5th Grade Math (Utah Core Standards)

Operations and Algebraic Thinking (5.OA)

• 5.OA.1 Use grouping symbols (parentheses, brackets, braces) in expressions and evaluate them.
• 5.OA.2 Write simple expressions for calculations and interpret expressions without evaluating them (e.g. 2 × (8 + 7)).
  • a. Write simple expressions that record calculations (e.g. 2 × (8 + 7)).
  • b. Interpret expressions without evaluating them (e.g. a product as a scaled sum).
• 5.OA.3 Make two number patterns from two rules, relate matching terms, and graph the resulting ordered pairs.

Number and Operations in Base Ten (5.NBT)

• 5.NBT.1 Know a digit is worth 10 times as much as one place to its right and 1/10 as much as one place to its left.
• 5.NBT.2 Explain patterns of zeros and decimal-point placement when multiplying or dividing by powers of 10; use whole-number exponents for powers of 10.
• 5.NBT.3 Read, write and compare decimals to thousandths.
  • a. Read and write decimals to thousandths in numerals, words and expanded form.
  • b. Compare decimals to thousandths by place value, recording with >, = and <.
• 5.NBT.4 Round decimals to any place.
• 5.NBT.5 Multiply multi-digit whole numbers fluently with the standard algorithm.
• 5.NBT.6 Divide up to four-digit numbers by two-digit numbers with place-value strategies, explained with equations, arrays or area models.
• 5.NBT.7 Do all four operations with decimals to hundredths using models and place-value strategies, linked to a written method.

Number and Operations—Fractions (5.NF)

• 5.NF.1 Add and subtract fractions and mixed numbers with unlike denominators by rewriting them with like denominators.
• 5.NF.2 Solve word problems adding and subtracting fractions with unlike denominators and check answers with benchmark fractions.
• 5.NF.3 Interpret a fraction as division (a/b = a ÷ b) and solve word problems whose answers are fractions or mixed numbers.
• 5.NF.4 Extend earlier work on multiplication to multiply whole numbers or fractions by a fraction.
  • a. Interpret (a/b) × q as a parts of q split into b equal parts, and make stories for such products.
  • b. Find areas of rectangles with fraction side lengths by tiling and show this equals multiplying the sides.
• 5.NF.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.6 Solve real-world problems multiplying fractions and mixed numbers.
• 5.NF.7 Extend earlier work on division to unit fractions divided by whole numbers and the reverse.
  • a. Interpret and compute a unit fraction divided by a whole number, e.g. (1/3) ÷ 4.
  • b. Interpret and compute a whole number divided by a unit fraction, e.g. 4 ÷ (1/5).
  • c. Solve real-world problems dividing unit fractions by whole numbers and whole numbers by unit fractions.

Measurement and Data (5.MD)

• 5.MD.1 Convert between units of different sizes in one measurement system and use this in multistep real-world problems.
• 5.MD.2 Make line plots of measurements in halves, quarters and eighths and solve problems using fraction operations.
• 5.MD.3 Recognize volume as a property of solid shapes and understand how volume is measured.
  • a. A unit cube (side 1 unit) has a volume of one cubic unit and is used to measure volume.
  • b. A solid packed with no gaps or overlaps by n unit cubes has a volume of n cubic units.
• 5.MD.4 Measure volume by counting unit cubes (cubic cm, in, ft or improvised units).
• 5.MD.5 Connect volume to multiplication and addition and solve volume problems.
  • a. Find the volume of a rectangular prism by packing with unit cubes and show it equals length × width × height or base area × height.
  • b. Use the volume formulas (length × width × height, base area × height) for rectangular prisms in problems.
  • c. Find volumes of solids made of two rectangular prisms by adding their volumes.

Geometry (5.G)

• 5.G.1 Understand the coordinate plane: perpendicular axes meeting at the origin, with points located by ordered pairs (x, y).
  • a. Know the axes are perpendicular number lines meeting at the origin, where both are 0.
  • b. Read an ordered pair in the first quadrant: the first number moves along the x-axis, the second along the y-axis.
• 5.G.2 Graph points in the first quadrant to represent problems and interpret the coordinates in context.
• 5.G.3 Know attributes of a category of 2-D shapes belong to all its subcategories (e.g. all squares are rectangles, so have right angles).
• 5.G.4 Classify 2-D shapes in a hierarchy based on their properties.