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Operations & Algebraic Thinking
  • Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
  • Multiply or divide to solve word problems involving multiplicative comparison, by using drawings and equations with a symbol for the unknown number to represent the problem
  • Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.
  • 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.
  • 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.
  • 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.
  • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers using symbols to record the results of comparisons.
  • Use place value understanding to round multi-digit whole numbers to any place.
  • Fluently add and subtract multi-digit whole numbers using the standard algorithm.
  • Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers
  • 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,
  • 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.
  • 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.
  • 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.
  • Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
  • 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.
  • Use decimal notation for fractions with denominators 10 or 100.
  • Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole.
  • Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
  • 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.
  • Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
  • 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.
  • An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
  • Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
  • Recognize angle measure as additive. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.
  • Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
  • 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.
  • 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.