When ns teach multi-digit multiplication to my fourth and 5th graders, I current it in many different ways, periodically to the dismay the parents and other teachers. They say, “Why nothing you teach castle the way we have constantly done it?” (Meaning the typical algorithm.) “It operated fine for me!” and it does occupational fine, if the students have the right to memorize and retain it. However teaching the other methods first—place worth sections, increased notation, and algebraic notation—allows students to develop far better understanding that why we execute what us do. And more times 보다 not, they remember it and also make fewer mistakes.

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The first method we discover is the location value sections an approach (see photo 1), i beg your pardon we also call the area model. This technique works very well, emphasizing place value that the numbers v expanded form and multiplying by powers of 10. In addition, it really uses the formula because that area the a rectangle by multiplying L X W for each the the internal rectangles. We usage this for 1 number x 4 digit, and also 2 digit x 2 digit, but some that my fifth grade students additionally use it for 2 digit x 3 digit or multiplication the decimals.

Once students understand that method, some relocate to expanded notation an approach (see photo 2). Students uncover it is similar to the very first method, but it does not use the rectangle. That is slightly an ext advanced, so not all the students usage it, but it is effective and makes sense. The numbers are still expanded, then multiplied through each various other number. In 2 digit x 2 digit, the four commodities are the very same as the four found using the place value sections method, then included together.

Then, some of the students will move to utilizing the algebraic notation an approach (see image 3). This is a an excellent way to show the distributive property, or what will later be dubbed the FOIL method when resolving binomials. Not numerous of my students will select this method, however I do show it to them. They normally think that is nice cool.

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Once us have operated through all three of those methods, I display them the shortcut an approach or the traditional algorithm (see photo 4). We stress why we use the zero placeholder as soon as we multiply the second digit in the 10s place, and also not just memorize the steps. By the end of 5th grade, most of the students are using the shortcut method, however a few will use among the other methods, i m sorry is fine with me. I always say, as lengthy as you obtain the best answer, usage the method that works ideal for you!


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Place worth Sections Method


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Expanded Notation Method


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Algebraic Notation Method


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Shortcut Method


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Mary deVille
Mary deVille has actually been to teach fourth and also fifth grade math at Euclid Park Elementary because that the past three years. Prior to that, she spent two decades teaching center school math at Paul Revere Elementary and also Charles Eliot. Throughout her tenure, Mary has held various management positions and also served together a mentor and also as a subject-area specialist. She received her 1–8 elementary to teach certificate from Cleveland State University and also holds a grasp of education and learning in middle qualities math from john Carroll University. Mary enjoys attending mathematics professional advancement and conferences whereby she continues to develop her mathematics expertise. When not in ~ school, mary is cooking or boating with her family.