Drawing Arrays

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SWBAT draw arrays when given written or verbal directions

Big Idea

Students use their knowledge of columns and rows to draw arrays. In the previous days, students built arrays--drawing arrays is a more abstract skill that forces students to visualize the array and internalize the concept of columns and rows.


8 minutes

We’re going to review what we learned yesterday by building arrays in our teams.  I divide students into groups of 3-5.    I hand each group a pile of counters (or another small item like cubes, beans, cheerios, etc.)    In your group, I want you to build an array that has four rows and three columns.

I walk around to check for understanding.   When students have finished, I ask themHow many rows does this array have?  How many columns does this array have?   How many total counters does this array have?  How did you make your array? 

Depending on time, student understanding, and student engagement, I do 2-5 more practice problems using the counters. 

 This activity allows students to make use of the structure of columns and rows that we have been learning about for the past two days (MP7). Students apply that structure to make their own arrays and draw conclusions about the total number of counters in their array.  Focusing on the structure of columns and rows enables students to build a deeper conceptual understanding of how to construct or draw an array--this understanding will aid them when we start to write equations for arrays. 


Introduction to New Material

10 minutes

So far, we have been building arrays using our bodies,  skittles, and counters. Sometimes, we need to build arrays without those tools.  Today we are going to practice building arrays by drawing them! 

I pass out white boards and white board markers and put a practice problem on the board.  I ask students to solve the practice problem on their white board.

The Basketball team stands in three rows and four columns.  Make an array to show how the Basketball team is standing.




When finished, I ask students to Turn and Talk: What strategy did you use to build this array?

Students may respond that they built each row first or that they started with the columns.  It does not matter which way they build the array as long as they are following the directions in the problem and not mistaking the columns from the rows.

After one practice problem, I do 1-3 more group practice problems, stopping after each problem to have one student share their answer and their strategy.  

Guided Practice

10 minutes

There are two options for guided practice: 

OPTION 1)  In partners, you are going to work on drawing an array.  Each group will get four practice problems.  Your job is to sit across from each other and quickly draw the array on your white board so that no one else can see it.  When finished, flip your white board over and show your partner.  Each person will check their partners' work before moving on to the next problem. 

( In order to quickly facilitate this partner work, I cut out the problems and put them in an envelope or bag for the students.  Then, I have the students pull out a practice problem from the envelope or bag, quickly solve it and then work together to check their work) 

OPTION 2)  I post the problems on large pieces of paper around the room.  Students do a gallery walk where they walk from question to question and draw each array on a blank piece of paper or on their white board.  When finished with the lesson, we come back together and go over a few of the problems from the gallery walk. 

When I taught this lesson, I chose to do option one because I wanted to give my students a chance to work in partners.  I provide two options here because I know all classes are different--option one provides an opportunity for students to work together and to explain their thinking orally.  Option two provides students with the opportunity to move around and to work independently.  If your class is confident with drawing arrays, option two might work well for you--this option does not provide as much support for students who are struggling. 

Independent Practice

10 minutes

Independent Practice is tiered by mathematical ability level: 

Group A: In need of intervention

Students in Group A will work with the teacher to draw arrays that have between 1 and 5 rows.  While the focus of this lesson is on drawing  arrays, cubes or counters should be available to Group A as a scaffold. 

Group B: Right on Track!

Students in Group B will work independently to draw arrays that have between 1 and 7 rows. 

Group C: Extension

Students in Group C will work independently to draw arrays that have between 1 and 10 rows. 


5 minutes

Now that we have practiced as a group and independently,  I want you to show me what you know on this exit ticket

I circulate as students work. Use the exit ticket scores to determine A/B/C groupings for tomorrow any necessary re-teaching.