# Fifth Grade

Math

Report Card Guide

Here you'll find what fifth grade students are learning in Math during each of the three marking periods (trimesters).

## First Trimester

- Number and Operations in Base Ten
- Number and Operations: Fractions
- Operations and Algebraic Thinking
- Measurement and Data
- Mathematical Practices

## Number and Operations in Base Ten

**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

- Multiplies multi-digit whole numbers using a variety of strategies, limited to problems involving:

## Number and Operations: Fractions

## Operations and Algebraic Thinking

**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

- 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

- 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

- Uses multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluates expressions containing these symbols.

## Measurement and Data

**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)

- (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

- Example: cubic feet, cubic centimeters, cubic units
- Finds volumes of solid figures composed of two non-overlapping right rectangular prisms

- Develops a strategy to find the volume of any rectangular prisms

## Mathematical Practices

**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

## Second Trimester

- Numbers and Operations in Base Ten
- Numbers and Operations: Fractions
- Operations and Algebraic Thinking
- Measurement and Data
- Mathematical Practices

## Numbers and Operations in Base Ten

**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

- 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

**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

- Multiplies multi-digit whole numbers

## Numbers and Operations: Fractions

**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

- Multiplies a whole number by a fraction and a fraction by a whole number

## Operations and Algebraic Thinking

**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

- Uses multiple grouping symbols

## Measurement and Data

**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

## Mathematical Practices

**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

## Third Trimester

- Number and Operations in Base Ten
- Numbers and Operations: Fractions
- Operations and Algebraic Thinking
- Geometry
- Measurement and Data
- Mathematical Practices

## Number and Operations in Base Ten

**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

- 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

**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

- Adds and subtracts whole numbers and decimals efficiently using a variety of strategies

## Numbers and Operations: Fractions

**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

- Solve word problems involving the division of whole numbers leading to answers in the form of fractions or mixed numbers

## Operations and Algebraic Thinking

**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

- Uses multiple grouping symbols

**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

- Generates two numerical patterns using two given rules

## Geometry

**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

- Identifies two-dimensional figures in a hierarchy based on properties

## Measurement and Data

**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

- Solve simple conversion problems

**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)

- (Formulas: V= l x w x h and V= B x h)

- Develops a strategy to find the volume of any rectangular prisms
- 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

## Mathematical Practices

**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