5th Grade Math (Massachusetts Curriculum Frameworks)

Operations and Algebraic Thinking (5.OA)

• 5.OA.A.1 Evaluate numerical expressions that use parentheses, brackets or braces.
• 5.OA.A.2 Write simple expressions for described calculations and interpret them without evaluating.
• 5.OA.B.3 Make two number patterns from two rules, relate matching terms, graph the ordered pairs and explain the relationship.

Number and Operations in Base Ten (5.NBT)

• 5.NBT.A.1 Know a digit is worth ten times as much one place to the left and a tenth as much one place to the right, including decimals.
• 5.NBT.A.2 Explain zero patterns when multiplying by powers of 10 and decimal point moves; use whole-number exponents for powers of 10.
• 5.NBT.A.3 Read, write and compare decimals to thousandths.
  • a. Read and write decimals to thousandths as numerals, number names and in expanded form.
  • b. Compare decimals to thousandths by place value, recording with >, = and <.
• 5.NBT.A.4 Use place value to round decimals to any place.
• 5.NBT.B.5 Multiply multi-digit whole numbers accurately and efficiently with the standard algorithm.
• 5.NBT.B.6 Divide up to four-digit dividends by two-digit divisors using place value and properties; explain with equations, arrays or area models.
• 5.NBT.B.7 Do the four operations with decimals to hundredths using models and strategies, relating multiplication and division too.

Number and Operations—Fractions (5.NF)

• 5.NF.A.1 Add and subtract fractions and mixed numbers with unlike denominators by rewriting them with like denominators.
• 5.NF.A.2 Solve word problems adding and subtracting fractions of the same whole; estimate with benchmark fractions to check answers.
• 5.NF.B.3 Understand a fraction as numerator divided by denominator; solve sharing problems with fraction or mixed-number answers.
• 5.NF.B.4 Extend multiplication so a fraction or whole number is multiplied by a fraction, using models such as area models.
  • a. Interpret (a/b) × q as a parts of q split into b equal parts; show products with fraction models.
  • b. Find areas of rectangles with fractional sides by tiling with unit-fraction squares and link to multiplying the sides.
• 5.NF.B.5 Understand multiplication as scaling (resizing).
  • a. Compare a product to one factor by looking at the other factor, without multiplying.
  • b. Explain why multiplying by a fraction greater than 1 makes a number bigger and by a fraction less than 1 makes it smaller.
• 5.NF.B.6 Solve real-world problems multiplying fractions and mixed numbers using models or equations.
• 5.NF.B.7 Divide a unit fraction by a whole number and a whole number by a unit fraction.
  • a. Interpret and find a unit fraction divided by a non-zero whole number, explaining with multiplication.
  • b. Interpret and find a whole number divided by a unit fraction, explaining with multiplication.
  • c. Solve real-world problems dividing unit fractions and whole numbers using models or equations.

Measurement and Data (5.MD)

• 5.MD.A.1 Convert between units within one measurement system and use this in multi-step real problems.
• 5.MD.B.2 Make a line plot (dot plot) of measurements in fractions of a unit and solve problems with fraction operations.
• 5.MD.C.3 Recognize volume as an attribute of solid shapes.
  • a. A cube with side 1 unit has a volume of one cubic unit.
  • b. A solid packed with n unit cubes has a volume of n cubic units.
• 5.MD.C.4 Measure volume by counting unit cubes (cubic cm, in, ft and non-standard units).
• 5.MD.C.5 Relate volume to multiplication and addition to solve volume problems.
  • a. Pack a right rectangular prism with unit cubes and show volume = edge lengths multiplied or base area × height.
  • b. Use V = l × w × h and V = B × h for rectangular prisms with whole-number edges.
  • c. Find volumes of solids made of two non-overlapping rectangular prisms by adding.

Geometry (5.G)

• 5.G.A.1 Understand the coordinate plane: perpendicular axes meeting at the origin, with points located by ordered pairs.
• 5.G.A.2 Plot points in the first quadrant to represent problems and interpret the coordinates in context.
• 5.G.B.3 Know attributes of a category of 2D shapes belong to all its subcategories (all squares have four right angles).
• 5.G.B.4 Classify 2D shapes in a hierarchy based on their properties.