5th Grade Math (Maryland MCCRS)

Number and Operation Sense – 5.NOS.A: The place value system

• 5.NOS.A.1 Explain that in a multi-digit number each place is worth ten times the place to its right.
• 5.NOS.A.2 Explain patterns in zeros and decimal point shifts when multiplying or dividing by powers of 10; use whole-number exponents.
• 5.NOS.A.3 Read, write, estimate, round and compare decimals to thousandths.
  • a. Read and write decimals as numerals, words and expanded form.
  • b. Estimate decimals with number lines, benchmarks and rounding to any place.
  • c. Compare decimals to thousandths by digit values and number lines; record with symbols.

Number and Operation Sense – 5.NOS.B: Operations with multi-digit whole numbers and decimals to hundredths

• 5.NOS.B.4 Multiply multi-digit whole numbers fluently.
  • a. Estimate products.
  • b. Use efficient strategies such as partial products or doubling and halving.
  • c. Use the standard algorithm.
  • d. Explain which strategy is most efficient.
• 5.NOS.B.5 Divide whole numbers with up to four-digit dividends and two-digit divisors.
  • a. Estimate quotients.
  • b. Use partial quotients.
  • c. Use properties and the inverse relationship with multiplication.
  • d. Link arrays, area models or equations to the division.
• 5.NOS.B.6 Add and subtract decimals to hundredths.
  • a. Estimate sums and differences.
  • b. Use models, drawings, place value strategies and properties.
  • c. Use an algorithm.
  • d. Explain which strategy is most efficient.
• 5.NOS.B.7 Multiply and divide decimals to hundredths in real-world contexts.
  • a. Estimate products and quotients.
  • b. Use models, drawings and arrays.
  • c. Use place value strategies such as partial products and partial quotients.
  • d. Use properties and the inverse relationship.
  • e. Connect models and equations to what the operations mean.

Number and Operation Sense – 5.NOS.C: Equivalent fractions to add and subtract

• 5.NOS.C.8 Add and subtract fractions with unlike denominators.
  • a. Estimate with benchmarks and check reasonableness.
  • b. Apply whole-number strategies to fractions.
  • c. Use equivalent fractions to make like denominators.
• 5.NOS.C.9 Solve word problems adding and subtracting fractions of the same whole, including unlike denominators, with models or equations.

Number and Operation Sense – 5.NOS.D: Multiply and divide fractions

• 5.NOS.D.10 Interpret a fraction as the numerator divided by the denominator in context.
• 5.NOS.D.11 Multiply a whole number by a fraction.
  • a. Estimate with benchmarks and check reasonableness.
  • b. Interpret the product as a fraction of the whole number, for fractions less than or greater than 1.
• 5.NOS.D.12 Multiply a fraction by a fraction.
  • a. Estimate with benchmarks and check reasonableness.
  • b. Apply whole-number strategies such as area models.
  • c. Use unit squares to find the area of a rectangle with fractional side lengths.
• 5.NOS.D.13 Multiply fractions when one or both factors are greater than 1.
  • a. Estimate with benchmarks and check reasonableness.
  • b. Apply strategies such as area models and partial products.
• 5.NOS.D.14 Interpret multiplication as scaling (resizing).
  • a. Compare a product with one factor by looking at the other factor, without calculating.
  • b. Explain when a product is bigger or smaller than the given number and link equivalent fractions to multiplying by 1.
• 5.NOS.D.15 Solve real-world problems that multiply fractions and mixed numbers.
• 5.NOS.D.16 Divide unit fractions by whole numbers and whole numbers by unit fractions in context.
  • a. Estimate quotients and check reasonableness.
  • b. Use models and equations for a unit fraction divided by a whole number.
  • c. Use models and equations for a whole number divided by a unit fraction.
  • d. Connect models and equations to the meaning of division.

Algebraic Thinking – 5.AT.A: Write and interpret numerical expressions

• 5.AT.A.1 Interpret and evaluate numerical expressions that use grouping symbols.
• 5.AT.A.2 Write expressions that record calculations and interpret them without evaluating.

Algebraic Thinking – 5.AT.B: Patterns and relationships

• 5.AT.B.3 Generate and analyze number patterns, including how two patterns relate, using tables, ordered pairs and graphs.
  • a. Generate a pattern from a rule and find relationships among its terms.
  • b. Generate two patterns from two rules and relate their corresponding terms.
  • c. Show the relationships with tables, ordered pairs and graphs.

Geometric Reasoning and Measurement – 5.GR.A: Relationships between measurement units

• 5.GR.A.1 Convert between standard units within one measurement system and use conversions in multistep problems.

Geometric Reasoning and Measurement – 5.GR.B: Classify plane figures by their properties

• 5.GR.B.2 Explain that properties of a category of shapes also belong to all its subcategories.
• 5.GR.B.3 Classify two-dimensional figures by their properties.
  • a. Classify triangles by angle size and side length.
  • b. Arrange quadrilaterals in a hierarchy by sides, angles and parallel or perpendicular sides.

Geometric Reasoning and Measurement – 5.GR.C: Volume and its link to multiplication

• 5.GR.C.4 Recognize volume as an attribute of solid figures and measure it by counting unit cubes that fill it with no gaps or overlaps.
• 5.GR.C.5 Relate volume to multiplication and addition and solve problems in context.
  • a. Find the volume of a right rectangular prism by layering unit cubes and show it equals edge lengths multiplied, or base area times height.
  • b. Apply V = l × w × h and V = B × h to prisms with whole-number edges.
  • c. Find the volume of composite solids by splitting them into non-overlapping prisms and adding.

Geometric Reasoning and Measurement – 5.GR.D: Graph points on the coordinate plane

• 5.GR.D.6 Describe the coordinate plane (perpendicular axes meeting at the origin) and plot and name first-quadrant points as ordered pairs.
• 5.GR.D.7 Graph first-quadrant points to represent problems and interpret the coordinates in context.

Reasoning with Data and Statistics – 5.DS.A: Represent and interpret data

• 5.DS.A.1 Ask and answer questions by collecting, organizing and summarizing data in context.
  • a. Make scaled bar graphs and line plots with halves, fourths and eighths.
  • b. Summarize graphs using mode, range and gaps, and draw conclusions.
  • c. Judge whether a graph represents the data accurately.