Explaining Our Equations and Writing about Arrays

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SWBAT explain why two different number sentences both describe an array

Big Idea

Students work to use words to explain why multiple number sentences all describe an array. Students use a criteria for success to help craft an "excellent mathematical equation"


10 minutes

It’s Valentine’s Day and I  have a lot of cookies for the class. I want you to help me arrange my Valentine’s Day cookies into an array with 5 rows with four cookies in each row.  On your white board, draw the array.

I have 2-3 students share out their arrays.

Now I want you to write 2 number sentences to explain your array.

I have 2-3  students share out their number sentences with an emphasis on WHY the number sentence is correct.  To do this we make the connection between the number sentences and their picture models.

Now I am going to hand you a sentence strip.  On this sentence strip, I want you to write why both number sentences for your array are correct. 

I give students a sentence starter to help them focus their answer and to model what a strong sentence sounds like.  While not every student in my class needs a sentence starter to write a strong explanation, these sentence starters help students when they are beginning to explain their thinking and set expectations for what a clear explanation sounds like. 

Introduction to New Material

10 minutes

Now that we have written a first response, I want us to look at the criteria for success for our mathematical explanations.  

I put this anchor chart on the board: 

Excellent Mathematical Explanations have:

 ___Mathematical vocabulary (columns, rows, number sentence, addends)

 __WHY (key word: because)

 ___Capital letters and the beginning of the sentence and periods at the end.


Now, let's read a few of our sentences and see if they are excellent mathematical explanations, and if not, let's discuss what we need to do to make them excellent. 

I pick three sentence to read (1 high/1 med/1 low). As you read through the sentences have the students determine whether they meet the criteria for success AND what those students could do to make their explanations stronger.  If students are struggling to give each other feedback, I encourage them to use the following sentence stems: 

"I liked the way that you.... "

"Next time, remember to..."

I give students these feedback sentence stems to model expectations for giving both positive and constructive feedback. Since many students are not used to giving each other feedback, I find that these sentence stems guide the conversation (in the past when I have not given students sentence stems, feedback has not been as precise or useful for students).  The sentence stems are a scaffold so that eventually students can give each other feedback and critique each other's arguments more freely. 

Guided Practice/Independent Practice

10 minutes

Now that we have reviewed our criteria for success, you are going to have a chance to practice writing excellent mathematical explanations using this checklist.

I allow students 5-8 minutes to answer the question.  As they work, I circulate and check in with students who might struggle with using the criteria for success. 

When finished, I have students come back together and invite students to read their writing.  As students read their writing, I encourage them to check to make sure that they are meeting all three parts of the criteria for success.  


Exit Ticket

10 minutes

Now that we have practiced writing about our arrays and have received feedback, I want you to show me what you know on this exit ticket.   Use the criteria for success to show me that you have mastered the material!

I allow students 5 minutes to finish the exit ticket.  If there is time, have one or two students read their exit ticket aloud and invite other students to give feedback on their work. 

I use this exit ticket to assess (1) Student understanding of arrays and writing equations for arrays, and (2) students' ability to explain their thinking about arrays using writing.  After reading the exit tickets, I put them in three piles: (A): In need of intervention, (B) Right on Track, and (C) Extension. Students whose exit tickets are placed in the A group receive intervention from me during my morning math review and during the next day's independent practice. Students in groups B and C will likely not receive intervention from me but may receive more challenging work on this concept during morning math review or during the next day's independent practice.