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 and some basic probability concepts. 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 (FRACT1A)
Participants investigate various area, linear, and set models used to develop fraction concepts. They examine how the models give meaning to parts and wholes, equivalence, ordering, and operations, and they compare the benefits and limitations of the models. Participants consider how children develop meaning and understanding of fractions through story problems.

FRACTION ADDITION AND SUBTRACTION (FRACT2)
Participants use linear models to explore equivalence, ordering, and procedures for addition and subtraction of fractions.

FRACTIONS AND DECIMALS (DEC)
Participants learn about terminating and repeating decimals. They explore strategies for converting between fraction and decimal notations. Participants play two games related to fractions and decimals, and they discuss the use of math games as a teaching strategy.

FRACTION MULTIPLICATION AND DIVISION CONCEPTS (FRACT3)
Participants learn how to build meaning for fraction concepts and operations through appropriate story situations. They examine some contexts for multiplication and division of fractions, they use the context to understand the inverse relationship between multiplication and division and to examine partitive (fair share) and quotative (measurement) division problems.

FRACTION MULTIPLICATION AND DIVISION PROCEDURES (FRACT4)
Participants use area, set, and linear models to understand and make sense of computational procedures for multiplication and division of fractions. The laws of arithmetic that facilitate the computational procedures are emphasized.

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.

DICE GAMES AND EXPECTATION (PROB2)
Participants gather data from two-dice experiments, and compare it to theoretical probabilities. They use the concept of mathematical expectation to make decisions. Participants use planning guides to plan a probability unit based on their textbook.

INTEGERS (INT)
Participants consider examples (temperature, height above sea level) where both positive and negative numbers are used in measurements. Participants examine a vector model and the charged particle model for the integers, and they see how integer operations are interpreted in each of these models. They also learn about absolute values.

THE TERMINATOR (TERM)
Participants make a chart to show decimal equivalents for fractions, and they use the chart to consolidate their understanding of terminating and repeating decimals. Participants discuss questions concerning rational and irrational numbers.

PROPORTIONS (PROP)
Participants analyze proportional relationships that arise from the linear model for fractions. They identify the equivalent fraction graphs as a “direct proportion,” and unit graphs as an “inverse proportion.” They then use unit pricing, unit conversions, proportions, and dimensional analysis as tools for comparison shopping. A discussion of confusing procedures associated with fractions and proportions is included.

CAHSEE (CAHSEE:NS)
Participants become familiar with the topics tested on the California High School Exit Exam (CAHSEE). They discuss several CAHSEE anchor problems and released items pertaining to number sense.

Number Line B (NLB)
Participants engage in a number line activity that provides practice for many important real number concepts. Participants discuss ways to incorporate the activities into their classroom teaching. This module uses periodic practice as an instructional technique.

Back to Course Descriptions