Checking the Reasonableness of Subtraction

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SWBAT check for reasonableness when subtracting multi-digit numbers.

Big Idea

Students will use rounding and compatible numbers to check for correct answers.

Teacher Demonstration

25 minutes

Reasoning for Teaching Multiple Strategies

During this Addition and Subtraction Unit, I truly wanted to focus on Math Practice 2: Reason abstractly and quantitatively.  I knew that if students learned multiple strategies of adding and subtracting numbers, I wouldn’t only be providing them with multiple pathways to learning, but I would also be encouraging students to engage in “quantitative reasoning” by “making sense of quantities and their relationships in problem situations.” By teaching students how to use a variety of strategies, such as using number lines, bar diagrams, decomposing, compensating, transformation, and subtracting from nines, I hoped students would begin to see numbers as units and quantities that can be computed with flexibility. 


I began this lesson by reviewing key vocabulary from past lessons: addend, sum, minuend, subtrahend, difference, checking for reasonableness, and compatible numbers. By teaching math vocabulary, students will have the tools to truly practice MP 3 (Constructing Viable Arguments). 


In order to continue teaching the process of checking for reasonableness and provide students with opportunities to put their mathematical reasoning into words, I created another Google Presentation using Google Drive Documents called Checking Subtraction prior to the lesson. Here are specific directions explaining How to Create a Google Presentation for Student Practice. Next, I was able to share this presentation with students using their student Google email accounts.

Students then copied the shared presentation and saved it in their math folders under the Google Drive. Once all students were successful at copying the presentation and making it their own,we discussed the first slide together, which was the Goal of the lesson: I can check for reasonableness when subtracting multi-digit numbers. This was also the page that students took ownership of their presentation by adding, "By: First & Last Name." This is important as student ownership always translates into higher motivation and learning.


After reviewing the importance of checking for reasonableness, I used the Teacher Model Slide to show students how to use the grid to complete the given algorithm. Next, I modeled how to answer the question: Is your answer reasonable? Again, I discovered yesterday that writing the explanation in paragraph form didn't match my students' computer skills and I knew my students would lose excitement and motivation quickly. Instead, I modeled how to  explain mathematical reasoning using a bulleted list. 

Guided Practice

Next, I wanted to provide students with step-by-step guidance, so, altogether, we completed the next slide: Guided Practice with Subtraction. Students showed their work in their own presentations while I modeled using a projection of my presentation. Modeling how to use this grid for the subtraction algorithm was a bit tricky. I showed students how to create lines to "cross off" numbers and how to use the extra space above the problem to showing where they borrowed units from numbers. To be honest, I was a bit leery of the technological constraints of the computer. However, I was pleasantly surprised when I saw how quickly students caught on!

After solving the algorithm altogether, we then took the time to explain how we knew our answer was reasonable using the space provided on the slide. By asking students to provide an explanation, students would be further developing practice MP 3 (Constructing Viable Arguments).



Student Practice

60 minutes

Same Partners

Today, I asked students to continue working with the same partners as yesterday. During partner work, sometimes students choose to work alone, but they frequently check answers with each other. 

Right to Work!

Immediately following guided practice, students got right to work Subtracting on the Computer. I took this time to roam about the room and provide extra support. 

Even though I was worried about students being able to show "borrowing" while subtracting on the computer, borrowing across zeros turned out to be the biggest problem during this time. 

I absolutely loved my conversation with this student: Borrowing Across Zeros! When I walked up to this student, he had proved that his answer was not reasonable. He had even written, "It is not reasonable." This was such a wonderful opportunity to review why we check for reasonableness in the first place! Here, I further conference with this student and provide some Reteaching. After this, the student was able to complete the problem: Finally There!.

Once students caught on to the process of borrowing across zeros, every student was successful. Here, one student who struggled at the beginning was successful on his own: Successfully Borrowing Across Zeros.

Here's an example of a completed student presentation: Student Presentation Example.



20 minutes

To make sure students were able to put their thinking into word form, I chose the following page as an exit task. This page is part of an amazing Bridges in Mathematics Unit found online: Exit Slip

During this time, I supported students who struggle with putting their thinking into words. Others completed the task quickly and compared answers at the back table: Students Checking Work.

The majority of students were proficient at explaining their thinking on the exit slip: Proficient Exit Slip.