This course focuses primarily on fraction concepts and operations. Area, set, and linear models are used to explore equivalence, ordering, and procedures for the basic arithmetic operations on fractions. Other topics include the decimal expansions of fractions; basic probability concepts; and integer concepts and operations. The course follows a problem-solving approach, in which participants learn to express solutions to problems in multiple ways: visually, algebraically, numerically, and verbally (the fourfold way). Prerequisite: Intermediate Algebra

FRACTION CONCEPTS: AREA MODELS (FCAM)
Participants use a fraction area model to explore part-whole replationships, equivalence, and operations. Participants examine, compare, and contrast some commonly used area models for fractions.

FRACTION CONCEPTS: LINEAR MODELS (FCLM)
Participants use fraction strips and a fraction array chart as linear models to further examine fraction concepts and operations. Participants use fraction sense-making strategies to locate fractions on a number line. Participants explore other linear models and compare their relative benefits and limitations.

LINKING FRACTION CONCEPTS TO DECIMALS AND PERCENTS (FCDP)
Participants use area, linear, and set models to explore fraction, decimal, and percent equivalence. Participants explore strategies for showing equivalent fractions.

GEOMETRIC PROBABILITY (PROB1)
Participants describe outcomes of probability experiments using lists, tree diagrams, and outcome grids. They gather data by random sampling, represent the data graphically, and observe the effect of sample size. Participants create circular spinners to match probabilities described in words and numbers.

INTEGER CONCEPTS (INTC)
Participants review the conventions for the order of operations. Participants explore integer concepts using realistic contexts, number lines, and a marker model.

INTEGER OPERATIONS (INTO)
Participants use an integer operations model that combines the markers model and temperature context to derive rules for integer operations. Participants observe patterns to support the integer operations rules.

RATIONAL NUMBER OPERATIONS: ADDITION AND SUBTRACTION (RNOAS)
Participants dissect the decimal addition and subtraction procedure to better understand why it works. Participants explore various strategies for additing and subtracting fractions, and discuss benefits and limitations of the strategies.

RATIONAL NUMBER OPERATIONS: MULTIPLICATION AND DIVISION (RNOMD)
Participants review the meaning of whole number multiplication and extend concepts to fraction multiplication. They multiply using an area model and connect it to a procedure. Participants write fraction division story problems, and develop skills in mapping the problems to pictures, numbers, and symbols. Participants explore meanings of partitive and measurement division.

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