4th Grade Mathematics

Students will analyze the relationship between adjacent place values, recognizing that a digit in one place represents ten times what it represents in the place to its right.

Students will read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Students will compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols.

Students will use place value understanding to round multi-digit whole numbers to any place.

Students will fluently add multi-digit whole numbers using the standard algorithm.

Students will fluently subtract multi-digit whole numbers using the standard algorithm.

Students will solve multi-step word problems involving addition and subtraction of whole numbers, assessing the reasonableness of answers.

Students will interpret multiplication equations as comparisons (e.g., 35 is 5 times as many as 7) and represent these comparisons.

Students will solve word problems involving multiplicative comparison using drawings and equations with a symbol for the unknown number.

Students will 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 properties of operations.

Students will 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.

Students will find all factor pairs for a whole number in the range 1-100 and determine whether a given whole number is prime or composite.

Students will generate a number or shape pattern that follows a given rule and identify apparent features of the pattern not explicit in the rule itself.

Students will explain why fractions are equivalent by using visual fraction models, paying attention to how the number and size of the parts differ even though the fractions themselves are the same size.

Students will compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction.

Students will understand addition and subtraction of fractions as joining and separating parts referring to the same whole, and decompose a fraction into a sum of fractions with the same denominator.

Students will add and subtract fractions with like denominators, including mixed numbers, by replacing mixed numbers with equivalent fractions, and/or by using properties of operations and the relationship between addition and subtraction.

Students will solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Students will apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Students will solve word problems involving multiplication of a fraction by a whole number.

Students will 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.

Students will use decimal notation for fractions with denominators 10 or 100.

Students will compare two decimals to hundredths by reasoning about their size and justify conclusions by using visual models or other strategies.

Students will draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

Students will recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

Students will measure angles in whole-number degrees using a protractor and sketch angles of specified measure.

Students will recognize angle measure as additive and solve addition and subtraction problems to find unknown angles on a diagram.

Students will 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.

Students will 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.

Students will identify line-symmetric figures and draw lines of symmetry.

Students will know relative sizes of measurement units within one system of units (e.g., km, m, cm; hr, min, sec).

Students will express measurements in a larger unit in terms of a smaller unit and record measurement equivalents in a two-column table.

Students will solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals.

Students will apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

Students will make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

Students will solve problems involving addition and subtraction of fractions by using information presented in line plots.