## Reflection: Developing a Conceptual Understanding Colorful Building Arrays - Section 2: Independent Practice

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.

Matching the Picture and the Number Sentence
Developing a Conceptual Understanding: Matching the Picture and the Number Sentence

# Colorful Building Arrays

Unit 16: Getting Ready to Multiply
Lesson 2 of 6

## Big Idea: Ever think of a city street as an endless display of arrays? In this lesson students will begin to recognize how often our world is organized in arrays.

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Standards:
Subject(s):
Math, Number Sense and Operations, repeated addition, arrays
50 minutes