Tag Archives: GCF

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.)

IMG_20110118_122521

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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