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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., 35 = 5 × 7, as 35 is 5 times as many as 7. Represent verbal multiplicative comparisons as equations.
- 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison.
- 4.OA.A.3 Solve multi-step whole-number word problems using the four operations, including problems in which remainders must be interpreted.
- 4.OA.A.3.a Represent these problems using equations with a letter standing for the unknown quantity.
- 4.OA.A.3.b 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.
- 4.OA.B.4.a Recognize that a whole number is a multiple of each of its factors.
- 4.OA.B.4.b Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.
- 4.OA.B.4.c Determine whether a given whole number in the range 1–100 is prime or composite.

- 4.OA.B.4 Find all factor pairs for a whole number in the range 1–100.
- 4.OA.C Generate and analyze patterns.
- 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify and explain 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 multi-digit whole numbers, less than or equal to 1,000,000.
- 4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in any place represents ten times as much as it represents in the place to its right.
- 4.NBT.A.2 Read and write multi-digit whole numbers using standard form, expanded form, and word form. Compare two multi-digit numbers based on meanings of the digits and each place, recording the results of comparisons with the symbols >, =, and <.
- 4.NBT.A.3 Use place value understanding or visual representation 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 on whole numbers less than or equal to 1,000,000.
- 4.NBT.B.4 Fluently use the standard algorithm for multi-digit whole-number addition and subtraction.
- 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.
- 4.NBT.B.5.a Use strategies based on place value and the properties of operations.
- 4.NBT.B.5.b 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.
- 4.NBT.B.6.a Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
- 4.NBT.B.6.b Illustrate and explain the calculation by using rectangular arrays, area models, and/or equations.

### 4.NF Number and Operations – Fractions

- 4.NF.A Extend understanding of fraction equivalence and ordering.
- 4.NF.A.1 Explain why a fraction
^{a}/_{b}is equivalent to a fraction^{n×a}/_{n×b}by using visual fraction models, with attention to how the numbers and sizes of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions, including fractions greater than 1. - 4.NF.A.2 Compare two fractions with different numerators and different denominators, by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½.
- 4.NF.A.2.a Recognize that comparisons are valid only when the two fractions refer to the same whole.
- 4.NF.A.2.b Record the results of comparisons with symbols >, =, or <, and justify the conclusions, by using a visual fraction model and/or verbal reasoning.

- 4.NF.A.1 Explain why a fraction
- 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, recording each decomposition by an equation. Justify the conclusions by using a visual fraction model and/or verbal reasoning.
- 4.NF.B.3.c Add and subtract mixed numbers with like denominators by replacing the 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 word problems involving addition and subtraction of fractions, including mixed numbers, with the same denominator. Justify the conclusions using a visual fraction model and/or verbal reasoning.

- 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
- 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 fraction by a whole number. - 4.NF.B.4.c Solve word problems involving multiplication of a fraction by a whole number e.g., by using visual fraction models and/or equations to represent the problem.

- 4.NF.B.4.a Understand a fraction

- 4.NF.B.3 Understand a fraction
- 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 Use decimal notation to represent fractions with denominators 10 or 100.
- 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size.
- 4.NF.C.7.a Recognize that comparisons are valid only when the two decimals refer to the same whole.
- 4.NF.C.7.b Record the results of the comparisons with the symbols >, =, and <, and justify the conclusions using visual representations and/or verbal reasoning.

### 4.MD Measurement and Data

- 4.MD.A Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
- 4.MD.A.1 Know relative sizes of measurement units within any one system of units.
- 4.MD.A.1.a Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.
- 4.MD.A.1.b Record measurement equivalents in a two-column table.

- 4.MD.A.2 Use the four operations to solve word problems involving measurements.
- 4.MD.A.2.a Include problems involving simple fractions or decimals.
- 4.MD.A.2.b Include problems that require expressing measurements given in a larger unit in terms of a smaller unit.
- 4.MD.A.2.c Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

- 4.MD.A.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

- 4.MD.A.1 Know relative sizes of measurement units within any one system of units.
- 4.MD.B Represent and interpret data.
- 4.MD.B.4 Make a line plot (dot plot) to show a set of measurements in fractions of a unit (
^{1}/_{2},^{1}/_{4},^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots (dot plots).

- 4.MD.B.4 Make a line plot (dot plot) to show a set of measurements in fractions of a unit (
- 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 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 An angle that turns through
*n*one-degree angles is said to have an angle measure of*n*degrees.

- 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
- 4.MD.C.7 Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems.
- 4.MD.C.7.a Use an equation with a symbol for the unknown angle measure.
- 4.MD.C.7.b 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.

- 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), 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 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.