Multiplication Strategies Part 3: Connecting to Place Value

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

Number Talks Part 2: Strategies and decomposing with 1st-3rd grade

by Cindy Elkins, OK Math and Reading Lady

For 1st -3rd grade students: Refer to “Number Talks Part I” (posted Nov. 12, 2016) for ways to conduct a Number Talk with KG and early 1st grade students (focusing on subitizing and number bonds). For students in 1st – 3rd grade, place extra emphasis on number bonds of 10.

Write a problem on the board, easel, or chart tablet with students sitting nearby to allow for focused discussion. Have the following available for reference and support: ten frame, part-part-whole template, base ten manipulatives, and a 0-100 chart. Present addition and subtraction problems to assist with recall of the following strategies. If time allows, post another similar problem so students can relate previous strategy to new problem. Students show thumbs up when they have an answer in mind. The teacher checks with a few on their answer. Then he/she asks, “How did you solve this problem?” The teacher writes how each student solved the problem.

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