5th Grade Math (West Virginia CCR Standards)

Operations and Algebraic Thinking – Write and interpret numerical expressions

• M.5.1 Use parentheses or brackets in numerical expressions and evaluate expressions that contain them.
• M.5.2 Write expressions that record calculations with numbers and interpret expressions without evaluating them.

Operations and Algebraic Thinking – Patterns and relationships

• M.5.3 Generate two number patterns from two rules, relate their corresponding terms and graph the ordered pairs.

Number and Operations in Base Ten – The place value system

• M.5.4 Recognize that a digit is worth ten times the place to its right and one tenth of the place to its left.
• M.5.5 Explain how multiplying or dividing a number, including a decimal, by a power of 10 changes it.
• M.5.6 Read, write and compare decimals to thousandths.
  • a. Read and write decimals as numerals, number names and expanded form.
  • b. Compare decimals to thousandths by the value of each digit, recording with >, = and <.
• M.5.7 Use place value to round multi-digit numbers, including decimals, to any place.

Number and Operations in Base Ten – Operations with multi-digit whole numbers and decimals to hundredths

• M.5.8 Multiply multi-digit whole numbers fluently (efficiently and accurately) with the standard algorithm.
• M.5.9 Find whole-number quotients with up to four-digit dividends and two-digit divisors using place value strategies, arrays or partial quotients.
• M.5.10 Add, subtract, multiply and divide decimals to hundredths with models, place value and properties, and explain the reasoning.

Number and Operations – Fractions – Equivalent fractions to add and subtract

• M.5.11 Add and subtract fractions with unlike denominators by rewriting them as equivalent fractions with like denominators.
• M.5.12 Solve word problems adding and subtracting fractions with models or equations and check with benchmark fractions.

Number and Operations – Fractions – Multiply and divide fractions

• M.5.13 Interpret a fraction as the numerator divided by the denominator and solve related division word problems.
• M.5.14 Multiply a fraction or whole number by a fraction.
  • a. Interpret (a/b) × q and fraction-times-fraction products as parts of a partition, with models and story contexts.
  • b. Find areas of rectangles with fractional side lengths and relate them to fraction products.
• M.5.15 Interpret multiplication as scaling and compare a product with its factors without multiplying.
  • a. Compare the size of a product with one factor based on the size of the other factor.
  • b. Explain how multiplying by a fraction greater or less than 1 changes a number, and link this to equivalent fractions.
• M.5.16 Solve real-world problems that multiply fractions and mixed numbers using models or equations.
• M.5.17 Divide unit fractions by whole numbers and whole numbers by unit fractions.
  • a. Interpret and compute a unit fraction divided by a nonzero whole number.
  • b. Interpret and compute a whole number divided by a unit fraction.
  • c. Solve real-world problems with both kinds of division using models or equations.

Measurement and Data – Convert units within a measurement system

• M.5.18 Convert between standard customary and metric units within one system and use conversions in multistep problems.

Measurement and Data – Represent and interpret data

• M.5.19 Make line plots of measurements in fractions of a unit and solve problems with fraction operations on the data.

Measurement and Data – Volume and its link to multiplication and addition

• M.5.20 Recognize volume as an attribute of solid figures and understand measuring it with unit cubes.
  • a. Know a unit cube has a volume of one cubic unit.
  • b. Know a solid packed with b unit cubes without gaps or overlaps has a volume of b cubic units.
• M.5.21 Measure volume by counting unit cubes in cubic cm, cubic in, cubic ft and improvised units.
• M.5.22 Relate volume to multiplication and addition and solve volume problems.
  • a. Show that packing a right rectangular prism with unit cubes gives the same volume as multiplying its edge lengths.
  • b. Apply V = l × w × h and V = B × h to prisms with whole-number edges.
  • c. Add the volumes of non-overlapping prisms to find the volume of a composite solid.

Geometry – Graph points on the coordinate plane

• M.5.23 Describe a coordinate system with perpendicular axes meeting at the origin and locate points with ordered pairs.
• M.5.24 Graph first-quadrant points to represent real-world problems and interpret the coordinates in context.

Geometry – Classify plane figures by their properties

• M.5.25 Understand that attributes of a category of plane figures belong to all its subcategories.
• M.5.26 Classify plane figures in a hierarchy based on their properties.