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Common Core for Mathematics

In Grade 4, instructional time should focus on three critical areas:

(1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends

(2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers

(3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

### Operations and Algebraic Thinking

### Number and Operations in Base Ten

### Number and Operations and Fractions

### Measurement and Data

### Geometry

Common Core for Mathematics

In Grade 4, instructional time should focus on three critical areas:

(1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends

(2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers

(3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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 word problems involving multiplicative comparison, e.g., by using 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 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.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.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.A.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.A.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 to record the results of comparisons. |

4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place. |

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. |

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.A.1 Explain why a fraction |

4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or 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. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |

4.NF.B.3, 4.NF.B.3a, 4.NF.B.3b Understand a fraction |

4.NF.B.3c C. Add and subtract mixed numbers with like denominators, e.g., 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.3d D. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. |

4.NF.B.4, 4.NF.B.4a, 4.NF.B.4b, 4.NF.B.4c Apply and extend previous understandings of
multiplication to multiply a fraction by a whole number. |

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 for fractions with denominators 10
or 100. |

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. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. |

4.MD.A.1 Know relative sizes of measurement units within one
system of units including km, m, cm; kg, g; lb, oz.; l,
ml; hr, min, sec. 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.A.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.A.3 Apply the area and perimeter formulas for rectangles in
real world and mathematical problems. |

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). Solve problems
involving addition and subtraction of fractions by using
information presented in line plots. |

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

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.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. |

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