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Topic: Measurement and Data 

Common Core Mathematics 3-5

 Cluster  Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
  Grade 3
   3.MD.2.Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.[Excludes multiplicative comparison problems (problems involving notions of “times as much”; see Glossary, Table 2)]
 Cluster  Represent and interpret data.
  Grade 3
   3.MD.3.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. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
   3.MD.4.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— whole numbers, halves, or quarters.
 Cluster  Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
  Grade 3
   3.MD.5.Recognize area as an attribute of plane figures and understand concepts of area measurement.
   3.MD.5.a.A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
   3.MD.5.b.A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
   3.MD.6.Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
   3.MD.7.Relate area to the operations of multiplication and addition.
   3.MD.7.a.Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
   3.MD.7.b.Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
   3.MD.7.c.Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
   3.MD.7.d.Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
 Cluster  Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
  Grade 3
   3.MD.8.Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
 Cluster  Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
  Grade 4
   4.MD.1.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 twocolumn table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
   4.MD.2.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. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
   4.MD.3.Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
 Cluster  Represent and interpret data.
  Grade 4
   4.MD.4.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. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
 Cluster  Geometric measurement: understand concepts of angle and measure angles.
  Grade 4
   4.MD.6.Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
   4.MD.7.Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
 Cluster  Convert like measurement units within a given measurement system.
  Grade 5
   5.MD.1.Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
 Cluster  Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
  Grade 5
   5.MD.3.Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
   5.MD.3.a.A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
   5.MD.3.b.A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
   5.MD.4.Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
   5.MD.5.Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
   5.MD.5.a.Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
   5.MD.5.b.Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems.
   5.MD.5.c.Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.