4.OA Operations & Algebraic Thinking
4.OA.A Use the four operations with whole numbers to solve problems
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4.OA.A.1Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. -
4.OA.A.2Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. -
4.OA.A.3Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.
4.OA.B Gain familiarity with factors and multiples
4.NBT Number & Operations in Base Ten
4.NBT.A Generalize place value understanding for multi-digit whole numbers
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4.NBT.A.1Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. -
4.NBT.A.2Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place. -
4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.
4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic
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4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm. -
4.NBT.B.5Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. -
4.NBT.B.6Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
4.NF Number & Operations — Fractions
4.NF.A Extend understanding of fraction equivalence and ordering
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4.NF.A.1Explain why a fraction a/b is equivalent to a fraction (n×a)/(n×b) by using visual fraction models. Use this principle to recognize and generate equivalent fractions. -
4.NF.A.2Compare two fractions with different numerators and different denominators. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.
4.NF.B Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers
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4.NF.B.3Understand a fraction a/b with a > 1 as a sum of fractions 1/b. -
4.NF.B.3.AUnderstand addition and subtraction of fractions as joining and separating parts referring to the same whole. -
4.NF.B.3.BDecompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. -
4.NF.B.3.CAdd and subtract mixed numbers with like denominators. -
4.NF.B.3.DSolve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. -
4.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. -
4.NF.B.4.AUnderstand a fraction a/b as a multiple of 1/b. -
4.NF.B.4.BUnderstand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. -
4.NF.B.4.CSolve word problems involving multiplication of a fraction by a whole number.
4.NF.C Understand decimal notation for fractions, and compare decimal fractions
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4.NF.C.5Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. -
4.NF.C.6Use decimal notation for fractions with denominators 10 or 100. -
4.NF.C.7Compare two decimals to hundredths by reasoning about their size. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
4.MD Measurement & Data
4.MD.A Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
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4.MD.A.1Know relative sizes of measurement units within one system of units. Record measurement equivalents in a two-column table. -
4.MD.A.2Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals. -
4.MD.A.3Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
4.MD.B Represent and interpret data
4.MD.C Geometric measurement: understand concepts of angle and measure angles
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4.MD.C.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. -
4.MD.C.5.AAn angle is measured with reference to a circle with its center at the common endpoint of the rays. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. -
4.MD.C.5.BAn angle that turns through n one-degree angles is said to have an angle measure of n degrees. -
4.MD.C.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. -
4.MD.C.7Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles.
4.G Geometry
4.G.A Draw and identify lines and angles, and classify shapes by properties of their lines and angles
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4.G.A.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. -
4.G.A.2Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category. -
4.G.A.3Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.