New York State's Grade 4 mathematics standards are designed to build a strong foundation in essential mathematical concepts. This guide breaks down the key areas, providing a clear understanding of what fourth-grade students are expected to learn and master. We'll explore each standard in detail, offering insights for parents, educators, and students alike.
Key Areas of Focus in NY Grade 4 Math
The New York State P-12 Common Core Learning Standards for Mathematics in Grade 4 cover several crucial areas:
- Operations and Algebraic Thinking: This focuses on developing fluency with multi-digit multiplication and division, understanding factors and multiples, and generating and analyzing patterns.
- Number and Operations in Base Ten: This section emphasizes understanding place value, performing operations with multi-digit numbers, and using rounding to estimate.
- Number and Operations—Fractions: Students learn to extend their understanding of fractions to include equivalence, comparison, and addition/subtraction of fractions with like denominators.
- Measurement and Data: This involves measuring angles using protractors, converting measurement units, and representing and interpreting data using line plots.
- Geometry: Students explore geometric figures, classify shapes based on their properties, and understand lines and angles.
Detailed Breakdown of Grade 4 Math Standards
Let's delve into each domain more deeply, providing examples to illustrate the concepts:
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. Example: Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.
- 4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison. Example: If a dog weighs 3 times as much as a cat and the cat weighs 5 pounds, how much does the dog weigh?
- 4.OA.A.3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations. Example: A baker makes 24 cookies. He sells 1/3 of them. Then he makes 12 more. How many cookies does he have now?
- 4.OA.C: Generate and analyze patterns.
- 4.OA.C.5: Generate a number or shape pattern that follows a given rule. Example: Create a pattern that starts with 3 and adds 5 each time.
Number and Operations in Base Ten
4.NBT.A: Generalize place value understanding for multi-digit whole numbers.
- 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. Example: Understanding that the 2 in 250 represents 200 while the 2 in 25 represents 20.
- 4.NBT.A.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
- 4.NBT.A.3: Use place value understanding 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.
- 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.
- 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.
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 number and size of the parts differ even though the two fractions themselves are the same size.
- 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.
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 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 decompositions, e.g., by using a visual fraction model.
- 4.NF.B.3.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.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Measurement and Data
4.MD.A: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
- 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.
- 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.
- 4.MD.A.3: 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).
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.
This detailed breakdown provides a comprehensive overview of the New York State Grade 4 mathematics standards. Remember to consult the official New York State Education Department website for the most up-to-date and complete information. Further resources, such as practice worksheets and online learning platforms, can supplement this understanding and aid in mastering these important concepts.
