NY Math Standards (3)

Recognize and classify polygons based on the number of sides and vertices (triangles, quadrilaterals, pentagons, and hexagons). Identify shapes that do not belong to one of the given subcategories. Note: Include both regular and irregular polygons, however, students need not use formal terms “regular” and “irregular.”

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. e.g., Partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Tell and write time to the nearest minute and measure time intervals in minutes. Solve one-step word problems involving addition and subtraction of time intervals in minutes. e.g., representing the problem on a number line or other visual model. Note: This includes one-step problems that cross into a new hour.

Measure and estimate liquid volumes and masses of objects using grams (g), kilograms (kg), and liters (l). Note: Does not include compound units such as cm3 and finding the geometric volume of a container.

Add, subtract, multiply, or divide to solve one-step word problems involving masses or liquid volumes that are given in the same units. Note: Does not include multiplicative comparison problems involving notions of “times as much.” e.g., using drawings (such as a beaker with a measurement scale) to represent the problem

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in a scaled picture graph or a scaled bar graph. e.g., Draw a bar graph in which each square in the bar graph might represent 5 pets.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

Recognize a square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

Recognize a plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Measure areas by counting unit squares. Note: Unit squares include square cm, square m, square in., square ft., and improvised units.

Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

Use tiling to show in a concrete case that the area of a rectangle with whole-number side length a and side length b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

Recognize area as additive. Find areas of figures composed of non-overlapping rectangles, and apply this technique to solve real world problems. Note: Problems include no more than one unknown side length.

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths or finding one unknown side length given the perimeter and other side lengths.

Identify rectangles with the same perimeter and different areas or with the same area and different perimeters.

Understand a unit fraction, 1/b, is the quantity formed by 1 part when a whole is partitioned into b equal parts. Understand a fraction a/b as the quantity formed by a parts of size 1/b. Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.

Represent a fraction 1/b on a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part starting at 0 locates the number 1/b on the number line.

Represent a fraction a/b on a number line by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Recognize and generate equivalent fractions. e.g., 1/2 = 2/4; 4/6 = 2/3. Explain why the fractions are equivalent, e.g., using a visual fraction model.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. e.g., Express 3 in the form 3 = 3/1, recognize that 6/3 = 2, and locate 4/4 and 1 at the same point on a number line.

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions. e.g., using a visual fraction model. Note: Without specifying the whole, the shaded area could represent the fraction 3/2 (if one square is the whole) or 3/4 (if the entire rectangle is the whole).

Use place value understanding to round whole numbers to the nearest 10 or 100.

Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Note: A range of algorithms may be used.

Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations. e.g., 9 × 80, 5 × 60

Understand that the digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones. e.g., 3,245 equals 3 thousands, 2 hundreds, 4 tens, and 5 ones.

Read and write four-digit numbers using base-ten numerals, number names, and expanded form. e.g., The number 3,245 in expanded form can be written as 3,245 = 3,000 + 200 + 40 + 5.

Interpret products of whole numbers. e.g., Interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. Describe a context in which a total number of objects can be expressed as 5 × 7.

Interpret whole-number quotients of whole numbers. e.g., Interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. e.g., using drawings and equations with a symbol for the unknown number to represent the problem

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. e.g., Determine the unknown number that makes the equation true in each of the equations: 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?

Apply properties of operations as strategies to multiply and divide. Note: Students need not use formal terms for these properties. e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication). 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30 (Associative property of multiplication). Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56 (Distributive property).

Understand division as an unknown-factor problem. e.g., Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Fluently solve single-digit multiplication and related divisions, using strategies such as the relationship between multiplication and division or properties of operations.

Know from memory all products of two one-digit numbers. e.g., Knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8.

Represent two-step word problems posed with whole numbers and having whole-number answers using the four operations, using equations or expressions with a letter standing for the unknown quantity. Note: Two-step problems need not be represented by a single expression or equation.

Assess the reasonableness of answers to two-step word problems using mental computation and estimation strategies including rounding.

Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table).