Mathematics

Power Standards

• #1: Write and evaluate numerical expressions (including those involving parentheses). (5.OA.1-2)
• #3: Use place value understanding to round whole numbers and decimals to any place. (5.NBT.4)
• #6: Use conversions within a given measurement system to solve multi-step, real-world problems. (5.MD.1)
• #7: Solve real-world and mathematical problems involving volume of rectangular prisms. (5.MD.5)

Concepts and Skills

Whole Number Operations:

• Write numerical expressions that contain grouping symbols.

Geometric Measurement:

• Justify the area formula for a rectangle with fractional side lengths by tiling.
• Recognize volume as an attribute of solid figures.
• Measure volumes by counting unit cubes and improvised units.
• Relate packing prisms with cubes to volume formulas.
• Find volumes of figures composed of right rectangular prisms
• Apply formulas to find volumes of rectangular prisms.

Measurement:

• Convert among measurement units within the same system

Power Standards

• #1: Write and evaluate numerical expressions (including those involving parentheses). (5.OA.1-2)
• #4: Add, subtract, multiply and divide with multi-digit whole numbers and with decimals to hundredths. (5.NBT.5-7)
• #6: Use conversions within a given measurement system to solve multi-step, real-world problems. (5.MD.1)

Concepts and Skills

Number/Operations:

• Understand the relationship between the places in multidigit numbers.
• Use whole-number exponents to denote powers of 10.
• Multiply whole numbers by powers of 10; explain the number of zeros in the product.
• Fluently multiply multidigit whole numbers.
• Divide multidigit whole numbers.

Measurement:

• Use measurement conversions to solve multi-step, real-world problems

Power Standards

• #1: Write and evaluate numerical expressions (including those involving parentheses). (5.OA.1-2)
• #4: Add, subtract, multiply and divide with multi-digit whole numbers and with decimals to hundredths. (5.NBT.5-7)
• #5: Solve number and word problems involving the addition and subtraction of fractions with unlike denominators (including mixed numbers). (5.NF.1-2)

Concepts and Skills

Whole Number Operations:

• Solve number stories involving whole-number division that leads to fractional answers.

Fractions/Fraction Operations:

• Interpret a fraction as division of a numerator by a denominator.
• Use estimates to reason about sums and differences of fractions.
• Solve number stories involving fraction addition and subtraction
• Add and subtract fractions with unlike denominators.
• Interpret (1/b) x q as 1 part of a partition of q into b equal parts. (For example, show that 1/3 x 4 means 4 broken into 3 equal parts.)

Power Standards

• #2: Read, write, and compare (using <, =, >) decimals to thousandths. (5.NBT.3)
• #3: Use place value understanding to round whole numbers and decimals to any place. (5.NBT.4)
• #4: Add, subtract, multiply and divide with multi-digit whole numbers and with decimals to hundredths. (5.NBT.5-7)
• #8: Represent real-world and mathematical problems by graphing points (first quadrant) and interpret points in the context of the situation. (5.G.2)

Concepts and Skills

Decimals

• Understand the relationship between the places in multidigit numbers.
• Represent decimals.
• Read and write decimals in expanded form.
• Compare and order decimals.
• Use place-value understanding to round decimals to any place.

Decimal Operations:

• Add and subtract decimals using models or strategies
• Explain decimal addition and subtraction strategies

Geometry/Algebraic Thinking:

• Understand and use a Cartesian coordinate grid in two dimensions.
• Represent problems by graphing points in the first quadrant
• Interpret coordinate values of points in context

Power Standards

• #5:  Solve number and word problems involving the addition and subtraction of fractions with unlike denominators (including mixed numbers). (5.NF.1-2)

Concepts and Skills

Fraction Operations:

• Add and subtract fractions and mixed numbers with unlike denominators
• Interpret (a/b) x q as a parts of a partition of q into b equal parts. (For example, show that 2/3 x 4 means 2 parts of 4 broken into 3 equal parts.)
• Multiply fractions by fractions
• Solve real-world problems involving fraction multiplication
• Explain the effects of multiplying by fractions equal to 1
• Create story contexts for fraction multiplication problems
• Interpret division of a unit fraction by a nonzero whole number and find quotients

Power Standards

• #1: Write and evaluate numerical expressions (including those involving parentheses). (5.OA.1-2)
• #2: Read, write, and compare (using <, =, >) decimals to thousandths. (5.NBT.3)
• #4: Add, subtract, multiply and divide with multi-digit whole numbers and with decimals to hundredths. (5.NBT.5-7)
• #5: Solve number and word problems involving the addition and subtraction of fractions with unlike denominators (including mixed numbers). (5.NF.1-2)
• #6: Use conversions within a given measurement system to solve multi-step, real-world problems. (5.MD.1)
  

Concepts and Skills

Decimal Operations:

• Multiply or divide decimals by powers of 10; explain the decimal-point placement in the answer
• Make and use estimates for decimal multiplication and division problems.
• Multiply and divide decimals using models or strategies.

Measurement:

• Use measurement conversions to solve multistep real-world problems

Data:

• Organize and represent data on line plots
• Solve problems involving fractional data on line plots

Geometric Measurement:

• Solve real-world problems involving volumes of figures composed of prisms.
• Recognize volume as an attribute of solid figures.

Power Standards

• #1: Write and evaluate numerical expressions (including those involving parentheses). (5.OA.1-2)
• #5: Solve number and word problems involving the addition and subtraction of fractions with unlike denominators (including mixed numbers). (5.NF.1-2)
• #6: Use conversions within a given measurement system to solve multi-step, real-world problems. (5.MD.1)
• #8: Represent real-world and mathematical problems by graphing points (first quadrant) and interpret points in the context of the situation. (5.G.2)
  

Concepts and Skills

Fraction Operations:

• Multiply mixed numbers by whole numbers, fractions, and mixed numbers.
• Interpret division of a whole number by a unit fraction and find quotients

Geometric Measurement:

• Justify the area formula for a rectangle with fractional side lengths by tiling.

Geometry:

• Understand that shapes in a subcategory have all the attributes of shapes in the parent category.
• Classify 2-D figures in a hierarchy based on properties.

Data:

• Organize and represent data on line plots

Geometry/Algebraic Thinking:

• Identify relationships between corresponding terms of two patterns
• Form ordered pairs from corresponding terms of patterns and graph them
• Interpret coordinate values of points in context

Power Standards

• #3: Use place value understanding to round whole numbers and decimals to any place. (5.NBT.4)
• #4: Add, subtract, multiply and divide with multi-digit whole numbers and with decimals to hundredths. (5.NBT.5-7)
• #5: Solve number and word problems involving the addition and subtraction of fractions with unlike denominators (including mixed numbers). (5.NF.1-2)
• #6: Use conversions within a given measurement system to solve multi-step, real-world problems. (5.MD.1)
• #8: Represent real-world and mathematical problems by graphing points (first quadrant) and interpret points in the context of the situation. (5.G.2)
  

Concepts and Skills

Geometric Measurement:

• Find the areas of rectangles with fractional side lengths by multiplying.
• Apply formulas to find volumes of rectangular prisms.

Whole Number Operations:

• Fluently multiply multidigit whole numbers.
• Divide multidigit whole numbers

Measurement:

• Use measurement conversions to solve multistep, real-world problems

Geometry/Algebraic Thinking:

• Represent problems by graphing points in the first quadrant.
• Interpret coordinate values of points in context.