Parent Letter to Indtroduce the use of manipulatives and representations to learn multiplication and division concepts and facts
As you know we will begin working on multiplication and division facts next week.
Memorizing the facts for ones, then twos, then threes, etc, is the sequence in which past generations have been taught multiplication facts. We may know the answers, but do we know the ways the answer has been determined? Can we explain how we came to the answer or the relationships that the numbers have?
Memorization is often done without thinking with or about a relationship that when understood will assist in the memorization process and the longevity of what is memorized. Thinking should be the main focus of mathematics before attempting to be automatized. This is what we will strive for in our classroom; encouraging our students to think about the relationships between the numbers, not just producing answers. Manpulatives are one way this can be accomplished. Pictures, diagrams, mental images, that represent these kinds of relationships. For example, groups of familiar objects that are packaged or grouped in specific quantities (peanut butter cups, wheels on a car, packages of gum, six and 12 packs of pop, eggs, players from one team on the basketball court during a game, combinations of outfits that can be made with two different shirts and two different shorts, the number of pieces of glass in a window that has a three by three pattern, the number of cards each person has if ten cards are distributed to five people, the pieces of candy if two Snickers bars are each cut into three pieces...) these examples and many more can be the source for students to develop the understanding of the relationships between numbers. Using manipulatives, drawing diagrams, and viewing pictures allow students to use their senses in order to manipulate real objects physically and representations mentally to create their own visualization to understand patterns, problems, and solutions for multiplication and division. Physically exploring with manipulatives and creating mental representations of mathematical ideas is going to be a constant theme in our mathematics class this year; to know the why and the how to justify and have confidence in our solutions by using mathematical thinking.
If you have questions about what we will be doing or would like additional information please contact me before or after school in the classroom or the school phone: number is 555-5555,