Arrays Focusing On Rows and Columns

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Objective

SWBAT interpret products of whole numbers using arrays.

Big Idea

Students develop a meaning of multiplication through the use of arrays.

Warm-Up

10 minutes

The warm up for this lesson is  a review of building arrays and focusing on the difference between columns and rows.  Using gestures to reinforce language, as I discuss the plan for this lesson I move my arm in front of me horizontally when using the vocabulary term row, and hold my arm in front of me vertically when using the vocabulary term column. Since this is a review lesson, I do a quick check on understanding, using the question, "Can you name the diagram that uses rows and columns?"  The response from some of the students is arrays. I make a point of echoing the word, and then write it on the board.

I ask the students to move their arms horizontally and say row.  I also explain that this is horizontal like the horizon.   Then, I repeat with vertical movements, and say this is movement is vertical like their vertebrae.  I use this vocabulary because it connects to content we have covered in science this year.

I repeat the gestures for rows and columns, while quickly saying the words first to see the gesture, and then switch it to give the gesture and the students provide the vocabulary.  You can also use students to help lead this vocabulary activity as well.

Once the students are consistent with the gestures and vocabulary, I explain they will be creating arrays on graph paper with multiplication number sentences to show rows and columns.  Students work with a partner, using dice with numbers to nine (or playing cards can be used) to create each array.  The first number rolled by partner A would be used for the rows, and the second number rolled by partner B would be the number for the columns.  Then they write the number sentence inside of the array and find the product.  

I use a specific structure for creating the number sentences because I want to emphasize the difference in the vocabulary.  Common Core standards do not require a set order of rows x columns, or columns x rows, and students should understand that the order of factors does not change the product. But initially, this allows me to structure student thinking so that the vocabulary "sticks".  I also apply the vocabulary to other real world contexts, including sitting in a row in a movie theater, and columns that hold up a building. 

Model the Task

5 minutes

Using the document camera and a student partner, I model the task of rolling the dice and drawing the array focused on rows and columns on the graph paper. 

For interest, I have the students use color with crayons or fine tip markers.  I also draw students' focus to precision when drawing the arrays on the graph paper (MP6).

I model two or three arrays on the graph paper, and then I have students refresh students' thinking by having students use the gestures to show me the rows and columns.  During this time, I am checking for understanding, on the look out for any students who may be confused so that I can help them as they are working on their own.  

Try It On Your Own

25 minutes

With their graph paper and dice in hand, the students work in partners to draw their array.  Each student is responsible for creating the arrays on his/her own paper. The dice I used for this activity are 10 sided dice, 0-9, and the zero is used for 10.  Their goal is to try to fill up their 8 1/2 x 11 graph paper entirely with arrays.

As the students are working together, I circulate through the room to check understanding, precision, progress, use of the vocabulary, and checking to see the strategy they are using to find the product.  Since this lesson is about the array concept, I am focusing on their use of rows and columns.  I observe their strategies to find the product of the number sentences. These include skip counting, area models, and one-to-one counting for each product. One thing I am watching is to see how they handle when they have an array repeated, or if them use the structure of the related fact such as 4 x 3 and then solving for 3 x 4.  (MP7)  I want to see the students using what they may have already solved as a fact is repeated. 

Wrap Up

5 minutes

The lesson closes with a student journal entry.  I ask them to record the vocabulary terms column and row with their own working definition of those words  to draw an array, and to record their thinking using this sentence frame.  

This array has _____ rows and _____ columns.  There are _______ items in this array. ___ x ___ = _____

I use this journal entry as a formative assessment on this skill.