In math recently we have been studying multiplication and division. We have been trying to learn our basic facts all year, through listening to Mr. Demaio's songs on Youtube, or by learning the "tricks" to help us remember our basic facts.
Although learning the basic facts is very important, it is also extremely important for students to understand what multiplication and division actually mean - i.e. adding or subtracting equal groups/amounts repeatedly.
In our program, we begin learning about multiplication as adding equal groups. We practice drawing both equal groups of objects as well as arrays to represent multiplication equations. Our first lesson is summarized in this link:
Our next lesson focused on using number lines to demonstrate repeated addition. Students were urged to recognize that the "hops" on the number line had to be equal in size, and we had to count the number of hops to find our solution. Here is a summary of the lesson:
After these two lessons, we began learning about division. This was actually a little easier for students to understand because they had developed a good understanding of equal groups from the multiplication lessons. We try to emphasize that in division, we are beginning with a large group and then sharing those items among groups equally. We also introduced the idea of remainder as the amount "left over" if we can't make another equal group. Here is the summary for our first division lesson:
Finally, we looked at division from the perspective of sharing out equal amounts, so we could determine how many groups we would end up with. This is the reciprocal property of multiplication and division - the order doesn't matter. For example, I can multiply 3 x 4 = 12 OR 4 x 3 = 12. Also, I can divide 12 / 3 = 4 OR 12 / 4 = 3. Here is the summary of the lesson:
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