K-12 Mathematics Standards: Grade 5
Skills available for Georgia Grade 5 math standards
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NR
Numerical Reasoning
Place value, multiplying by powers of 10, multiplication and division of multi-digit numbers, fractions, decimal numbers, numerical expressions
5.NR.1 Use place value understanding to solve real-life, mathematical problems.
5.NR.1 Use place value understanding to solve real-life, mathematical problems.
5.NR.1.1: Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NR.1.1: Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NR.1.2: Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to 103.
Exponents and powers of ten
Multiply by powers of ten
Divide by powers of ten
Multiply and divide by powers of ten
5.NR.1.2: Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to 103.
Exponents and powers of ten
Multiply by powers of ten
Divide by powers of ten
Multiply and divide by powers of ten
5.NR.2 Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems.
5.NR.2 Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems.
5.NR.2.1: Fluently multiply multi-digit (up to 3-digit by 2-digit) whole numbers to solve authentic problems.
Multiply by 1-digit numbers
Multiply by 2-digit numbers
Multiply three or more numbers
Multiplication strategies
5.NR.2.1: Fluently multiply multi-digit (up to 3-digit by 2-digit) whole numbers to solve authentic problems.
Multiply by 1-digit numbers
Multiply by 2-digit numbers
Multiply three or more numbers
Multiplication strategies
5.NR.2.2: Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems.
2-digit and 3-digit dividends
4-digit dividends
Division strategies
5.NR.2.2: Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems.
2-digit and 3-digit dividends
4-digit dividends
Division strategies
5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models.
5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models.
5.NR.3.1: Explain the meaning of a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
5.NR.3.1: Explain the meaning of a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
5.NR.3.2: Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies.
Compare fractions
Order fractions
5.NR.3.2: Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies.
Compare fractions
Order fractions
5.NR.3.3: Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.
Add fractions
Subtract fractions
Add and subtract fractions
Add and subtract mixed numbers
5.NR.3.3: Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.
Add fractions
Subtract fractions
Add and subtract fractions
Add and subtract mixed numbers
5.NR.3.4: Model and solve problems involving multiplication of a fraction and a whole number.
Multiply unit fractions by whole numbers
Multiply fractions by whole numbers
Fractions of a number
5.NR.3.4: Model and solve problems involving multiplication of a fraction and a whole number.
Multiply unit fractions by whole numbers
Multiply fractions by whole numbers
Fractions of a number
5.NR.3.5: Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.
5.NR.3.5: Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.
5.NR.3.6: Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
Divide unit fractions by whole numbers
Divide whole numbers by unit fractions
Divide unit fractions and whole numbers
5.NR.3.6: Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
Divide unit fractions by whole numbers
Divide whole numbers by unit fractions
Divide unit fractions and whole numbers
5.NR.4 Read, write, and compare decimal numbers to the thousandths place, and round and perform operations with decimal numbers to the hundredths place to solve relevant, mathematical problems.
5.NR.4 Read, write, and compare decimal numbers to the thousandths place, and round and perform operations with decimal numbers to the hundredths place to solve relevant, mathematical problems.
5.NR.4.1: Read and write decimal numbers to the thousandths place using base ten numerals written in standard form and expanded form.
Models for decimal numbers
Expanded form
5.NR.4.1: Read and write decimal numbers to the thousandths place using base ten numerals written in standard form and expanded form.
Models for decimal numbers
Expanded form
5.NR.4.2: Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Compare decimal numbers
Order decimal numbers
5.NR.4.2: Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Compare decimal numbers
Order decimal numbers
5.NR.4.3: Use place value understanding to round decimal numbers to the hundredths place.
5.NR.4.3: Use place value understanding to round decimal numbers to the hundredths place.
5.NR.4.4: Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies.
Add decimals
Subtract decimals
Add and subtract decimals
Add and subtract money
5.NR.4.4: Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies.
Add decimals
Subtract decimals
Add and subtract decimals
Add and subtract money
5.NR.5 Write, interpret, and evaluate numerical expressions within authentic problems.
5.NR.5 Write, interpret, and evaluate numerical expressions within authentic problems.
5.NR.5.1: Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations.
Evaluate numerical expressions
Write numerical expressions
Interpret numerical expressions
5.NR.5.1: Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations.
Evaluate numerical expressions
Write numerical expressions
Interpret numerical expressions
PAR
Patterning & Algebraic Reasoning
Generating patterns, plotting ordered pairs in the first quadrant
5.PAR.6 Solve relevant problems by creating and analyzing numerical patterns using the given rule(s).
5.PAR.6 Solve relevant problems by creating and analyzing numerical patterns using the given rule(s).
5.PAR.6.1: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table.
5.PAR.6.1: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table.
5.PAR.6.2: Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane.
5.PAR.6.2: Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane.
MDR
Measurement & Data Reasoning
Measurements within the metric system, measurement conversions and time as a unit of measurement
5.MDR.7 Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions.
5.MDR.7 Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions.
5.MDR.7.1: Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time.
Customary units
Metric units
Multi-step word problems
5.MDR.7.1: Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time.
Customary units
Metric units
Multi-step word problems
5.MDR.7.2: Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
Bar graphs
Line plots
5.MDR.7.2: Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
Bar graphs
Line plots
5.MDR.7.3: Convert among units within the metric system and then apply these conversions to solve multistep, practical problems.
5.MDR.7.3: Convert among units within the metric system and then apply these conversions to solve multistep, practical problems.
5.MDR.7.4: Convert among units within relative sizes of measurement units within the customary measurement system.
5.MDR.7.4: Convert among units within relative sizes of measurement units within the customary measurement system.
GSR
Geometric & Spatial Reasoning
Properties of polygons and rectangular prisms, classify polygons
5.GSR.8 Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.
5.GSR.8 Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.
5.GSR.8.1: Classify, compare, and contrast polygons based on properties.
Polygons
Triangles
Quadrilaterals
5.GSR.8.1: Classify, compare, and contrast polygons based on properties.
Polygons
Triangles
Quadrilaterals
5.GSR.8.2: Determine, through exploration and investigation, that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category.
5.GSR.8.2: Determine, through exploration and investigation, that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category.
5.GSR.8.3: Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems.
5.GSR.8.3: Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems.
5.GSR.8.4: Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems.
5.GSR.8.4: Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems.