by C. Elkins, OK Math and Reading Lady
In Multiplication, Part 3 I will focus on 3 strategies for double digit numbers: area model, partial products, and the bowtie method. Please also refer back to my Dec. 6th post on Number Talks for 3rd-5th grade where I mentioned these and other basic strategies for multiplication. I highly recommend helping students learn these methods BEFORE the standard algorithm because it is highly linked to number sense and place value. With these methods, students should see the magnitude of the number and increase their understanding of estimation and the ability to determine the reasonableness of their answer. Then, when they are very versed with these methods, learn the standard algorithm and compare side by side to see how they all have the same information, but in different format. Students then have a choice of how to solve. Try my “Choose 3 Ways” work mat as bell work or ticket in the door. Get it free here.
Area Model: This method can be illustrated with base ten manipulatives for a concrete experience. Remember the best methods for student learning (CPA) progresses from concrete (manipulatives) to pictorial (drawings, templates, pictures) to abstract (numbers only). Using a frame for a multiplication table, show the two factors on each corner (see examples below for 60 x 5 and 12 x 13). Then fill in the inside of the frame with base ten pieces that match the size of the factors. You must end up making a complete square or rectangle. This makes it relatively easy to see and count the parts: 60 x 3 and 5 x 3 for the first problem and (10 x 10) + (3 x 10) + (2 x 10) + (2 x 3) for the second. I’ve included a larger problem (65 x 34) in case you are curious what that looks like. The first 2 could be managed by students with materials you have in class, but I doubt you want to tackle the last one with individual students – nor do you probably have that many base ten pieces. A drawing or model would be preferred in that case. The point of the visual example is then to connect to the boxed method of the area model, which I have shown in blank form in the examples . . . and with pictures below. I also included a photo from another good strategy I saw on google images (sorry, I don’t know the author) which also shows 12 x 13 using graph paper. Continue reading