Grade 4

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Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as much as 5). Represent verbal/written statements of multiplicative comparisons as multiplication equations.4.OA.A.1

Multiply or divide to solve contextual problems involving multiplicative comparison, and distinguish multiplicative comparison from additive comparison4.OA.A.2

Solve multi-step contextual problems (posed with whole numbers and having whole-number answers using the four operations) including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity.4.OA.A.3

Find factor pairs for whole numbers in the range 1–100 using models. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is prime or composite and whether the given number is a multiple of a given one-digit number.4.OA.B.4

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.4.OA.C.5

Recognize that in a multi-digit whole number (less than or equal to 1,000,000), a digit in one place represents 10 times as much as it represents in the place to its right.4.NBT.A.1

Read and write multi-digit whole numbers (less than or equal to 1,000,000) using standard form, word form, and expanded notation (e.g. the expanded notation of 4256 is written as (4 x 1000) + (2 x 100) + (5 x 10) + (6 x 1)). Compare two multi-digit numbers based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship.4.NBT.A.2

Round multi-digit whole numbers to any place (up to and including the hundred-thousand place) using understanding of place value and use a number line to explain how the number was rounded.4.NBT.A.3

Fluently add and subtract within 1,000,000 using efficient strategies and algorithms.4.NBT.B.4

Multiply 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.4.NBT.B.5

Find 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.4.NBT.B.6

Explain why a fraction a/b is equivalent to a fraction (a x n)/(b x n) or (a ÷ n)/(b ÷ n) using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.4.NF.A.1

Compare two fractions with different numerators and different denominators by creating common denominators or common numerators or by comparing to a benchmark such as 0 or ½ or 1. Recognize that comparisons are valid only when the two fractions refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions.4.NF.A.2

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.4.NF.B.3

Apply and extend understanding of multiplication as repeated addition to multiply a whole number by a fraction.4.NF.B.4

Express 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.5

Read and write decimal notation for fractions with denominators 10 or 100. Locate these decimals on a number line.4.NF.C.6

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions.4.NF.C.7

Measure and estimate to determine relative sizes of measurement units within a single system of measurement involving length, liquid volume, and mass/weight of objects using customary and metric units.4.MD.A.1

Solve one- or two-step real-world problems involving whole number measurements (including length, liquid volume, mass/weight, time, and money) with all four operations within a single system of measurement. (Contexts need not include conversions.)4.MD.A.2

Know and apply the area and perimeter formulas for rectangles in real world and mathematical contexts.4.MD.A.3

Make a line plot to display a data set of measurements in fractions of the same unit (½ or ¼ or 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.4.MD.B.4

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint; and understand concepts of angle measurement.4.MD.C.5

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.4.MD.C.6

Recognize 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 on a diagram in real-world and mathematical problems. (e.g., by using an equation with a symbol for the unknown angle measure).4.MD.C.7

Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in two-dimensional figures.4.G.A.1

Classify 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. Classify triangles based on the measure of the angles as right, acute, or obtuse.4.G.A.2

Recognize and draw lines of symmetry for two-dimensional figures.4.G.A.3