
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place its left.

Read and write decimals to thousandths using baseten numerals, number names and expanded form.

Compare two decimals to thousandths based on meanings of the digits in each place, using >,=, and < symbols to record the results of comparisons.

Fluently multiply multidigit whole numbers using the standard algorithm.

Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit 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.

Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (⅔) x 4 = 8/3, and create a story context for this equation. Do the same with (⅔) x (⅘) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. For example, create a story context for (⅓) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (⅓) ÷ 4 = 1/12 because (1/12) x 4 = ⅓.

Interpret division of whole number by a unit fraction and compute such quotients. For example, create a story context for 4 ÷ (⅕), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (⅕) = 20 because 20 x (⅕) = 4.

Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions.

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.