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Subject Area - CC.2:
Mathematics
  • Standard Area - CC.2.1: Numbers and Operations
  • Grade Level - CC.2.1.6: GRADE 6
Standard - CC.2.1.6.D.1

Understand ratio concepts and use ratio reasoning to solve problems.

Eligible Content:
5 Total
PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
  • Anchor Descriptor - M06.A-R.1.1 Represent and/or solve realworld and mathematical problems using rates, ratios, and/or percents.
    • Eligible Content - M06.A-R.1.1.1 Use ratio language and notation (such as 3 to 4, 3:4, 3/4) to describe a ratio relationship between two quantities. Example 1: “The ratio of girls to boys in a math class is 2:3 because for every 2 girls there are 3 boys.” Example 2: “For every five votes candidate A received, candidate B received four votes.”
    • Eligible Content - M06.A-R.1.1.2 Find the unit rate a/b associated with a ratio a:b (with b ≠ 0) and use rate language in the context of a ratio relationship. Example 1: “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” Example 2: “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
      • Alternate Eligible Content - M06.A-R.1.1.2a Identify the ratio that matches a given statement and/or representation.
        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 - M06.A-R.1.1.3 Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios.
    • Eligible Content - M06.A-R.1.1.4 Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
      • Alternate Eligible Content - M06.A-R.1.1.4a Solve a 1-step real-world problem given the unit rate.
        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 - M06.A-R.1.1.5 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percentage.
      • Alternate Eligible Content - M06.A-R.1.1.5a Calculate a percent of a quantity as a rate per 100.
        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.
Standard - CC.2.1.6.E.1

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Eligible Content:
1 Total
PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
  • Anchor Descriptor - M06.A-N.1.1 Solve real-world and mathematical problems involving division of fractions.
    • Eligible Content - M06.A-N.1.1.1 Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) ÷ (3/4), explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces can be cut from a 15 1/2-foot board?
Standard - CC.2.1.6.E.2

Identify and choose appropriate processes to compute fluently with multi-digit numbers.

Eligible Content:
1 Total
PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
  • Anchor Descriptor - M06.A-N.2.1 Compute with multi-digit numbers using the four arithmetic operations with or without a calculator.
    • Eligible Content - M06.A-N.2.1.1 Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.
      • Alternate Eligible Content - M06.A-N.2.1.1a Solve a problemusing up to 3-digit whole numbers and any of the four operations.
        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.
  • Anchor Descriptor - M06.A-N.2.2 Apply number theory concepts (specifically, factors and multiples).
    • Eligible Content - M06.A-N.2.2.1 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
      • Alternate Eligible Content - M06.A-N.2.2.1a Identify multiplesfor numbers 5, 10, 25, or 100.
        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 - M06.A-N.2.2.2 Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express 36 + 8 as 4(9 + 2).
Standard - CC.2.1.6.E.3

Develop and/or apply number theory concepts to find common factors and multiples.

Eligible Content:
3 Total
Assessments
Materials & Resources
  • Standard Area - CC.2.1: Numbers and Operations
  • Assessment Anchor - A1.1.1:

    Operations with Real Numbers and Expressions

    • 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).
      • Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
        • 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).
          • Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
            • 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.
              • Anchor Descriptor - M06.A-N.2.1 Compute with multi-digit numbers using the four arithmetic operations with or without a calculator.
                • Eligible Content - M06.A-N.2.1.1 Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.
                  • Alternate Eligible Content - M06.A-N.2.1.1a Solve a problemusing up to 3-digit whole numbers and any of the four operations.
                    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.
              • Anchor Descriptor - M06.A-N.2.2 Apply number theory concepts (specifically, factors and multiples).
                • Eligible Content - M06.A-N.2.2.1 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
                  • Alternate Eligible Content - M06.A-N.2.2.1a Identify multiplesfor numbers 5, 10, 25, or 100.
                    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 - M06.A-N.2.2.2 Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express 36 + 8 as 4(9 + 2).
                Standard - CC.2.1.6.E.4

                Apply and extend previous understandings of numbers to the system of rational numbers.

                Eligible Content:
                6 Total
                PASA DLM
                Essential Elements (EE)
                Assessments
                Materials & Resources
                • Anchor Descriptor - M06.A-N.3.1 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values and locations on the number line and coordinate plane.
                  • Eligible Content - M06.A-N.3.1.1 Represent quantities in real-world contexts using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge).
                    • Alternate Eligible Content - M06.A-N.3.1.1a Identify a specific integer in a real-world context.
                      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 - M06.A-N.3.1.2 Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself (e.g., –(–3) = 3; 0 is its own opposite).
                    • Alternate Eligible Content - M06.A-N.3.1.2a Identify the opposite of a number onthenumber line.
                      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 - M06.A-N.3.1.3 Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane.
                    • Alternate Eligible Content - M06.A-N.3.1.3a Locate positive and negative numbers on the number line.
                      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.
                • Anchor Descriptor - M06.A-N.3.2 Understand ordering and absolute value of rational numbers.
                  • Eligible Content - M06.A-N.3.2.1 Write, interpret, and explain statements of order for rational numbers in real-world contexts. Example: Write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.
                  • Eligible Content - M06.A-N.3.2.2 Interpret the absolute value of a rational number as its distance from 0 on the number line and as a magnitude for a positive or negative quantity in a real-world situation. Example: For an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars, and recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
                  • Eligible Content - M06.A-N.3.2.3 Solve real-world and mathematical problems by plotting points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
                    • Alternate Eligible Content - M06.A-N.3.2.3a Identify points in all four quadrants of the coordinate plane.
                      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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