Common Core State Standards for Mathematics Standards for Mathematical Practice [K-12]
Attend to precision. [K-12]
Measurement and Data [K - 5]
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. [3]
6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3]
5. Recognize area as an attribute of plane figures and understand concepts of area measurement. [3]
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]
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]
7. Relate area to the operations of multiplication and addition. [3]
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]
b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. [3]
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]
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. [3]
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. [3]
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. [3]
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. [4]
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. [4]
Geometric measurement: understand concepts of angle and measure angles. [4]
5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. [4] 6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. [4]
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. [4]
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. [5]
4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5]
3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. [5]
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]
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]
5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. [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]
b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. [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. [5]
Geometry [K - 8]
Reason with shapes and their attributes. [1 - 3]
1. 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 (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3]
2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. [3]
Draw and identify lines and angles, and classify shapes by properties of their lines and angles. [4]
1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. [4]
2. 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. [4]
3. 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. [4]
Graph points on the coordinate plane to solve real-world and mathematical problems. [5]
1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). [5]
2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5]
Classify two-dimensional figures into categories based on their properties. [5]
3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. [5]
4. Classify two-dimensional figures in a hierarchy based on properties. [5]
