5th Grade Math (Colorado Academic Standards)

Standard 1: Number and Quantity

• MA.5.NBT.A Understand the place value system.
  • 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.
  • 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.
  • 3. Read, write and compare decimals to thousandths.
  • 3.a. Read and write decimals to thousandths in numerals, words and expanded form.
  • 3.b. Compare decimals to thousandths by place value, recording with >, = and <.
  • 4. Round decimals to any place.
• MA.5.NBT.B Compute with multi-digit whole numbers and decimals to hundredths.
  • 1. Multiply multi-digit whole numbers fluently with the standard algorithm.
  • 2. Divide up to four-digit numbers by two-digit numbers with place-value strategies, explained with equations, arrays or area models.
  • 3. Do all four operations with decimals to hundredths using models and place-value strategies, linked to a written method.
• MA.5.NF.A Add and subtract fractions using equivalent fractions.
  • 1. Add and subtract fractions and mixed numbers with unlike denominators by rewriting them with like denominators.
  • 2. Solve word problems adding and subtracting fractions with unlike denominators and check answers with benchmark fractions.
• MA.5.NF.B Extend multiplication and division to fractions.
  • 1. Interpret a fraction as division (a/b = a ÷ b) and solve word problems whose answers are fractions or mixed numbers.
  • 2. Extend earlier work on multiplication to multiply whole numbers or fractions by a fraction.
  • 2.a. Interpret (a/b) × q as a parts of q split into b equal parts, and make stories for such products.
  • 2.b. Find areas of rectangles with fraction side lengths by tiling and show this equals multiplying the sides.
  • 3. Understand multiplication as scaling (resizing).
  • 3.a. Compare a product to one factor by looking at the other factor, without multiplying.
  • 3.b. Explain why multiplying by a fraction greater than 1 makes a number bigger and by a fraction less than 1 makes it smaller.
  • 4. Solve real-world problems multiplying fractions and mixed numbers.
  • 5. Extend earlier work on division to unit fractions divided by whole numbers and the reverse.
  • 5.a. Interpret and compute a unit fraction divided by a whole number, e.g. (1/3) ÷ 4.
  • 5.b. Interpret and compute a whole number divided by a unit fraction, e.g. 4 ÷ (1/5).
  • 5.c. Solve real-world problems dividing unit fractions by whole numbers and whole numbers by unit fractions.

Standard 2: Algebra and Functions

• MA.5.OA.A Write and interpret numerical expressions.
  • 1. Use grouping symbols (parentheses, brackets, braces) in expressions and evaluate them.
  • 2. Write simple expressions for calculations and interpret expressions without evaluating them (e.g. 2 × (8 + 7)).
• MA.5.OA.B Analyze patterns and relationships.
  • 1. Make two number patterns from two rules, relate matching terms, and graph the resulting ordered pairs.

Standard 3: Data, Statistics, and Probability

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

Standard 4: Geometry

• MA.5.G.A Graph points on the coordinate plane to solve problems.
  • 1. Understand the coordinate plane: perpendicular axes meeting at the origin, with points located by ordered pairs (x, y).
  • 2. Graph points in the first quadrant to represent problems and interpret the coordinates in context.
• MA.5.G.B Classify two-dimensional figures by their properties.
  • 1. Know attributes of a category of 2-D shapes belong to all its subcategories (e.g. all squares are rectangles, so have right angles).
  • 2. Classify 2-D shapes in a hierarchy based on their properties.