Excellent Mathematical Explanations

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SWBAT explain why a comparison statement is true or false using place value vocabulary.

Big Idea

Students use place value vocabulary to write excellent mathematical explanations about why a comparison statement is true or false.

Entrance Ticket

5 minutes

I give students an entrance ticket.  As they complete the problem on the entrance ticket, I look at student responses and gauge student strengths and weaknesses.

Entrance Ticket:

Use the statement below to answer the following questions:

8 hundreds and 3 ones  >   8 hundreds and 2 tens

Part A:  Is this statement true or false?

Part  B:  Explain your reasoning using words or pictures.   How do you know? 

Introduction to New Material

10 minutes

I ask two or three students to share out their answers. As they share out their answers, I make sure to ask guiding questions (if necessary) and point out exemplar responses to part b (explain your reasoning).

When finished, I display an anchor chart entitled “Excellent Mathematical Explanations”

 Anchor chart:


Excellent Mathematical Explanations have:

__Place value vocabulary (hundreds, tens, ones) 


___ Why the answer is true or false (key word: because)


__Capital letters at the beginning of each sentence and periods at the end.


 This anchor chart provides a criteria for success for students so that they clearly know what an "excellent mathematical explanation" needs to include.  These simple guidelines help focus students' thinking and writing about math concepts. This tool is especially useful for students who are new to writing about and talking about their mathematical thinking. 

We are going to read two explanations. As we read these explanations, we are going to see if the explanations are excellent mathematical explanations or not.  I read the example explanations below.

Explanation 1:

This number sentence is false because I can tell that 820 is bigger than 803.

Explanation 2:

The number sentence is false because 820 is larger than 803.  8 hundreds and 2 tens is greater than 8 hundreds and three ones because a ten is larger than a one and 820 has two tens while 803 has 0 tens. 

I have students work in groups or as a whole group to determine which statement meets the expectations and what both students could do to improve. 

(In explanation one, the student states his/her answer but does not use place value vocabulary or explain why he/she know that 820 is greater than 803.  In contrast, explanation two explains why 820 is larger than 803 using place value vocabulary--the student explains that ten is larger than a one and that 820 has two tens while 803 has 0 tens)


Guided Practice

10 minutes
Now, I am going to give you a chance to use our check list and write your own excellent mathematical explanations!  As you write your explanations use the checklist on the side of your paper to make sure that you are meeting each expectation. 

As students work, I circulate and encourage them to check their work against the check list. 


After students have finished, I have two or three students read aloud their explanation.  After they read, I have students give feedback using the criteria for success and the sentence stems :

I liked the way you______________  

Next time, you should ___________________. 

These sentence stems aid students in giving appropriate positive and constructive feedback.  Since many students do not have experience with giving feedback these sentence stems give them a "vehicle" to give their teammates feedback.  Giving students the tools that they need to give accurate and effective feedback increases the rigor in the lesson. 

Friday Skills Assessment/ Weekly Assessment

15 minutes

Now it is time to take everything we have learned and work on on our FSA (Friday quiz).  I want to see who can meet our goal of 85% mastery or higher!  Work hard today!

I circulate as students take the quiz.

If time remains at the end of the class, I will go over a few test items with the class and  show exemplar work.