**If you are not currently teaching students, there is a non-teaching format for this course. Please contact the instructor, Ron Kremer rkremer@dominicancaonline.com for details.**

* “Multiplication”* gives greater meaning to multiplication concepts through interactive activities that the teacher may use with their whole class or in learning centers with small groups. The activities are consistent with common core standards and can easily be adapted to the needs of all students. (Most of the activities have extensions or modifications that allow the teacher to “tailor” the materials to the needs of their students.)

The course is structured so that the teacher can choose the assignments they want to accomplish depending on the number of units (1, 2, or 3) they are taking, or select the assignments most appropriate for the students they are teaching. **1 Credit/Unit **(staff training component, 4 student activities 1 extension, 1 reflection) **2 Credits/Units **(staff training component, 7 student activities 3 extensions, 2 reflections) **3 Credits/Units **(staff training component, 10 student activities 5 extensions, 4 reflections)

## From the Instructor

Leaving third grade without memorizing the “times tables” is like going skydiving without a parachute! The fall doesn’t kill you… it’s the sudden stop at the end that’s the problem. Students may “fall” through several grades without too much trouble, until they reach fifth or sixth grade. Suddenly things become overwhelming! For example, one-fifth grade common core standard states:

Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths. Or for something simpler; estimate trial quotients while solving a long division problem with a two-digit divisor.

By the sixth grade many students still do not have “number fluency.”

This is an interactive, hands-on, experience-based course for teaching multiplication concepts. There are a variety of activities that introduce or reinforce multiplication skills in a range of levels of difficulty, from kindergarten through middle school.

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

Most of the activities have extensions or modifications that allow the teacher to “tailor” the content to the needs of their students. If there is an activity you wish to use, but it is at a level of difficulty not appropriate for your students the instructor will be pleased to help you modify that activity so that it is appropriate.

By repeated exposure in many different settings students will gradually become familiar with the basic multiplication facts as well as more complex concepts.

- It is almost “taboo” for teachers to give timed tests to see if their students have memorized the multiplication facts. In this course there are a number of recreational opportunities where, in the process of playing a game, the students will shorten their response time.
- There are a number of activities where students will create visual models of multiplication facts. For example: arrays or matrices showing rows of candy, or illustrations of repeated additions (like a group of ladybugs on a leaf, all of them with the same number of spots). Building three-dimensional models of rectangular prisms and finding their volumes will give students concrete experience in multiplying three factors.
- There are several opportunities for students to apply multiplication concepts to real world situations. For example: Doing research on dinosaurs and writing two-step word problems for their classmates to solve.

This course is most appropriate for teachers of second grade through middle school, particularly those who know the importance of experience-based learning in small groups. Teachers who prefer large group instruction will be able to successfully teach this course with sufficient manipulatives.

This course may not be appropriate for teachers who prefer traditional instructional methods.

Turn student frustration and avoidance into self-assurance and mastery with this collection of explorations, games, and puzzles that provide a concrete context for multiplication concepts.

## Course Overview

“Multiplication” gives greater meaning to multiplication concepts through interactive activities that the teacher may use with their whole class or in learning centers with small groups. Most of the activities have extensions or modifications that allow the teacher to “tailor” the materials to the needs of their students. This is a handson, experience-based course for teaching multiplication concepts.

## Course Objectives:

The teacher will:

- Develop engaging student mathematical materials.
- Prepare/construct interactive activities that can be used in learning centers or with the whole class.
- Model multiplication concepts in a variety of presentations, in particular using equal additions, arrays, and factor trees.

## Course Relation to CCS or other Professional Standards

This course aligns to the standards for: K-12 California’s Common Core Content Standards for Mathematics:

**Grade two –** Operations and Algebraic Thinking

5. Use repeated addition and counting by multiples to demonstrate multiplication.

**Grade Three** – Operations and Algebraic Thinking

7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

**Geometric Measurement**

7. Relate area to the operations of multiplication and addition.

**Grade Four** – Operations and Algebraic Thinking

4. Find all factor pairs for a whole number in the range 1-100.

**Grade Five** – Operations and Algebraic Thinking

2.1 Express a whole number in the range 2-50 as a product of its prime factors. For example, find the prime factors of 24 and express 24 as 2x2x2x3.

**Measurement and Data**

5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths…

## Instructor

### Ron Kremer

B.A., M.A. in Elementary Education, Elementary mathematics and science emphasis40 years: General elementary grade teacher, school district staff trainer, and staff developer for California Science Implementation Network. Author and guest speaker at state level conferences for mathematics. Recognized for exemplary work in the field of education by the Johns Hopkins Institute for the Academic Advancement of Youth. My goal is to convince teachers of the importance of "discovery learning" using open-ended, hands-on explorations. I like working on projects around the home with my family. I sing tenor in our church choir and volunteer tutor at Shriners Children's Hospital."