**You must be currently teaching students to successfully complete this course.**

Fractions can be abstract. This course endeavors to make them as concrete as possible. The level of difficulty ranges from simply cutting shapes into halves, fourths and eighths to build 3-dimensional models of mixed decimal fractions. Students will engage in a variety of explorations using manipulatives to discover fractional relationships.

Fractions can be very abstract and counterintuitive. The larger the denominator, the smaller the unit fraction? Imagine multiplying two numbers and the product is smaller than either factor! Divide two numbers and the quotient is larger than the dividend! Help! (Sounds like something out of Alice in Wonderland.)

This course endeavors to make fractions as concrete as possible. Children need to experience many “real world,” hands-on activities in order to develop a number sense for fractions. They need to divide things in half, measure liquids, weigh objects, play with toy clocks, etc.

The level of difficulty for the activities ranges from simply cutting paper shapes into halves, fourths, and eighths… to building three-dimensional models of mixed decimals using heavy grid paper, scissors, and scotch tape.

As often as possible the student activities are presented as independent learning centers, but can be easily taught as whole class activities. One drawback to whole class activities is the need for enough manipulatives. By working in a small group you only need enough manipulatives for five or six students at a time.

The course instructor is willing to work with you in modifying an activity to make it more appropriate to the needs of your students.

When children are taught abstract concepts without the conceptual development that comes from concrete interactions with manipulatives they often become confused. Confusion is the root of frustration and aversion. In this setting self-esteem takes a beating!

Working in small groups at learning centers has several important advantages that help ease the above problems:

- It allows more participation and involvement.
- Less manipulatives are needed.
- It develops independent skills.
- It encourages the interpersonal interactions of communication, sharing, teamwork, and responsibility.

This course is most appropriate for teachers of second grade through middle school, particularly those who enjoy using learning centers for small group instruction. Teachers who prefer large group instruction will be able to teach this course, but to be successful they will need enough manipulatives for the whole class.

This course may not be appropriate for teachers who prefer pencil, paper, and book-based activities.

“Teaching Elementary Mathematics – Fractions” is designed to give abstract concepts a concrete, experience-based context, in a small group setting that fosters mathematical reasoning. Even with the simplest explorations the students are treated as mathematicians, collecting data, comparing and evaluating the results.

Fractions can be very abstract. This course endeavors to make them as concrete as possible. The level of difficulty ranges from simply cutting shapes into halves, fourths, and eighths… to building three-dimensional models of mixed decimals using heavy grid paper and scotch tape. As often as possible the student activities are presented as independent learning centers, but can be easily taught as whole class activities.

The teacher will:

1. Collect/develop mathematical materials and manipulatives that engage students in interactive,

exploratory activities.

2. Model fraction concepts in a variety of presentations, in particular, simple unit fractions at the primary

levels, and equivalent common fractions and decimal fractions at the intermediate levels.

3. Provide opportunities for students to engage in open-ended problem-solving using scientific method:

Collecting data from an exploration, posting and evaluating the data, looking for patterns and organizing

the data in order to find missing solutions.

**Course Relation to CCS or other Professional Standards**

This course aligns to the standards for: 2010 K-12 California’s Common Core Content Standards for Mathematics. Following are examples of some of the standards that are related to the activities in this course.

**Grade Three** – Number and Operations: Fractions

2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3. b. Recognize and generate simple equivalent fractions.

**Grade Four** – Number and Operations: Fractions

3. c. Add and subtract mixed numbers with like denominators.

d. Solve word problems involving addition and subtraction of fractions.

**Grade Five** – Number and Operations: Fractions

1. Add and subtract fractions with unlike denominators.

7. Add, subtract, multiply… decimals to hundredths, using concrete models or drawings.