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Teaching Multiplication & Division Facts Together

Using Schema vs. Rote Memorization

“A schema is composed of organized personal background knowledge, and it acts as a filing system that has been set up to organize past experiences and interpret future experiences...Think of this background information as a hook on which to hang new information or a file folder into which new information can be integrated.” *

* Quote from How to Teach Balanced Reading and Writing, Bonnie Burns, 2006.

Connect to Division

7X6=42: Many students may know that beetles are insects and that insects have six legs. For students lacking that prior knowledge, background information is provided (see screenshots above) in the Lesson 6 videos. Another familiar schema used in the “7 Beetles” Chant is with patterns of sound. Rhythm and rhyme aid recall and allow students to remember this chant with little effort. Learning this simple rhyme provides the needed background knowledge into which the introduced facts, 7X6 and 6X7, are applied. Some students need only hear “7 beetles, 6 legs, walking to the zoo...” a few times to permanently store these factors (6 and 7) with the product of 42.

3X4=12 and 7X8=56: The schema used here is counting. Consecutively saying “1,2,3,4” comes naturally to most students, as does “5,6,7,8.” Presenting the multiplication facts 3X4 and 7X8 using this existing schema assists the learner in applying meaning to these facts, allowing for easier recall. Aiding memory, also (for all facts in the chant group) is the use of rhythm.

student think about Multiplication fact


After viewing the Lesson Six video, 7 and 6, when seen together, trigger the “7 Beetles” chant and students can quickly recall the product- 42. The reason that flashcards, electronic flashcards, and many internet games are not very effective is because seeing/hearing 7x6 ,6x7, etc. does not trigger anything in the students’ mind. A schema for that information was never established! For those methods to be effective, Multiplication facts need to be made meaningful first, which is exactly what Factivation!® does.

If the goal is to increase fact retention and quickly develop fluency, then Multiplication facts need to be made meaningful. Meaningful facts are not only easier to recall, but much more interesting to learn, resulting in students
being excited about Multiplication and math, in general.




42÷6 =7: With the “7 Beetles” chant background knowledge now established, students confronting the division facts 42÷6 or 42÷7 can easily apply that new information to what is already known (that 6,7,and 42 belong together). Students gain a complete understanding of the reciprocity of Multiplication and Division when taught to apply the Factivation!® strategies to BOTH operations.


Final note on schema:


“Schemas are clusters of knowledge about an event or object abstracted from prior experience with the object (we tend to recall objects that fit our conception of the situation better than ones that do not).” 

Let’s apply that definition to learning math facts:

Schemas are bits of knowledge about a Multiplication/Division fact taken from prior experience with the fact. (Students tend to recall these facts better than others.) The Factivation!® videos provide this prior knowledge, so facts are quickly learned and retained.

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