Next Generation Learning Standards: Grade 5
Skills available for New York fifth-grade math standards
Domain
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5.OA
Operations and Algebraic Thinking
Write and interpret numerical expressions.
5.OA.1 Apply the order of operations to evaluate numerical expressions.
5.OA.1 Apply the order of operations to evaluate numerical expressions.
5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
Analyze patterns and relationships.
5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
5.NBT
Number and Operations in Base Ten
Understand the place value system.
5.NBT.1 Recognize 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.NBT.1 Recognize 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.NBT.2 Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
Exponents and powers of ten
Multiply by powers of ten
Divide by powers of ten
Multiply and divide by powers of ten
5.NBT.2 Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
Exponents and powers of ten
Multiply by powers of ten
Divide by powers of ten
Multiply and divide by powers of ten
5.NBT.3 Read, write, and compare decimals to thousandths.
5.NBT.3 Read, write, and compare decimals to thousandths.
5.NBT.3a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
Base-ten numerals
Number names
Expanded form
5.NBT.3a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
Base-ten numerals
Number names
Expanded form
5.NBT.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
5.NBT.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
5.NBT.4 Use place value understanding to round decimals to any place.
5.NBT.4 Use place value understanding to round decimals to any place.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.5 Fluently multiply multi-digit whole numbers using a standard algorithm.
Multiply by 2-digit numbers
Multiply by 3-digit numbers
5.NBT.5 Fluently multiply multi-digit whole numbers using a standard algorithm.
Multiply by 2-digit numbers
Multiply by 3-digit numbers
5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
2-digit and 3-digit dividends
4-digit dividends
Strategies
5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
2-digit and 3-digit dividends
4-digit dividends
Strategies
5.NBT.7 Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations: add and subtract decimals to hundredths; multiply and divide decimals to hundredths. Relate the strategy to a written method and explain the reasoning used.
Add and subtract
Multiply decimals and whole numbers
Multiply two decimals
Divide
Mixed operations
5.NBT.7 Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations: add and subtract decimals to hundredths; multiply and divide decimals to hundredths. Relate the strategy to a written method and explain the reasoning used.
Add and subtract
Multiply decimals and whole numbers
Multiply two decimals
Divide
Mixed operations
5.NF
Number and Operations—Fractions
Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Add fractions
Subtract fractions
Add and subtract mixed numbers
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Add fractions
Subtract fractions
Add and subtract mixed numbers
5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
Like denominators
Unlike denominators
5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
Like denominators
Unlike denominators
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.4a: Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.
Multiply fractions by whole numbers
Multiply two fractions
Multiply mixed numbers
5.NF.4a: Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.
Multiply fractions by whole numbers
Multiply two fractions
Multiply mixed numbers
5.NF.4b: Find the area of a rectangle with fractional side lengths by tiling it with rectangles of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Multiply fractions with models
Area and perimeter
5.NF.4b: Find the area of a rectangle with fractional side lengths by tiling it with rectangles of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Multiply fractions with models
Area and perimeter
5.NF.5 Interpret multiplication as scaling (resizing).
5.NF.5 Interpret multiplication as scaling (resizing).
5.NF.5a: Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.5a: Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.5b: Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case). Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
5.NF.5b: Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case). Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers.
Fractions
Mixed numbers
5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers.
Fractions
Mixed numbers
5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
5.NF.7a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
5.NF.7a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
5.NF.7b: Interpret division of a whole number by a unit fraction, and compute such quotients.
5.NF.7b: Interpret division of a whole number by a unit fraction, and compute such quotients.
5.NF.7c: Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.
5.NF.7c: Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.
5.MD
Measurement and Data
Convert like measurement units within a given measurement system.
5.MD.1 Convert among different-sized standard measurement units within a given measurement system when the conversion factor is given. Use these conversions in solving multi-step, real world problems.
Customary units
Metric units
Multi-step word problems
5.MD.1 Convert among different-sized standard measurement units within a given measurement system when the conversion factor is given. Use these conversions in solving multi-step, real world problems.
Customary units
Metric units
Multi-step word problems
Represent and interpret data.
5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
5.MD.3a: Recognize that a cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.
5.MD.3a: Recognize that a cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.
5.MD.3b: Recognize that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.3b: Recognize that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units.
5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units.
5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
5.MD.5a: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.
5.MD.5a: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.
5.MD.5b: Apply the formulas V =l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
5.MD.5b: Apply the formulas V =l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
5.MD.5c: Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
5.MD.5c: Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
5.G
Geometry
Graph points on the coordinate plane to solve real-world and mathematical problems.
5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond.
5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond.
5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
Classify two-dimensional figures into categories based on their properties.
5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
Attributes of quadrilaterals
Types of quadrilaterals
Quadrilateral relationships
5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
Attributes of quadrilaterals
Types of quadrilaterals
Quadrilateral relationships
5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
Polygons
Triangles
Quadrilaterals
5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
Polygons
Triangles
Quadrilaterals