5th Grade Mathematics

5th Grade Math Description

Grade 5 students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions and develop fluency in calculating sums and differences of fractions. Students develop understanding of why division procedures work based on the meaning of base-tem numerals and properties of operations. They apply their understandings of models for decimals, decimal notation, and properties of operations to add, subtract, multiply, and divide decimals and develop fluency in these computations. Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill a space. Students decompose threedimensional shapes and find volumes of rectangular prisms by decomposing them into layers of arrays of cubes. For instruction and learning, students will use both the 5th Grade and Course 1 Math Connects Textbooks, Spiral Math review daily, fact practice, Accelerated Mathematics, and other supplemental materials for instruction.


5th Grade Main Topics

Number and Number Sense

  • Understand place value and use concepts to round numbers
  • Recognize benchmark fractions and decimals
  • Compare rational numbers and use comparison symbols (<, >, +)
  • Investigate prime, composite, even, and odd numbers

Computation and Estimation

  • Use properties of operations to add, subtract, multiply and divide rational numbers in decimal notation and solve problems
  • Use properties of operations to add and subtract numbers in fraction notation
  • Investigate the order of operations and use it to evaluate expressions

Measurement and Geometry

  • Measure perimeter, area, and volume
  • Identify equivalent measures in the metric system
  • Work with elapsed time
  • Measure and classify angles and classify triangles
  • Identify measurable characteristics of circles

Probability and Statistics

  • Construct sample spaces to determine probabilities
  • Compare and contrast measures of center
  • Describe mean as fair share
  • Collect, organize, and interpret data 

Patterns, Functions, and Algebra

  • Investigate the concept of variable and equations
  • Investigate properties of real numbers 

5th Grade Standards for Mathematical Practice 

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.


5th Grade Year in a Glance


Chapter 1 Number Sense

  1. Millions Period
  2. Billions Period
  3. Decimals
  4. Equivalent Decimals
  5. Positive and Negative numbers
  6. Compare Positive and Negative Numbers
  7. Roman Numerals

Chapter 2 Addition and Subtraction

  1. Properties
  2. Add Large Numbers
  3. Add Decimals
  4. Subtract Large Numbers
  5. Subtract Decimals
  6. Add & Subtract Input Tables
  7. Compensation and Word Problems

Chapter 3 Multiplication

  1. Multiplication Properties
  2. Prime & Composite Numbers
  3. Distributive Property
  4. 1-Digit Multipliers (Estimation, Word Problems, Money)
  5. 2-Digit Multipliers (Estimation, Word Problems, Input/output tables)
  6. Multiply and Estimate
  7. 3-Digit Multipliers
  8. Factor Trees
  9. Exponent Form

Chapter 4 Geometry Lines and Angles

  1. Points, Lines, and Planes
  2. Rays and Angles
  3. Measuring Angles
  4. Measure and Draw
  5. Triangles
  6. Circles
  7. Graphing Figures

Chapter 5 Division 1-Digit Divisors

  1. 1-Digit Quotients
  2. 1-2 Digit Quotients
  3. 2-3-Digit Quotients
  4. Zero in the Quotient
  5. 4-Digit Dividends
  6. Estimate
  7. Short Form Division

Chapter 6 Fractions

  1. Compare and Order Fractions
  2. Rename Fractions
  3. Improper Fractions and Mixed Numbers
  4. Compare Mixed Numbers
  5. Common Factors
  6. Lowest Terms
  7. More Lowest Terms
  8. Guess and Check

Chapter 7 Division 2-Digit Divisors

  1. Multiples of 10
  2. 1-Digit Quotients
  3. Adjust the Quotient
  4. 2-Digit Quotients Interpret a Remainder
  5. 4-Digit Dividends
  6. 3-Digit Quotients
  7. More 3-Digit Quotients
  8. Division Practice
  9. Order of Operations

Chapter 8 Time and Customary Measurements

  1. Time
  2. Elapsed Time
  3. Linear Measurement
  4. Rename Measurements
  5. Weight and Capacity
  6. Temperature
  7. Measurement Problems

Chapter 9 Fractions: Adding and Subtracting

  1. Add Like Fractions
  2. Subtract Like Fractions
  3. Add Unlike Fractions
  4. Subtract Unlike Fractions
  5. Least Common Multiple
  6. Compare Fractions
  7. Least Common Denominator
  8. Add and Subtract Unlike Fractions
  9. Add and Subtract Mixed Numbers
  10. Add and Subtract Fractions
  11. Factoring to Compare Fractions

Chapter 10 Equations

  1. Expressions
  2. Equations
  3. Balanced Equations
  4. Equations in Word Problems

Chapter 11 Geometry: Perimeter and Area

  1. Quadrilateals and Other Polygons
  2. Perimeter and Circumference
  3. Classify Triangles
  4. Aea
  5. Area of Triangle
  6. Perimeter and Area

Chapter 12 Fractions: Multiplication and Division

  1. Multiply a Whole Number and a Fraction
  2. Find a Fraction of a Whole Number
  3. Find a Fraction of a Fraction
  4. Multiply a Mixed Number
  5. Multiply Mixed Numbers
  6. Divide a Whole Number by a Fraction
  7. Divide a Fraction by a Fraction
  8. Use reciprocals to divide Fractions
  9. Divide Fractions
  10. The World of Fractions

Chapter 13 Decimals: Multiplication and Division

  1. Decimals
  2. Rounding Decimals
  3. Compare and Multiply
  4. Multiply Decimals
  5. Estimate and Multiply
  6. Division: Decimal by a 1-digit Divisor
  7. Quotients Less Than One
  8. Zero in the Quotient
  9. Powers of Ten
  10. Solve Problems Backwards

Chapter 14 Geometry Surface Area and Volume

  1. 3-Dimensional Figures
  2. Prisms and Pyramids
  3. Surface Area
  4. Volume
  5. More Volume
  6. MOre Surface Area and Volume

Chapter 15 Metric Measurement

  1. Metric Measurement:Linear
  2. More Linear Measurement
  3. Metric Measurement: Capacity and Mass
  4. Celsius Temperature
  5. Add and Subtrct Metric Units

Chapter 16 Ratios, Proportions and Percents

  1. Ratios
  2. Equivalent Ratios
  3. Map Scales
  4. Rates
  5. Rates and Percents
  6. Decimals and Percents
  7. Percent of a Number
  8. Probability

Chapter 17 Integers

  1. Positive and Negative Numbers
  2. Adding Positive and Negative Numbers
  3. Subtracting Negative Nmbers
  4. Adding and Subtracting Integers

Chapter 18 Data and Graphs

  1. Line Plot and Stem-and-Leaf-Plot
  2. Double Bar and Double Line Graphs
  3. Picto Graphs and Circle Graphs