Fifth Grade
Math
Report Card Guide

Solves problems and computes accurately with whole numbers and decimals

• Uses whole numbers to compute accurately (straight computation or word problems)
   
  • Multiplies multi-digit whole numbers using a variety of strategies, limited to problems involving: 
    • 1 digit by 2 digit 
    • 1 digit by 3 digit
    • 2 digit by 2 digit
       
  • Finds whole-number quotients of whole numbers with up to 3 digit dividends and 2 digit divisors using a variety of strategies (including the application of the  multiplication/division relationship) 
     
  • Interprets remainders in a division story problem based on story context
     
  • Interprets and solves multi-step problems using all four operations 

Uses the understanding of equivalency to add and subtract fractions 

• Solves addition and subtraction problems involving fractions (straight computation or word problems)
   
  • Adds and subtracts fractions, including mixed numbers, with unlike denominators using multiple methods and representations

Interprets and evaluates numerical expressions using order of operations

• Analyzes and completes calculations by applying the order of operations 
   
  • Uses multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluates expressions containing these symbols.
     
  • Understands that grouping symbols within a numerical expression can change the value of the expression
     
    • Example 2 + 5 x 6= 32       (2 + 5) x 6 = 42
       
  • Writes simple expressions that model calculations with numbers 
     
    • Example: Expresses the calculation “add 8 and 7, then multiply by 2” as (8 + 7) x 2
       
  • Interprets numerical expressions without evaluating them
     
    • Example: Recognizes that 3 x (18,932+ 921) is three times as large as  18,932 + 921 

Organizes, represents and interprets data using appropriate scale on a variety of graphs

• Organizes and displays data in tallies, tables, charts, pictographs and bar graphs, and uses a title, appropriate scale, and labels
   
• Interprets and answers single and multi-step questions based on data 
   
• Solve problems involving addition and subtraction of fractions by using information presented in line plots

Applies concepts of volume to solve problems and relates volume to multiplication and to addition 

• Uses, describes, and develops procedures to solve problems involving volume
   
  • Develops a strategy to find the volume of any rectangular prisms 
     
    • (Formulas: V= l x w x h and V= B x h)
       
  • Explores the effect on volume when the dimensions of a box change
     
  • Uses appropriate units to measure volume 
     
    • Example: cubic feet, cubic centimeters, cubic units
       
  • Finds volumes of solid figures composed of two non-overlapping right rectangular   prisms

Strategically applies concepts and processes to make sense of problems and solve them

• Makes sense of mathematical problems and perseveres in solving them
   
• Uses structures such as place value and properties of operations to solve problems
   
• Creates and uses mathematical models to represent a problem situation
   
• Uses appropriate tools strategically to solve problems
   
• Recognizes regularities and applies them when solving other related problems
   
• Uses math vocabulary to clearly explain and justify mathematical reasoning  and critique the reasoning of others 

Applies place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals 

• Demonstrates understanding of place value of whole numbers and decimals, and compare quantities or magnitudes of numbers
   
  • Demonstrates an understanding that in a multi-digit number, a digit in one place represents 10 times what it represents in the place to its right or 1/10 of what it represents in the place to its left
     
  • Explains patterns in the number of zeros of the product when multiplying a number by powers of 10 
     
  • Uses whole-number exponents to denote powers of 10 
     
  • Reads and writes decimals to thousandths using base-ten numerals, word form, and expanded form
     
  • Compares two decimals to thousandths based on meanings of the digits in each place using >, = and < symbols
     
  • Rounds decimals to the ones, tenths, hundredths, or thousandths place

Solves problems and computes accurately with whole numbers and decimals

• Uses whole numbers to compute accurately (straight computation or word problems)
   
  • Multiplies multi-digit whole numbers
     
  • Finds whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors
     
  • Interprets remainders in a division story problem based on story context
     
  • Interprets and solves multi-step problems using all four operations

Applies previous understandings of multiplication and division concepts to fractions

• Solves multiplication and division problems involving fractions (straight computation or word problems)
   
  • Multiplies a whole number by a fraction and a fraction by a whole number
     
  • Multiplies a fraction (including mixed numbers) by a fraction
     
  • Demonstrates an understanding of multiplication as scaling (resizing)
     
  • Example: Explain why the product of  3 x 1/3  is less than 3 
     
  • Divides unit fractions by whole numbers and whole numbers by unit fractions  

Interprets and evaluates numerical expressions using order of operations

• Analyzes and completes calculations by applying the order of operations 
   
  • Uses multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluates expressions containing these symbols.
     
