Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result `2/5` + `1/2` = `3/7`, by observing that `3/7` < `1/2`.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, `sf(2/3)` + `sf(5/4)` = `sf(8/12)` + `sf(15/12)` = `sf(23/12)`. In general, `a/b` + `c/d` = `((ad + bc))/(bd)`.
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and `sf (1/10)` of what it represents in the place to its left.
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.
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.
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Classify two-dimensional figures in a hierarchy based on properties.
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.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
