Writing Equations for Arrays

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Objective

SWBAT write repeated addition equations for arrays.

Big Idea

After spending several days building and drawing arrays, students use what they know about adding groups to create repeated addition number sentences to represent their arrays.

Opening/Hook

5 minutes

I start class by giving each student an entrance ticket:

At the cookie store, the cookies are arranged in 5 rows with three cookies in each row.  Draw an array to show how the cookies are arranged.  

When students are finished with the entrance ticket, I have one or two students share out their answer by drawing the array on the board or sharing their answer underneath the document camera.

 Guiding Questions:  How many cookies are in each column?  How many cookies are in each row? How many cookies are there total? 

Introduction to New Material

10 minutes

Today we are going to work on building number sentences for an array.  When we make a number sentence for an array, we are able to quickly determine what the total is.

I want you to turn and talk with your partner about this question: How did you figure out how many total cookies were in our cookie array?

As students discuss, I circulate to check for understanding and listen to student strategies.  Some students might have counted by ones, others might have counted by threes, others may have counted by 5s. 

Now,  on the back of your entrance ticket, I want you to write a number sentence that models the way that you counted the total. What number sentence could we use for our cookie array?

Some students might not know where to begin, but I encourage them to think about how many are in each row and how they could add the rows together.

Now, I want you to turn and tell your partner about your number sentence and explain how you determined your answer. 

When finished with the turn and talk, I ask students to share their number sentences and share WHY they chose that number sentence.  Some students may say 5+5+5, others may say  3+3+3+3+3.  Is one answer correct or are both correct?

[If students are struggling, I model how to add each row and each column to make a number sentence. If students are not struggling, I allow them to do the majority of the thinking and talking here.]

Note: Some students might also subitize the rows and columns (i.e: they may say that the equation is 6+6+3 for the cookie array).  In this case, I ask them how they saw each six (3+3) in order to keep the focus on the rows and columns.  This doubling strategy is an important skill, but when making equations for arrays, the number sentence needs to match the array. 

Depending on student understanding, time, and student engagement, I might give another example:

I want you to tell me all of the number sentences for the following array:

XXX

XXX

XXX

XXX

Turn and Talk:  What number sentence could we use for this array?

When finished with the turn and talk, I ask students to share their number sentences and share WHY they chose that number sentence.  Some students may say 3+3+3+3 others may say  4+4+4. 

I ask students: Is one answer correct or are both correct?

Guided Practice

10 minutes

Prior to the lesson, I post the attached arrays around the room.

During our guided practice, we are going to do a gallery walk!  I have put arrays around the room. You are going to walk around the room and write down the number sentences for each array in your math journal. 

As students circulate, I make sure to identify any common misconceptions and ask guiding questions:  Why did you choose that number sentence?  What is another number sentence you could use here? 

Independent Practice

10 minutes

Independent Practice is tiered based on ability level.

Group A: In need of intervention

I will work with students to write the equations for each array underneath the array on a two sided worksheet (use the first two pages of the attached worksheets). These students should focus on finding ONE equation for each array today. 

Group B: Right on Track!

Students will write the equations for each array underneath the array on three worksheets.  These students should focus on finding TWO addition equations for each array today.

Group C: Extension

Students will write the equations for each array on this worksheet. These students should focus on finding TWO addition equations for each array today and a multiplication equation as well if they already know about multiplication.  Students in group C are also expected to write the sum of their addition number sentences. 

NOTE: When I taught this lesson, I intended to do a mini-lesson with group C about the connection between multiplication and skip counting and how we can write multiplication number sentences for arrays.  However, we ran out of time and I did not have a chance to work with this group.  I was impressed, however, to see that several of the students in that group had created an accurate multiplication number sentence on their own. If you have time, I suggest spending some time with your group C and discussing how skip counting connects to multiplication.  If not, simply asking them to find a third number sentence may lead students to make these kind of connections on their own! 

 

Closing

5 minutes

Today, we wrote number sentences for our arrays.  Before we leave, I want you to write number sentences for this array using your white board and marker. 

XXX

XXX

XXX

XXX

I have one student come up to the board and share their answer.  (This process is shown in the attached video). 

This final task will allow me as the teacher to determine which students understand the concept and which students need more time and/or intervention to conceptualize writing number sentences to describe arrays.