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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.2 Multiply or divide to solve word problems involving multiplicative comparison, by using strategies including, but not limited to, drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
- 4.OA.A.3 Solve multi-step word problems posed with whole numbers, including problems in which remainders must be interpreted.
- 4.OA.A.3A Represent these problems using equations with a letter standing for the unknown quantity.

- 4.OA.A.3B Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

- 4.OA.B Develop understanding of factors and multiples.
- 4.OA.B.4 Demonstrate an understanding of factors and multiples.
- 4.OA.B.4A Find all factor pairs for a whole number in the range 1-100.
- 4.OA.B.4B Recognize that a whole number is a multiple of each of its factors.

- 4.OA.B.4D Determine whether a given whole number in the range 1-100 is prime or composite.

- 4.OA.B.4C Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.

- 4.OA.B.4 Demonstrate an understanding of factors and multiples.
- 4.OA.C Generate and analyze patterns.
- 4.OA.C.5 Given a pattern, explain a rule that the pattern follows and extend the pattern. 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.D Generalize place value understanding for multi-digit whole numbers (limited to numbers less than or equal to 1,000,000).
- 4.NBT.D.1 Recognize 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.D.2 Read 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, using >, =, and < symbols.
- 4.NBT.D.3 Use place value understanding to round multi-digit whole numbers to any place.

- 4.NBT.E Use place value understanding and properties of operations to perform multi-digit arithmetic (limited to whole numbers less than or equal to 1,000,000).
- 4.NBT.E.4 Add and subtract multi-digit whole numbers using place value strategies including the standard algorithm.
- 4.NBT.E.5 Use strategies based on place value and the properties of multiplication to:
- 4.NBT.E.5A Multiply a whole number of up to four digits by a one-digit whole number.
- 4.NBT.E.5B Multiply a pair of two-digit numbers.
- 4.NBT.E.5C Use appropriate models to explain the calculation, such as by using equations, rectangular arrays, and/or area models.

- 4.NBT.E.6 Use strategies based on place value, the properties of multiplication, and/or the relationship between multiplication and division to find quotients and remainders with up to four-digit dividends and one-digit divisors. Use appropriate models to explain the calculation, such as by using equations, rectangular arrays, and/or area models.

### 4.NF Number and Operations-Fractions

- 4.NF.F Extend understanding of fraction equivalence and ordering (limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100).
- 4.NF.F.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 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.F.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 1/2.
- 4.NF.F.2A Recognize that comparisons are valid only when the two fractions refer to the same whole.
- 4.NF.F.2B Record the results of comparisons with symbols >, =, or <.
- 4.NF.F.2C Justify the conclusions by using a visual fraction model.

- 4.NF.F.1 Explain why a fraction
- 4.NF.G Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100).
- 4.NF.G.3 Understand a fraction
*a*/b with*a*> 1 as a sum of unit fractions (1/b).- 4.NF.G.3A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- 4.NF.G.3B Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions by using a visual fraction model.
- 4.NF.G.3C Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction, and/or by using properties of addition and the relationship between addition and subtraction.
- 4.NF.G.3D Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

- 4.NF.G.4 Apply and extend an understanding of multiplication by multiplying a whole number and a fraction.
- 4.NF.G.4A Understand a fraction
*a*/b as a multiple of 1/b. - 4.NF.G.4B 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.G.4C Solve real-world problems involving multiplication of a fraction by a whole number, using visual fraction models and equations to represent the problem.

- 4.NF.G.4A Understand a fraction

- 4.NF.G.3 Understand a fraction
- 4.NF.H Understand decimal notation for fractions, and compare decimal fractions.
- 4.NF.H.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.H.6 Use decimal notation for fractions with denominators 10 or 100.
- 4.NF.H.7 Compare and order decimal numbers to hundredths and justify by using concrete and visual models. Record the results of comparisons with the words “is greater than,” “is equal to,” “is less than,” and with the symbols >, =, and <.

### 4.MD Measurement and Data

- 4.MD.I Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
- 4.MD.I.1 Know relative sizes of measurement units within one system of units including, but not limited to, km, m, cm; kg, g; lb, oz.; l L, ml; hr, min, sec; ft, in., gal., qt. pt., c.. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
- 4.MD.I.2 Use 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, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
- 4.MD.I.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

- 4.MD.J Represent and interpret data.
- 4.MD.J.4 Make a line plot to display a data 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.

- 4.MD.K Geometric measurement: understand concepts of angle and measure angles.
- 4.MD.K.5 Regarding angles:
- 4.MD.K.5A Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint.
- 4.MD.K.5B Understand concepts of angle measurement. An angle is measured with reference to a circle with its center at the common endpoint of the rays.

- 4.MD.K.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
- 4.MD.K.7 Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

- 4.MD.K.5 Regarding angles:

### 4.G Geometry

- 4.G.L Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
- 4.G.L.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
- 4.G.L.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.L.3 Identify line-symmetric figures. Recognize and draw lines of symmetry for two-dimensional figures.