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New York Standards

New York 5th Grade Math Standards

All 26 New York math standards for 5th grade, each explained in plain English. The official wording is one click away under each one.

26 standards

Operations and Algebraic Thinking

3 standards
Write and interpret numerical expressions.
NY-5.OA.1
Find the value of expressions by doing operations in the right order, like 3 + 4 × 2 = 11 because multiplying comes before adding.
Official wording
Apply the order of operations to evaluate numerical expressions.
NY-5.OA.2
Write simple expressions for calculations given in words, like double the sum of 8 and 7, and tell what an expression shows without working it out.
Official wording
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
Analyze patterns and relationships.
NY-5.OA.3
Make two number patterns from two rules, like add 3 and add 6, compare the matching terms, and graph the pairs on a coordinate plane.
Official wording
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.

Number and Operations in Base Ten

7 standards
Understand the place value system.
NY-5.NBT.1
Know that each place is worth ten times the place to its right and one tenth of the place to its left.
Official wording
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.
Common Core 5.NBT.1
NY-5.NBT.2
Use exponents for powers of 10, like 10³ = 1,000, and explain the patterns in zeros and decimal point moves when multiplying or dividing by them.
Official wording
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.
NY-5.NBT.3
Read and write decimals to thousandths, like 347.392, in words and expanded form, and compare two decimals digit by digit.
Official wording
Read, write, and compare decimals to thousandths.aRead and write decimals to thousandths using base-ten numerals, number names, and expanded form.bCompare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Common Core 5.NBT.3
NY-5.NBT.4
Round decimals to any place, like 3.467 to the nearest hundredth.
Official wording
Use place value understanding to round decimals to any place.
Common Core 5.NBT.4
Perform operations with multi-digit whole numbers and with decimals to hundredths.
NY-5.NBT.5
Multiply multi-digit whole numbers quickly and accurately using a standard written method, like 346 × 27.
Official wording
Fluently multiply multi-digit whole numbers using a standard algorithm.
NY-5.NBT.6
Divide up to four-digit numbers by two-digit numbers with place-value strategies, and show the thinking with equations, arrays or area models.
Official wording
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.
Common Core 5.NBT.6
NY-5.NBT.7
Add, subtract, multiply, and divide decimals to hundredths using models, drawings, and place value strategies, and explain how the written work matches.
Official wording
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.

Number and Operations—Fractions

7 standards
Use equivalent fractions as a strategy to add and subtract fractions.
NY-5.NF.1
Add and subtract fractions and mixed numbers with unlike denominators by first rewriting them with a common denominator, like 2/3 + 5/4 = 8/12 + 15/12.
Official wording
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.
NY-5.NF.2
Solve word problems that add or subtract fractions of the same whole, including unlike denominators, and use benchmarks like 1/2 to check that answers make sense.
Official wording
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.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
NY-5.NF.3
See a fraction as a division, like 3/4 = 3 ÷ 4, and solve sharing problems whose answers are fractions or mixed numbers, like 3 pizzas split among 4 people.
Official wording
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.
NY-5.NF.4
Multiply a fraction by a whole number or another fraction, like 2/3 × 4 = 8/3, and find areas of rectangles with fraction side lengths by tiling and by multiplying.
Official wording
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction.aInterpret 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.bFind 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.
NY-5.NF.5
Predict the size of a product without multiplying, like knowing 3/4 × 12 is less than 12 and 5/4 × 12 is more, and explain why.
Official wording
Interpret multiplication as scaling (resizing).aCompare 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.bExplain 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 = a/b × n/n to the effect of multiplying a/b by 1.
NY-5.NF.6
Solve real-world problems that multiply fractions and mixed numbers, like finding 2/3 of a 1 1/2-pound bag of nuts.
Official wording
Solve real world problems involving multiplication of fractions and mixed numbers.
NY-5.NF.7
Divide a unit fraction by a whole number, like 1/3 ÷ 4 = 1/12, or a whole number by a unit fraction, like 4 ÷ 1/5 = 20, and use this in real-world problems.
Official wording
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement until grade 6 (NY-6.NS.1).aInterpret division of a unit fraction by a non-zero whole number, and compute such quotients.bInterpret division of a whole number by a unit fraction, and compute such quotients.cSolve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.

Measurement and Data

5 standards
Convert like measurement units within a given measurement system.
NY-5.MD.1
Convert between units within one measurement system when the conversion is given, like 5 cm to 0.05 m, and use this in multistep real-world problems.
Official wording
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.
Represent and interpret data.
NY-5.MD.2
Make a line plot of measurements in halves, quarters, and eighths, and use fraction operations to answer questions about it, like sharing water equally among beakers.
Official wording
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.
NY-5.MD.3
Understand volume as the space inside a solid, measured by how many unit cubes fill it without gaps or overlaps.
Official wording
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.aRecognize 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.bRecognize 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.
Common Core 5.MD.3
NY-5.MD.4
Measure volume by counting unit cubes, in cubic centimeters, cubic inches, cubic feet or made-up units.
Official wording
Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units.
Common Core 5.MD.4
NY-5.MD.5
Find the volume of a box-shaped prism with the formulas V = l × w × h and V = b × h, and add up the volumes of two prisms joined together.
Official wording
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.aFind 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.bApply 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.cRecognize 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.
Common Core 5.MD.5

Geometry

4 standards
Graph points on the coordinate plane to solve real-world and mathematical problems.
NY-5.G.1
Explain how a coordinate plane works, with two perpendicular number lines meeting at the origin, and how an ordered pair tells how far to move along each axis.
Official wording
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.
NY-5.G.2
Graph real-world data as points in the first quadrant of a coordinate grid and explain what each point’s coordinates mean.
Official wording
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.
Common Core 5.G.2
Classify two-dimensional figures into categories based on their properties.
NY-5.G.3
Explain that features of a shape group belong to every smaller group within it, like all rectangles have four right angles, so all squares do too.
Official wording
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
NY-5.G.4
Sort two-dimensional shapes into a hierarchy by their properties, like quadrilaterals, then parallelograms, then rectangles, then squares.
Official wording
Classify two-dimensional figures in a hierarchy based on properties.
Common Core 5.G.4

The official New York documents

New York State Next Generation Mathematics Learning Standards, Copyright 2017, New York State Education Department, used with permission.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.