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G.7 - Expressions and Equations

This text resource illustrates the Standards Map for the Grade 7 Expressions and Equations 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 > EE

    Expressions and Equations (EE)

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

    Use properties of operations to generate equivalent expressions.

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

    Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

    Content Skills Learning Targets Big Ideas Essential Questions
    Properties
    Strategies
    3 - Apply (properties of operations)
    2 - Add (linear expressions with rational coefficients)
    3 - Apply (strategies from properties of operations)
    2 - Subtract (linear expressions with rational coefficients)
    2 - Factor (linear expressions with rational coefficients)
    3 - Expand (linear expressions with rational coefficients)
    3 - I can apply properties of operations.
    2 - I can add linear expressions with rational coefficients.
    3 - I can apply strategies from the properties of operations.
    2 - I can subtract linear expressions with rational coefficients.
    2 - I can factor linear expressions with rational coefficients.
    3 - I can expand linear expressions with rational coefficients.
    A. One can add, subtract, factor and expand linear expressions with rational coefficients by applying strategies from the properties of operations.
    A.1 What are the properties of operations?
    A.2 What strategies can be derived from these properties of operations to add linear expressions with rational coefficients?
    A.3 What strategies can be derived from these properties of operations to subtract linear expressions with rational coefficients?
    A.4 What strategies can be derived from these properties of operations to factor linear expressions with rational coefficients?
    A.5 What strategies can be derived from these properties of operations to expand linear coefficients?
  5. Common Core Mathematics: G.7 > EE > C.1 > S.2

    Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

    For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Understand (Relationships in rewritten expressions)
    6 - Rewrite (Expressions)
    2 - I can understand the relationships in the quantities of rewritten expressions.
    6 - I can rewrite expressions from problem context in different forms.
    A. One can write expressions from a problem context in different forms and understand how the quantities in the different forms are related.
    A.1 How does one write an expression from a problem context?
    A.2 How does one rewrite an expression in different forms?
    A.3 How are the quantities in rewritten expressions related?
  6. Common Core Mathematics: G.7 > EE > C.2

    Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

  7. Common Core Mathematics: G.7 > EE > C.2 > S.3

    Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

    For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

    Content Skills Learning Targets Big Ideas Essential Questions
    Rational numbers
    Properties of operations
    3 - Solve (multi-step problems)
    3 - Solve (real life problems)
    1 - Use (tools strategically to work problems with numbers in any form)
    3 - Apply (properties of operations)
    2 - Calculate (numbers in any form)
    3 - Convert (numbers from one form to any other form)
    5 - Assess (reasonableness of answers)
    1 - Use (mental computation)
    1 - Use (estimation strategies)
    3 - I can solve multi-step problems.
    3 - I can solve real life problems.
    1 - I can use tools strategically to work problems with numbers in any form.
    3 - I can apply the properties of operations.
    2 - I can calculate numbers in any form.
    3 - I can convert numbers from one form to any other form.
    5 - I can assess the reasonableness of my answers.
    1 - I can use mental computation to check the reasonableness of my answers.
    1 - I can use estimation strategies to check the reasonableness of my answers.
    A. One can solve multi-step and real-life problems with numbers in any form.
    B. It is wise to assess the reasonableness of an answer in any problem.
    A.1 How does one solve real life problems?
    A.2 How does one solve mathematical problems?
    A.3 What are the properties of operations?
    B.1 How does one use mental computation to check for answer reasonableness?
    B.2 How does one use estimation strategies to check for answer reasonableness?
  8. Common Core Mathematics: G.7 > EE > C.2 > S.4

    Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

    1. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
    2. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

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