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Occasionally, my job requires that I do some travel.

As I was getting ready for my most recent trip, my husband said to me, “You do realize that you are 91 miles away from 900,000.”

In airline speak, that means that I have flown almost 900,000 miles with the airline since I signed up for their frequent flier program.

So, my first question is how many miles have I flown?

My goal this year is to hit the one million mile mark.

And that makes my second question, how many miles do I need to fly to reach the one million mile mark?

How do you think your kiddos would answer my two questions, and what strategies and reasoning do you think they might use?

Multiplication and the SPRITE Christmas Tree

The last week before school let out for Winter break, I shared a photo of a “tree” made from a bunch of 12-packs of SPRITE topped with a 12-pack of FANTA. The top row had one 12-pack of FANTA, the second row had two 12-packs of SPRITE, the third row had three 12-packs of SPRITE, and the bottom row was made of thirteen 12-packs of SPRITE.

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Every time I walked past the SPRITE tree, on my way into the store over the 2 glorious weeks of winter break, I was reminded that I never went back and finished the second post about the tree. And then today, when I stopped to pick up a few things at the store, the spot by the front doors where the tree had been, was empty.

When I got home, I found the box of one-inch tiles and created a picture of the SPRITE tree.

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Then, I started moving the rows of “12-packs” so that they formed a rectangle.

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Now, I had 7 rows of thirteen “12-packs of soda” sitting on my table.IMG_6067

As I looked at the rectangle, I thought about how powerful it would be for kids if we could help them see that if they split the one large rectangle into two smaller rectangles; one rectangle made up of 7 rows of ten and a second rectangle made up of 7 rows of three, finding the amount of cans in the SPRITE tree becomes a much more manageable task.  At this point in the whole process, the tiles were getting to be annoying and not very helpful. It was time to use a different representation of the problem–a drawing.

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It was much easier to continue to work on the task using the drawing, Labels, ideas, computation notes and solutions can be recorded, and used for further reference and in conversations. Annotated illustrations are a favorite tool of mine.

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Now, all that was left was to figure out how many cans of soda would be inside all of the 12-packs that were used to create the tree.

One method that students might use to determine the number of cans of soda would be to multiply 91 by 12. I am really a fan of kids using properties of place value to figure out the count in a multiplication situation. They can do quite a lot of the work using mental math and computation strategies, and these are very helpful skills to have.

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Another method that kiddos might consider using is to determine the number of cans of soda in the seventy 12-packs and add that to the number of sodas in the twenty-one 12-packs, as seen in the array (or the area model) in the drawing below. This method, often referred to as partial product, is a really helpful strategy for students to understand and be able to use with confidence. The total number of cans is 1092, when 840 is added to 252.

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A third method might be to find the total number of cans in the 7 rows of 156 cans. When students apply the properties of place value to 156 x 7, they find that there are 1092 cans in the tree.

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At this point in this project, my son came in from after school practice and asked what I was doing. (I did have quite a bit of stuff out on the table.) I explained that I was thinking about the different methods that elementary kids might use to figure out how many cans of soda were in the SPRITE tree. He looked at the tiles and all of the notes and drawings I had on the large gridded chart paper, and said, “Mom, why don’t you just multiply the 91 x 12? You can borrow the calculator on my phone if you don’t feel like figuring it out in your head or writing it out on your paper.”

Just a some thoughts on multiplying multi-digit numbers and helping kids make some sense of how to find the count of objects in a multiplication situation.