5.OA Operations & Algebraic Thinking
5.OA.A Write and interpret numerical expressions
5.NBT Number & Operations in Base Ten
5.NBT.A Understand the place value system
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5.NBT.A.1Recognize 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.A.2Explain 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. Use whole-number exponents to denote powers of 10. -
5.NBT.A.3Read, write, and compare decimals to thousandths. -
5.NBT.A.3.ARead and write decimals to thousandths using base-ten numerals, number names, and expanded form. -
5.NBT.A.3.BCompare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols. -
5.NBT.A.4Use place value understanding to round decimals to any place.
5.NBT.B Perform operations with multi-digit whole numbers and with decimals to hundredths
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5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm. -
5.NBT.B.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. -
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
5.NF Number & Operations — Fractions
5.NF.A Use equivalent fractions as a strategy to add and subtract fractions
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5.NF.A.1Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions. -
5.NF.A.2Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense to estimate and assess the reasonableness of answers.
5.NF.B Apply and extend previous understandings of multiplication and division to multiply and divide fractions
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5.NF.B.3Interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. -
5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. -
5.NF.B.4.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. -
5.NF.B.4.BFind the area of a rectangle with fractional side lengths by tiling it with unit squares. Show that the area is the same as would be found by multiplying the side lengths. -
5.NF.B.5Interpret multiplication as scaling (resizing). -
5.NF.B.5.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. -
5.NF.B.5.BExplain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number, and why multiplying by a fraction less than 1 results in a product smaller than the given number. -
5.NF.B.6Solve real-world problems involving multiplication of fractions and mixed numbers. -
5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. -
5.NF.B.7.AInterpret division of a unit fraction by a non-zero whole number, and compute such quotients. -
5.NF.B.7.BInterpret division of a whole number by a unit fraction, and compute such quotients. -
5.NF.B.7.CSolve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.
5.MD Measurement & Data
5.MD.A Convert like measurement units within a given measurement system
5.MD.B Represent and interpret data
5.MD.C Geometric measurement: understand concepts of volume
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5.MD.C.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement. -
5.MD.C.3.AA 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.C.3.BA 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.C.4Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. -
5.MD.C.5Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. -
5.MD.C.5.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. Represent threefold whole-number products as volumes. -
5.MD.C.5.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. -
5.MD.C.5.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.
5.G Geometry
5.G.A Graph points on the coordinate plane to solve real-world and mathematical problems
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5.G.A.1Use 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. -
5.G.A.2Represent 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.B Classify two-dimensional figures into categories based on their properties
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5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. -
5.G.B.4Classify two-dimensional figures in a hierarchy based on properties.