How to Use Example and Non-Example in Math with Two-Digit Subtraction

Comparing examples and non-examples in math is a great way to better understand math concepts. The process of comparing the two can help to highlight what the concept is about and how to use it in different situations.

By examining both examples and non-examples, students can develop skills in identifying similarities and differences while enhancing problem-solving abilities.

Additionally, analyzing these side-by-side promotes a deeper understanding of the concept itself. This type of comparison encourages critical thinking skills and fosters an understanding that will be useful later on when more complicated concepts are encountered.

Here is how I have used example and non-example in math with two-digit subtraction.

Why I chose to do an example and non-example activity with two-digit subtraction

Many students struggle with two-digit subtraction due to a weak foundation in number sense and difficulty comprehending math concepts. I took a common mistake that I see students use, not regrouping when doing mental math, and expanded on which answer was correct or incorrect.

We looked at an example and non-example type of comparison to help understand subtraction with regrouping (or crossing a ten).

Because they lack number sense, I hesitate to teach students the traditional algorithm. I want to develop students’ understanding of solving problems.  Ideally, I’d like them to add or subtract within 100 mentally, not using paper.  So far, we’ve looked at how to use a number line and how to break apart the numbers.

How to Present an Example and Non-Example Problem to Students

When I presented this to students, I presented it as a problem many students had difficulty solving last year.  I told the students that I students last year, I came up with two answers, 42 and 38.  I purposely put the wrong answer on the left side so students would see it first.  We read from left to right and naturally “see” the left side of a paper first.

Share and discuss the incorrect and correct answers

I had students share with a partner which answer they thought was correct and why it was the correct answer before sharing it with the whole group.  When sharing with the whole group, we started with 42, and the students answered the image above:

• 90-50=40
• 7-5=2
• 40+2=42

Because we started with 42, everyone thought it was the “right” answer and no one volunteered to tell me how they got 38.  I mean no one.  

I called on a student who I knew had answered it correctly but was hesitant to share because he thought he was wrong, and asked him to explain his answer. He had difficulty explaining his thinking (he’s an English learner and is great in math but not language), so another student helped him finish up the thinking so we could scribe it.

Discuss Different Ways to See and Solve the Problem

Distribute the Minus Sign: We talked about how -57 is really -50 and -7 and how the problem is not 7 ones – 5 ones, but 5 ones – 7 ones.  Through the rectangles on the left-hand side, we also demonstrated how students had made new numbers when they reversed the one’s place.

Use Negative Numbers: I showed them another way to do the problem we had done in class, but that students couldn’t remember.  We set up the problem to get a negative answer.  I have a number line in my room that goes down to -10 so students can use it for these purposes.  

None of my students did this year, but I had a few who did last year.  The negative number also reinforces the idea that there are numbers below 0, a concept that upper-grade teachers often struggle to solidify after years of primary math that stops at 0.

Reflect on Students’ Misconceptions about Numbers and Operations and Plan Meaningful Activities to Address Them

After working on this problem, I realized that students didn’t understand that 93 = 80 + 13. So we worked on expanding two-digit numbers (which they can do) and then decomposing a ten (which they could kind of do in isolation but not apply to subtraction).  

How do you teach students how to solve two-digit addition problems?  Do you follow a specific scope and sequence?  Our math curriculum is horrible, so I tend to do my own thing, but it’s a lot of work and thinking time.

FREE Two-Digit Addition and Subtraction Activities

You might like a few pages from some of my two-digit addition and subtraction products if you teach second grade. I’ve compiled this PDF of resources as a sampler from several different products that emphasize all the work we do in our classroom to develop these strategies in depth.

Different components of the sampler can be used in whole groups or small groups and are perfect for helping your students think creatively when solving multi-digit addition and subtraction problems.