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### 4.OA Operations and Algebraic Thinking

- 4.OA.A Use the four operations with whole numbers to solve problems.
- 4.OA.A.1 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 many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations.
- 4.OA.A.2 Multiply or divide to solve contextual problems involving multiplicative comparison, and distinguish multiplicative comparison from additive comparison.
- 4.OA.A.3 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. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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

- 4.OA.C Generate and analyze patterns.
- 4.OA.C.5 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.NBT Number and Operations in Base Ten

- 4.NBT.A Generalize place value understanding for multidigit whole numbers.
- 4.NBT.A.1 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.2 Read and write multi-digit whole numbers (less than or equal to 1,000,000) using standard form, word form, and expanded form (e.g. the expanded form of 4256 is written as 4 x 1000 + 2 x 100 + 5 x 10 + 6 x 1). Compare two multidigit numbers based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship.
- 4.NBT.A.3 Round multi-digit whole numbers to any place (up to and including the hundred-thousand place) using understanding of place value.

- 4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic.
- 4.NBT.B.4 Fluently add and subtract within 1,000,000 using appropriate strategies and algorithms.
- 4.NBT.B.5 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.6 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.NF Number and Operations – Fractions

- 4.NF.A Extend understanding of fraction equivalence and comparison.
- 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (a x n/(b x n) or (a ÷ n)/(b ÷ n) by 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.2 Compare two fractions with different numerators and different denominators by creating common denominators or common numerators or by comparing to a benchmark fraction such as 1/2. 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.B Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
- 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
- 4.NF.B.3.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- 4.NF.B.3.b Decompose a fraction into a sum of fractions with the same denominator in more than one way (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8), recording each decomposition by an equation. Justify decompositions by using a visual fraction model.
- 4.NF.B.3.c Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction.
- 4.NF.B.3.d Solve contextual problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

- 4.NF.B.4 Apply and extend previous understandings of multiplication as repeated addition to multiply a whole number by a fraction.
- 4.NF.B.4.a Understand a fraction a/b as a multiple of 1/b.
- 4.NF.B.4.b Understand a multiple of a/b as a multiple of 1/b and use this understanding to multiply a whole number by a fraction.
- 4.NF.B.4.c Solve contextual problems involving multiplication of a whole number by a fraction (e.g., by using visual fraction models and equations to represent the problem).

- 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
- 4.NF.C Understand decimal notation for fractions and compare decimal fractions.
- 4.NF.C.5 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.6 Read and write decimal notation for fractions with denominators 10 or 100. Locate these decimals on a number line.
- 4.NF.C.7 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.MD Measurement and Data

- 4.MD.A Estimate and solve problems involving measurement.
- 4.MD.A.1 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.2 Solve one- or two-step real-world problems involving whole number measurements with all four operations within a single system of measurement including problems involving simple fractions.
- 4.MD.A.3 Know and apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

- 4.MD.B Represent and interpret data.
- 4.MD.B.4 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.

- 4.MD.C Geometric measurement: understand concepts of angle and measure angles.
- 4.MD.C.5 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.a Understand that an angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle.
- 4.MD.C.5.b Understand that an angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. An angle that turns through n one-degree angles is said to have an angle measure of n degrees and represents a fractional portion of the circle.

- 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
- 4.MD.C.7 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.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

### 4.G Geometry

- 4.G.A Draw and identify lines and angles and classify shapes by properties of their lines and angles.
- 4.G.A.1 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.2 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. Recognize right triangles as a category and identify right triangles.
- 4.G.A.3 Recognize and draw lines of symmetry for two-dimensional figures.