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Operations & Algebraic Thinking
  • Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
  • 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.
  • Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
  • Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
  • Apply properties of operations as strategies to multiply and divide. Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.
  • Understand division as an unknown-factor problem.
  • Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.
  • Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.
  • Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
  • Use place value understanding to round whole numbers to the nearest 10 or 100.
  • Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
  • Understand a fraction 1/b as 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.
  • Understand a fraction as a number on the number line; represent fractions on a number line diagram.
  • Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
  • Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes.
  • Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
  • 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 scaled bar graphs.
  • 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.
  • Recognize area as an attribute of plane figures and understand concepts of area measurement.
  • Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
  • Relate area to the operations of multiplication and addition.
  • Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length.
  • Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category.
  • Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.