  • Understands that grouping symbols within a numerical expression can change the  value of the expression
     
  • Writes simple expressions that model calculations with numbers 
     
  • Interprets numerical expressions without evaluating them

Organizes, represents and interprets data using appropriate scale on a variety of graphs

• Organizes and displays data in tallies, tables, charts, pictographs, and bar graphs, and uses a title, appropriate scale, and labels
   
• Interprets and answers single and multi-step questions based on data 
   
• Solve problems involving  computation of fractions by using information presented in line plots

Strategically applies concepts and processes to make sense of problems and solve them

• Makes sense of mathematical problems and perseveres in solving them
   
• Uses structures such as place value and properties of operations to solve problems
   
• Creates and uses mathematical models to represent a problem situation
   
• Uses appropriate tools strategically to solve problems
   
• Recognizes regularities and applies them when solving other related problems
   
• Uses math vocabulary to clearly explain and justify mathematical reasoning  and critique the reasoning of others 
   
• Calculates accurately and efficiently and uses clear and concise notation and vocabulary to record and explain work

Applies place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals 

• Demonstrates understanding of place value of whole numbers and decimals, and compare quantities or magnitudes of numbers
   
  • Demonstrates an understanding that in a multi-digit number, a digit in one place represents 10 times what it represents in the place to its right or 1/10 of what it represents in the place to its left
     
  • Explains patterns in the number of zeros of the product when multiplying a number by powers of 10 
     
  • Uses whole-number exponents to denote powers of 10 
     
  • Reads and writes decimals to thousandths using base-ten numerals, word form, and expanded form
     
  • Compares two decimals to thousandths based on meanings of the digits in each place using >, = and < symbols
     
  • Rounds decimals to the ones, tenths, hundredths, or thousandths place

Solves problems and computes accurately with whole numbers and decimals

• Uses whole numbers and decimals to compute accurately (straight computation or word problems)
   
  • Adds and subtracts whole numbers and decimals efficiently using a variety of strategies
     
  • Multiplies multi-digit whole numbers and decimals (to hundredths)
     
  • Divides multi-digit whole numbers and decimals (to hundredths)
     
  • In division with decimals, divides as with whole numbers and REASONS to determine the position of the decimal point
     
  • Interprets and solves multi-step problems using all four operations

Uses the understanding of equivalency to add and subtract fractions 

• Solves addition and subtraction problems involving fractions (straight computation or word problems)
   
  • Adds and subtracts fractions, including mixed numbers, with unlike denominators using multiple methods and representations

Applies previous understandings of multiplication and division concepts to fractions

• Solves multiplication and division problems involving fractions (straight computation or word problems)
   
  • Solve word problems involving the division of whole numbers leading to answers in the form of fractions or mixed numbers
     
  • Multiplies a whole number by a fraction and a fraction by a whole number
     
  • Multiplies a fraction (including mixed numbers) by a fraction
     
  • Demonstrates an understanding of multiplication as scaling (resizing)
     
  • Example: Explain why the product of  3 x 1/3  is less than 3 
     
  • Divides unit fractions by whole numbers and whole numbers by unit fractions  

Interprets and evaluates numerical expressions using order of operations

• Analyzes and completes calculations by applying the order of operations 
   
  • Uses multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluates expressions containing these symbols
     
  • Understands that the use of  grouping symbols can change the value of an expression 
     
  • Writes simple expressions that model calculations with numbers 
     
  • Interprets numerical expressions without evaluating them

Generates and analyzes patterns and relationships 

• Creates, extends, and analyzes number patterns
   
  • Generates two numerical patterns using two given rules
     
  • Identifies apparent relationships between corresponding terms of two patterns with the same starting number that follow different rules

Graphs and interprets points on a coordinate grid to solve real world and mathematical problems

• Identifies parts of the coordinate plane (x-axis, y-axis and origin) and the ordered pair 
   
• Represents real-world and mathematical problems by plotting points in quadrant 1 of the coordinate plane

Classifies two-dimensional figures into categories based on an understanding of their properties 

• Uses basic properties to classify two-dimensional figures
   
  • Identifies two-dimensional figures in a hierarchy based on properties
     
  • Classifies two-dimensional figures based on properties

Solves problems using conversion within given measurement system

• Converts between different-sized measurement units within the U.S. Customary or Metric systems
   
• Uses a table of measurement equivalencies to:
   
  • Solve simple conversion problems
     
  • Solve multi-step, real-world problems involving conversions

Organizes, represents and interprets data using appropriate scale on a variety of graphs

• Organizes and displays data in tallies, tables, charts, pictographs, bar graphs, and line graphs and uses a title, appropriate scale, and labels
   
• Interprets and answers single and multi-step questions based on data 
   
• Solve problems involving computation of fractions by using information presented in line plots

Applies concepts of volume to solve problems and relates volume to multiplication and to addition 

• Uses, describes, and develops procedures to solve problems involving volume
   
  • Develops a strategy to find the volume of any rectangular prisms 
     
    • (Formulas: V= l x w x h and V= B x h)
       
• Explores the effect on volume when the dimensions of a box change
   
• Uses appropriate units to measure volume  Ex: cubic feet, cubic centimeters, cubic units
   
• Finds volume of solid figures composed of two non-overlapping right rectangular prisms

Strategically applies concepts and processes to make sense of problems and solve them

• Makes sense of mathematical problems and perseveres in solving them
   
• Uses structures such as place value and properties of operations to solve problems
   
• Creates and uses mathematical models to represent a problem situation
   
• Uses appropriate tools strategically to solve problems
   
• Recognizes regularities and applies them when solving other related problems
   
• Uses math vocabulary to clearly explain and justify mathematical reasoning  and critique the reasoning of others 
   
• Calculates accurately and efficiently and uses clear and concise notation and vocabulary to record and explain work