Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
Identify and name triangles based on angle size (right, obtuse, acute).
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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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. Use this principle to recognize and generate equivalent fractions.
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
Identify and name all quadrilaterals with 2 pairs of parallel sides as parallelograms.
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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Use drawings and equations with a symbol for the unknown number to represent the problem.
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.
Recognize an angle that turns through n one-degree angles is said to have an angle measure of n degrees.
Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Identify and name all quadrilaterals with four right angles as rectangles.
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a whole number by a fraction.
Understand a fraction a/b as a multiple of 1/b.
Add and subtract mixed numbers with like denominators.
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
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.
Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
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