Beth McKenna VILLAGE ELEMENTARY SCHOOL-YORK, YORK, ME
2nd Grade Math : Unit #16 - Getting Ready to Multiply : Lesson #2

Colorful Building Arrays

Objective: SWBAT create arrays independently, generate addition sentences and then use the arrays to create a city picture
Standards: 2.OA.C.4 MP7
Subject(s): Math
60 minutes
1 Warm Up - 10 minutes

I begin today's lesson with fluency practice in repeated addition. I orally dictate the following problems for students to solve:

2 + 2+ 2 =  ,        4 + 4+ 4 + 4 =,       5 + 5 + 5 =  The students record their responses in their math journals. I ask students how they solved the problems, and reinforce any students who suggested using arrays, or finding the doubles fact and then counting on. I know arrays are relatively new, but I am wondering if anyone has yet internalized the idea.

We discussed arrays in the previous lesson.  I ask students if they remember the word array? Who can show me an array somewhere in the room? Can you describe the array? (10 by 10 array for the number grid, etc.) I take several different suggestions from around the room. 

I tell students that today we will be working with arrays. 

2 Independent Practice - 20 minutes

Today I ask students to create some colorful arrays using squares of paper glued onto a larger sheet. 

I model how to read the directions (build a 4 by 3 array), I take the colored squares and glue them on to make 4 rows with 3 in each row. I check that I have 4 rows and 3 in each row. I remind students to check their arrays before gluing the squares on and to remember that if they set down 4 to mark the rows, they already have 1 in each row so they only need to add 2 more in each row to get 3. Even when students say 4 rows of 3, they often forget that that first row they set up counts as one of the 3 in the row. It takes a little practice for students to remember that a 4 by 3 or 4 rows of 3 array should only have 3 in each row.

Below my array I write 3 + 3 + 3 + 3 = 12

I place a variety of 1 inch colored squares in the middle of each set of desks. I hand each child a large 12 x18)  piece of black paper. I hand each student a set of directions for making arrays. (I print off 3 different sets to allow for variety in the arrays that are created.) I check with the students to make sure they know that they must follow the directions, build the arrays and write the addition sentence below (above) the array.

I tell students to leave a little space between each array. They are welcome to have another large piece of paper if they fill up the first one. I give students about 15 minutes to build as many arrays as they can.

I walk around to make sure students understand how to build the array and create the math sentence from it. I help students who may be struggling with the concept. 

Matching the Picture and the Number Sentence
Developing a Conceptual Understanding

In this lesson I want students to strengthen their understanding of how arrays help us to show a repeated addition problem, and that the array can be used to find the answer to the problem. Arrays also set up the conceptual understanding that will lead children to multiplication.

At the beginning of the lesson I drew a 7 by 2 array on the board. (I chose this because it was not one that any child would be building during the lesson.) I drew my array and asked for help to write an addition sentence. 

The first student suggest 10 + 4 = 14. There were 14 squares in my array, but they were not grouped to show 10 + 4. I suggested to the child that while 10 + 4 matched the number of squares, it did not look like my picture. I pointed to my rows of squares. 

The next child suggest that he knew 8 + 8 was 16 so it could be 8 + 8 - 2 = 16 - 2. Again, I reminded the students that my picture didn't show 8 + 8 - 2. 

I asked the class how many squares were in the first row? (7). How many in the second row? (7). Could someone make a math sentence using the number of squares in each row? Finally a child said 7 + 7 = 14. At that point another student offered 2+2+2+2+2+2+2 = 14. 

It seems so obvious sometimes to the teacher that it is hard to see where student understanding of the concept breaks down. To me the rows were so clear, that it was obvious that the sentence was 7 +7. But the students were not seeing things in rows. They were counting the squares and then making up a number sentence that had the same answer as the number of squares. 

Their understanding of the concept of how arrays worked and could be useful was not yet developed. I hoped that by having them build a series of arrays independently, they would begin to grasp the concept of how arrays can help to solve math problems (currently with addition, and later with multiplication.) If they grasp the concept now with addition, early multiplication will be much clearer. 

3 Creating Murals - 15 minutes

I tell students that they will now work in small groups to create a city mural using their arrays, and adding city details to complete their murals.

I explain that they can cut out their different arrays, and use them to create buildings, city blocks, bus windows, street signs, etc. They are welcome to cut out other things (car wheels, streetlights, etc.) or to draw on their murals to complete the picture. 

I let students choose their  groups of 4 students each, and ask them to take their arrays, and talk to their groups for 3 minutes about what they want to include in their pictures. They should agree on how to lay things out on the mural. I ask that the number sentences be glued on with the arrays. 

At the end of 3 minutes I tell students they may begin their pictures. They will need to work together to complete their posters so we quickly review group work rules before beginning. 

While students work on their murals, I circulate around the room providing support as needed.

An extension might be to ask a group to find the total value of their city by adding the total of all arrays. I would suggest this to a group that had worked quickly and grasped the concept of building arrays. 

4 Sharing - 5 minutes

Students have a chance to stand up and share their murals with the rest of the class. I hang up the murals for others to see.