Bridge Math

Bridge Math is a course intended to build upon concepts taught in previous courses to allow students to gain a deeper knowledge of the real and complex number systems as well as the structure, use, and application of equations, expressions, and functions. Functions emphasized include linear, quadratic and polynomial. Students continue mastery of geometric concepts such as similarity, congruence, right triangles, and circles. Students use categorical and quantitative data to model real life situations and rules of probability to compute probabilities of compound events.

Bridge Math includes the following domains and clusters:

· The Real Number System
o Usepropertiesofrationalandirrationalnumbers.
· Quantities
o Reasonquantitativelyanduseunitstosolveproblems.
· The Complex Number System
o Performarithmeticoperationswithcomplexnumbers.
· Seeing Structure in Expressions
o Writeexpressionsinequivalentformstosolveproblems.
· Arithmetic with Polynomials and Rational Expressions
o Performarithmeticoperationsonpolynomials.
o Understandtherelationshipbetweenzerosandfactorsofpolynomials.
· Creating Equations

o Create equations that describe numbers orrelationships.

Reasoning with Equations and Inequalities
o Understandsolvingequationsasaprocessofreasoningandexplainthereasoning. o Solveequationsandinequalitiesinonevariable.
o Solvesystemsofequations.
o Represent and solve equations and inequalities graphically.

· Interpreting Functions
o Understandtheconceptofafunctionandusefunctionnotation.
o Interpretfunctionsthatariseinapplicationsintermsofthecontext. o Analyzefunctionsusingdifferentrepresentations
· Similarity, Right Triangles, and Trigonometry
o Understandsimilarityintermsofsimilaritytransformations.
o Definetrigonometricratiosandsolveproblemsinvolvingrighttriangles.
· Circles
o Findarclengthsandareasofsectorsofcircles.
· Geometric Measurement and Dimension

o Visualize relationships between two-dimensional and three-dimensionalobjects.

· Modeling with Geometry
o Applygeometricconceptsinmodelingsituations.
· Interpreting Categorical and Quantitative Data
o Summarize,represent,andinterpretdataonasinglecountormeasurementvariable. o Summarize,represent,andinterpretdataontwocategoricalandquantitativevariables. o Interpretlinearmodels.
· Conditional probability and the Rules of Probability

o Usetherulesofprobabilitytocomputeprobabilitiesofcompoundeventsinauniformprobability model.

Mathematical Modeling

Mathematical Modeling is a Standard for Mathematical Practice (MP4) and a Conceptual Category. Specific modeling standards appear throughout the high school standards indicated with a

star (★). Where an entire domain is marked with a star, each standard in that domain is a modeling standard.

Standards for Mathematical Practice

Being successful in mathematics requires the development of approaches, practices, and habits of mind that need to be in place as one strives to develop mathematical fluency, procedural skills, and conceptual understanding. The Standards for Mathematical Practice are meant to address these areas of expertise that teachers should seek to develop in their students. These approaches, practices, and habits of mind can be summarized as “processes and proficiencies” that successful mathematicians have as a part of their work in mathematics. Additional explanations are included in the main introduction of these standards.

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.