When i teach multi-digit multiplication come my fourth and 5th graders, I existing it in many different ways, occasionally to the dismay the parents and other teachers. They say, “Why don’t you teach lock the way we have always done it?” (Meaning the conventional algorithm.) “It functioned fine for me!” and it does work-related fine, if the students deserve to memorize and also retain it. But teaching the other approaches first—place value sections, expanded notation, and algebraic notation—allows students come develop far better understanding of why we carry out what we do. And an ext times 보다 not, castle remember it and make fewer mistakes.

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The an initial method we discover is the location value sections technique (see photo 1), i m sorry we likewise call the area model. This an approach works very well, emphasizing place value the the numbers with expanded type and multiply by powers of 10. In addition, the really offers the formula because that area of a rectangle by multiply L X W because that each of the internal rectangles. We use this for 1 digit x 4 digit, and also 2 digit x 2 digit, however some that my 5th grade students likewise use it because that 2 digit x 3 number or multiplication of decimals.

Once students recognize that method, some relocate to expanded notation technique (see image 2). Students find it is comparable to the an initial method, yet it go not use the rectangle. It is slightly more advanced, so no all the students usage it, but it is effective and makes sense. The numbers room still expanded, climate multiplied by each other number. In 2 number x 2 digit, the four assets are the exact same as the four uncovered using the location value sections method, then included together.

Then, few of the student will relocate to using the algebraic notation an approach (see photo 3). This is a an excellent way to demonstrate the distributive property, or what will later on be called the FOIL an approach when fixing binomials. Not many of mine students will pick this method, however I do show it come them. They typically think the is nice cool.

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Once we have functioned through all three of those methods, I display them the shortcut an approach or the standard algorithm (see image 4). We stress and anxiety why we usage the zero placeholder when we main point the 2nd digit in the tens place, and also not simply memorize the steps. By the finish of 5th grade, many of the students are using the shortcut method, yet a couple of will use among the other methods, i m sorry is fine with me. I constantly say, as long as you get the right answer, usage the an approach that works finest for you!


Place worth Sections Method


Expanded Notation Method


Algebraic Notation Method


Shortcut Method

Mary deVille
Mary deVille has been teaching fourth and also fifth grade mathematics at Euclid Park Elementary for the previous three years. Prior to that, she spent twenty years teaching center school math at Paul Revere Elementary and Charles Eliot. During her tenure, Mary has held various leadership positions and also served together a mentor and also as a subject-area specialist. She obtained her 1–8 elementary to teach certificate indigenous Cleveland State University and holds a master of education in middle grades math from john Carroll University. Mary enjoys attending math professional advancement and conferences whereby she proceeds to develop her mathematics expertise. Once not at school, mary is cooking or boating through her family.