sums of rational numbers in real world contexts.
    D. One can use their understanding of subtraction to find the distance between two numbers on a number line, which can be applied to real world contexts.
    E. Rational numbers can be added and subtracted by appliying the properties of operations.
    A.1 How do you add rational numbers?
    A.2 How do you subtract rational numbers?
    A.3 How do you represent adding on a number line?
    A.4 How do you represent subtraction on a number line?
    B.1 What are additive inverses?
    B.2 What happens when you add additive inverses?
    C.1 What happens when you add additive inverses?
    C.2 How do you describe addition in real world contexts?
    D.1 How do you find the distance between two rational numbers on a number line?
    D.2 How do you find the distance between any two rational numbers?
    D.3 What real world situations will the principle of distance apply to?
    E.1 How do you find the distance between two rational numbers on a number line?
    E.2 How do you find the distance between any two rational numbers?
    E.3 What real world situations will the principle of distance apply to?
    E.4 What are the properties of operations?
    E.5 How do you apply these properties of operations to adding and subtracting rational numbers?
  5. Common Core Mathematics: G.7 > NS > C.1 > S.2

    Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

    1. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world context.
    2. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real- world contexts.
    3. Apply properties of operations as strategies to multiply and divide rational numbers.
    4. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
    Content Skills Learning Targets Big Ideas Essential Questions
    Understandings
    Rational numbers
    a. Properties
    a. Context
    b. Division
    b. Context
    c. Rational numbers
    c. Properties
    d. Division
    3 - Apply (previous understandings of multiplication and division)
    2 - Extend (previous understandings of multiplication and division)
    2 - Multiply (rational numbers)
    2 - Divide (rational numbers)
    2 - a. Understand (Multiplication)
    2 - a. Interpret (Products)
    2 - a. Describe (Division)
    2 - b. Understand (Division)
    2 - b. Interpret (Quotients)
    2 - b. Describe (Context)
    3 - c. Apply (Strategies)
    2 - c. Multiply (Rational numbers)
    2 - c. Divide (Rational numbers)
    2 - d. Convert (Rational number)
    1 - d. Know (Decimal forms)
    3 - I can apply my previous understandings of multiplication and division.
    2 - I can extend my previous understandings of multiplication and division of fractions to multiply and divide rational numbers.
    2 - I can multiply rational numbers.
    2 - I can divide rational numbers.
    2 - a. I understand that multiplication is extended from fractions to rational numbers.
    1 - I can interpret products of rational numbers.
    1 - I can describe real world contexts involving products of rational numbers.
    2 - b. I understand that integers can be divided, provided the divisor is not zero.
    2 - b. I can interpret quotients of rational numbers.
    2 - b. I can describe real world contexts involving quotients of rational numbers.
    3 - c. I can apply properties of operations as strategies to multiply and divide rational numbers.
    2 - c. I can multiply rational numbers.
    2 - c. I can divide rational numbers.
    2 - d. I can convert a rational number to a decimal.
    1 - d. I know that the decimal form of a rational number either terminates or repeats.
    A. One can multiply and divide rational numbers.
    B. Multiplication of rational numbers requires that the operations continue to satisfy the properties of operations.
    C. All integers can be divided, given the divisor is not zero, and the result is a rational number.
    D. One can apply the properties of operations as strategies to multiply and divide rational numbers.
    E. Rational numbers can be converted to decimals that either terminate or repeat.
    A.1 How does one multiply fractions?
    A.2 How does one divide fractions?
    A.3 What is a rational number?
    B.1 How does one multiply rational numbers?
    B.2 What are the properties of operations?
    B.3 How does one use the distributive property?
    B.4 What are the rules for multiplying signed numbers?
    B.5 How does one interpret products of rational numbers?
    B.6 How does one describe real world contexts?
    C.1 Why can the divisor not be zero?
    C.2 How does one divide integers?
    C.3 What is a rational number?
    C.4 Why is –(p/q)=(-p)/q=p/(-q)
    C.5 How does one interpret quotients of rational numbers?
    D.1 What are the properties of operations?
    D.2 How does one use the distributive property?
    D.3 What are the rules for multiplying signed numbers?
    D.4 How does one interpret products of rational numbers?
    E.1 How does one convert a rational number to a decimal?
  6. Common Core Mathematics: G.7 > NS > C.1 > S.3

    Solve real-world and mathematical problems involving the four operations with rational numbers.

    Content Skills Learning Targets Big Ideas Essential Questions
    3 - Solve (Mathematical problems)
    3 - Solve (Real world problems)
    3 - I can solve mathematical problems involving operations of rational numbers.
    3 - I can solve real world problems involving operations of rational numbers.
    A. One can solve mathematical and real world problems that involve operations with rational numbers.
    A.1 What is a complex fraction?
    A.2 How do you add basic and complex fractions?
    A.3 How do you subtract basic and complex fractions?
    A.4 How do you multiply basic and complex fractions?
    A.5 How do you divide basic and complex fractions?
    A.6 How do you determine which operation to use when solving real world and mathematical problems?

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