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### 4.NBT Number Sense and Operations in Base Ten

- 4.NBT.A Use place value understanding and properties of operations to perform multi-digit arithmetic with numbers up to one million.
- 4.NBT.A.1 Round multi-digit whole numbers to any place.
- 4.NBT.A.2 Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form.
- 4.NBT.A.3 Compare two multi-digit numbers using the symbols >, = or <, and justify the solution.
- 4.NBT.A.4 Understand that in a multi-digit whole number, a digit represents 10 times what it would represents in the place to its right.
- 4.NBT.A.5 Demonstrate fluency with addition and subtraction of whole numbers.
- 4.NBT.A.6 Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution.
- 4.NBT.A.7 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution.

### 4.NF Number Sense and Operations in Fractions

- 4.NF.A Extend understanding of fraction equivalence and ordering. (Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12 and 100.)
- 4.NF.A.1 Explain and/or illustrate why two fractions are equivalent.
- 4.NF.A.2 Recognize and generate equivalent fractions.
- 4.NF.A.3 Compare two fractions using the symbols >, = or <, and justify the solution.

- 4.NF.B Extend understanding of operations on whole numbers to fraction operations.
- 4.NF.B.4 Understand addition and subtraction of fractions as joining/composing and separating/decomposing parts referring to the same whole.
- 4.NF.B.5 Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification.
- 4.NF.B.6 Solve problems involving adding and subtracting fractions and mixed numbers with like denominators.
- 4.NF.B.7 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
- 4.NF.B.8 Solve problems involving multiplication of a fraction by a whole number.

- 4.NF.C Understand decimal notation for fractions, and compare decimal fractions. (Denominators of 10 or 100)
- 4.NF.C.9 Use decimal notation for fractions with denominators of 10 or 100.
- 4.NF.C.10 Understand that fractions and decimals are equivalent representations of the same quantity.
- 4.NF.C.11 Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form.
- 4.NF.C.12 Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution.

### 4.RA Relationships and Algebraic Thinking

- 4.RA.A Use the four operations with whole numbers to solve problems.
- 4.RA.A.1 Multiply or divide to solve problems involving a multiplicative comparison.
- 4.RA.A.2 Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer.
- 4.RA.A.3 Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution.

- 4.RA.B Work with factors and multiples.
- 4.RA.B.4 Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number.
- 4.RA.B.5 Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100.

- 4.RA.C Generate and analyze patterns.
- 4.RA.C.6 Generate a number pattern that follows a given rule.
- 4.RA.C.7 Use words or mathematical symbols to express a rule for a given pattern.

### 4.GM Geometry and Measurement

- 4.GM.A Classify 2-dimensional shapes by properties of their lines and angles.
- 4.GM.A.1 Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines.
- 4.GM.A.2 Classify two-dimensional shapes by their sides and/or angles.
- 4.GM.A.3 Construct lines of symmetry for a two-dimensional figure.

- 4.GM.B Understand the concepts of angle and measure angles.
- 4.GM.B.4 Identify and estimate angles and their measure.
- 4.GM.B.5 Draw and measure angles in whole-number degrees using a protractor.

- 4.GM.C Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
- 4.GM.C.6 Know relative sizes of measurement units within one system of units.
- 4.GM.C.6.a Convert measurements in a larger unit in terms of a smaller unit.

- 4.GM.C.7 Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money.
- 4.GM.C.8 Apply the area and perimeter formulas for rectangles to solve problems.

- 4.GM.C.6 Know relative sizes of measurement units within one system of units.

### 4.DS Data and Statistics

- 4.DS.A Represent and analyze data.
- 4.DS.A.1 Create a frequency table and/or line plot to display measurement data.
- 4.DS.A.2 Solve problems involving addition and subtraction by using information presented in a data display.
- 4.DS.A.3 Analyze the data in a frequency table, line plot, bar graph or picture graph.