MATHEMATICS BIG IDEAS
PDE Standards Aligned Systems
The base-ten number system is a way to organize, represent, and compare numbers using groups of ten and place value.
Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it.
The likelihood of an event occurring can be described numerically and used to make predictions.
Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
The same number sentence (e.g., 12 - 4 = 8) can be associated with different concrete or real world situations, AND different number sentences can be associated with the same concrete or real world situation.
Numerical quantities and calculations can be estimated by using numbers that are close to the actual values, but easier to compute.
Some attributes of objects are measurable, e.g., length, mass, capacity, and can be quantified.
Measures can be estimated by using known referents.
Patterns exhibit relationships that can be extended, described, and generalized.
Two- and three-dimensional objects can be described, classified, and analyzed by their attributes, and their location can be described quantitatively.
Spatial reasoning and visualization are ways to orient thinking about the physical world.
There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
Objects can be transformed in an infinite number of ways. Transformations can be described and analyzed mathematically.
Numerical measures describe the center and spread of numerical data.
Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
Two variable quantities are proportional if their values are in a constant ratio. The relationship between proportional quantities can be represented as a linear function.
Similarity relationships between objects are a form of proportional relationships. Congruence describes a special similarity relationship between objects and is a form of equivalence.
The set of real numbers has infinite subsets including the sets of whole numbers, integers, rational, and irrational numbers.
Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
Degree and direction of linear association between two variables is measurable.
Some geometric relationships can be described and explored as functional relationships.
Mathematical statements can be justified through deductive and inductive reasoning and proof.
