Step by Step Directions for Multiplying mixed numbers using a Visual Model

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mixed numbers

Yesterday we played a fun game that allowed our children to get familiar with arrays and how they can help us multiply mixed numbers.

Today it is time to begin creating the arrays!

I would begin by getting your trusty base ten blocks out and have your students build a 1  1/10 x 1 3/10 array.

Before you begin, remind your eager children that an array must always be a rectangle, or if you can get them to tell you that it is even better! Also let them know that the flat will equal one whole today. Discuss what the long equals and the cube equals. They should be able to answer this by knowing what the flat is worth.

Know it is time for the fun part. Begin building the array.  Start with 1  1/10 and build it vertically. I’m all for asking questions instead of telling.

How many flats do I need? How many longs? How many cubes.

Direct the students to place one flat and one long vertically on their desks.



Then move on to 1 3/10. Discuss that this fraction will be horizontal. Again, ask the same questions though you might add a twist. How many flats do I need to add to my area? The answer is none. You already have one whole going horizontally. You do not need to add another. All that needs to be added is 3/10.


Finally, ask your brilliant children what is wrong with the array. If you have spent enough time with arrays they should recognize that it is not a rectangle. Again, ask what could be done to fix it. I’m sure that someone will come up with the idea to add cubes to finish up the array.


Once they have added the cubes it is time to add up the base ten blocks.

1 + 3/10 + 1/10 + 3/100 = 1  43/100

I would like to add that I did all this in my head. I added the pictures later and double checked myself. Years ago if you had asked me to do 1  1/10 x 1  3/10 in my head I would have laughed at you. Now, visualizing the model has allowed me to be able to figure this out without writing a single thing down.

Depending on the needs of your students, you can do a few more using the base ten blocks or you can move on to the FREEBIE.

It will take you step by step in how to teach your students to build a visual model in their math journals. Then there are a few word problems for them to solve and a few arrays for the students to look at and figure out the dimensions.

I highly recommend that each student have a journal with grid paper . It is imperative that they use the grids to help them draw and then figure out any problem presented to them. The also need colored pencils so that they can shade each part a different color. This helps them when it comes to adding up the array.

Check in tomorrow to get some FREE word problems, and let me know how this lesson goes. I love hearing from you.

You’ve Got This


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