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Subject Area - CC.2:
Mathematics
  • Standard Area - CC.2.2: Algebraic Concepts
  • Grade Level - CC.2.2.7: GRADE 7
Standard - CC.2.2.7.B.3

Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.

Eligible Content:
5 Total
PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
  • Assessment Anchor - A1.1.1

    Operations with Real Numbers and Expressions
    • Anchor Descriptor - A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).
      • Eligible Content - A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).
      • Eligible Content - A1.1.1.1.2

        Simplify square roots (e.g., √24 = 2√6).
    • Anchor Descriptor - A1.1.1.2 Apply number theory concepts to show relationships between real numbers in problem solving settings.
      • Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
    • Anchor Descriptor - A1.1.1.3 Use exponents, roots and/or absolute value to solve problems.
      • Eligible Content - A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
    • Anchor Descriptor - A1.1.1.4 Use estimation strategies in problem-solving situations.
      • Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
    • Anchor Descriptor - A1.1.1.5 Simplify expressions involving polynomials.
      • Eligible Content - A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
      • Eligible Content - A1.1.1.5.2

        Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
      • Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
  • Assessment Anchor - M07.B-E.2 Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.
    • Anchor Descriptor - M07.B-E.2.1 Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers.
      • Eligible Content - M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. 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 an hour (or 1.1 × $25 = $27.50).
    • Anchor Descriptor - M07.B-E.2.2 Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems.
      • Eligible Content - M07.B-E.2.2.1 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. Example: The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
        • Alternate Eligible Content - M07.B-E.2.2.1a Select an algebraic expression (equations or inequalities) using addition or subtraction of fractions, decimals, or positive/negative integers to solve a 1-step real-world problem.
          Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
      • Eligible Content - M07.B-E.2.2.2 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, and graph the solution set of the inequality. Example: A salesperson is paid $50 per week plus $3 per sale. This week she wants her pay to be at least $100. Write an inequality for the number of sales the salesperson needs to make and describe the solutions.
    • Anchor Descriptor - M07.B-E.2.3 Determine the reasonableness of the answer(s) in problemsolving situations.
      • Eligible Content - M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem. Example: If you want to place a towel bar that is 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.
        • Alternate Eligible Content - M07.B-E.2.3.1a Identify a reasonable solution in the context of a problem using the four basic operations and numbers under 20.
          Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
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