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. |