Tag Archives: factoring

Factoring Numbers

factree

Factoring, as used in elementary school,  is the act of changing a number into numbers that multiply to produce the original number. For example, 12 can be factored to 3×4. 3 and 4 are called factors of 12.

In the photo above, a “factor tree” is used to help identify the factors. I have often seen the factor tree used as the initial approach to teaching factors. I’ve also seen it used as the primary means of providing intervention for students struggling with factoring.  Think about that. Students who didn’t understand the initial instruction that likely involved the mathy approach shown above were provided the SAME approach.

Math topics can be presented with a more concrete introduction which can allow for more in-depth understanding. The photo below shows a CRA approach to factoring. This approach can be used as part of UDL or as an instructional strategy for intervention.

 

cra-approach-to-factoring

 

 

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Hands on Approach to Factoring out the GCF

gcf-cards-set-up-photo

Factors are “things being multiplied”, e.g. 2 and 3 are factors of 6.

Factoring polynomials like 5×2 + 15 above is one of the most challenging algebra topics, especially for students with special needs. To make these problems more accessible a more concrete approach is possible. The photo above shows how finding a greatest common factor (GCF) is possible using a hands on, visual approach. Click on this link to a folder with a document explaining this approach and with a document that is a master for these card cutouts.

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Graphic better than FOIL

Typically, multiplying two binomials is presented with FOIL. This approach is problematic for two reasons: it is a mneumonic for a purely symbolic representation and it is also an isolated strategy that does not connect well to prior knowledge.

FOIL

Another approach is to use a graphic organizer and context. In the photo below I presented students with the scenario of expanding my patio (under the guise of being so popular I needed more space to entertain). The top figure shows the expansion of length alone. This allows for a simple distributive problem and (and eventually factoring out the GCF). The bottom figure shows an expansion of length and width which leads to multiplying binomials. Students would see that the area of the new patio is computed with (6 + x)(5 + x) which is the same as finding the area of each individual rectangle (presented in photo at the bottom). (This is useful for factoring trinomials as well.)

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This scaffolded approach is effective because it presents the concept in a different representation, it connects to prior knowledge of distributive property (useful for memory storage) and it is connected to prior knowledge of area of rectangles so it has meaning.

Subsequent problems would use the boxes as a graphic organizer (see photo below).

multiply binomials

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