Introducing Subtraction with Regrouping Through Inquiry

A few weekends ago, I went to a great workshop on ‘Teaching and Learning through Inquiry’ by Kath Murdoch and came back to work inspired. My class was ready to start using regrouping to subtract 3-digit numbers, and I wanted to help my students get a deep understanding of why we regroup.

Inquiry learning is very different from a traditional lesson. Instead of the teacher telling students exactly what they need to do, students investigate a question, taking the learning into their own hands.

The Provocation

To make the lesson have real world meaning, I began with a situation someone could actually find themselves in.

I love Mentos. I love them so much so that I bought some huge packs from the grocery store. I already ate some, but I still have 2 single Mentos, 2 packs of ten, and one big pack of 100 left (the pack of 100 is actually 10 packs of 10 – like you could get from Costco).

As a class we then worked out that 2 units, 2 tens, and 1 hundred is 122 Mentos.

As much as I love Mentos, my sister enjoys them even more. As a present, I decided to give her 98 of them.

Once I give her the Mentos, how many will I have left?

 

Working in Groups

Students then got into groups and got to work. They had already done 3-digit subtraction without regrouping, so they knew how to line up the numbers correctly.

Additionally, I gave them base 10 blocks to use as manipulatives and poster paper to draw on. What came next were some amazing discussions on what to do now.

My Job

As the students discussed what to do and tried things, it was my job to walk around and ask questions about student thinking as well as provide scaffolding where needed.

A common mistake for 2^nd graders to make is this:

Instead of telling them what they did wrong, I asked questions like:

• When you subtract, is your answer bigger or smaller than the answer you started with?
  • Smaller
• Is 176 bigger or smaller than 122?
  • Bigger
• What do you think happened there?
  • Oh, you can’t take 8 from 2!

When students were completely stumped, I would ask questions to help guide their thinking.

• If you can’t take 8 from 2, where can you take from?
  • No answer
• If I have 122 Mentos, do I have enough to give 98 away?
  • Yes
• If I have enough to give 98 away, then it’s possible. So where can I get those extra units from?
  • Can you take from the tens place?
• Why not? Try it!

The Results

The results of the inquiry lesson were great. Once the groups had found their answers, they shared their posters and thinking with the class. Although they did it in different ways, all 3 of the groups were able to get to the concept of why we regroup – if we don’t have enough units, we need to borrow from the tens place. If we don’t have enough tens, we need to borrow from the hundreds.

                 

As you can see, one of the groups did get the answer wrong. This was great, because it got us to the conversation of why that happened.

Debriefing

Once the groups had explained their thinking, we brought the analogy back to the packs of Mentos to make sure everyone understood exactly what we were doing.

Together, we drew these conclusions:

I have 1 pack of 100, 2 packs of 10, 2 single Mentos. When I give my sister the 8 Mentos (I always start with the units place), I see that I don’t have enough, so I open a new pack of 10. Now I have 12 single Mentos. 12-8=4. I’m left with 4 in the units place.

To give my sister the other 90 Mentos, I look at the 10s place. I only have 1 pack of 10 left now that I opened the other, so I need to open the pack of 100. When I do that, I now have 11 packs of ten. 11 tens – 9 tens = 2 tens. I have 2 in the tens place.

My Conclusions

I could have just used the Mentos analogy and explained how to subtract with regrouping, done a few practice problems and sent the students off to practice on their own. Although that would have surely gone smoothly, setting up the lesson in this way really allowed students to think more critically about the situation and why we subtract the way that we do. I think this has helped them have a deeper understanding of the concept as well as continue to develop their critical thinking skills.

By @SGroshell