Week 6: Subtracting Multi-Digit Numbers with Multiple Renaming (Regrouping)

Hello! Welcome to Week 6 of my blog entry! 

This week in my class, we are working on subtracting multi-digit numbers. Students have learned to subtract 4, 5, and 6-digit numbers. My students know how to solve 456,788-34,207. 

Today, we have pivoted to subtracting multi-digit numbers with multiple renaming. This is a big challenge for the students since it requires them to remember which numbers to rename and when to do it, in order to be correct. 

So, students are given a problem: 114,436-75,787. 

What is unique about this problem is that the digits in the ones, tens, hundreds, thousands, and ten thousands places are all greater in 75,787 than they are in 114,436. What this means is students must look next door until they find a value that can be subtracted. Unfortunately, that doesn't exist in this problem, so they must identify the number in each subsequent place value, then rename each number so that it can be subtracted.

So, the 1 in the hundred thousands place becomes 0, the 1 in the ten thousands place becomes 11, but since we are borrowing, 11 becomes 10. The same goes for 4 which becomes 14, but then becomes 13. The same goes for the following number 4, becomes 14, then 12. Finally, 3 becomes 13, then 12, and 6 becomes 16. 

Now, we don't have to rename further because we can subtract 7 from 16. 

This problem becomes easier to solve now that the place values of the top number have been renamed or "regrouped." The correct different is 38,649.

Even for students who showed confidence and proficiency with subtraction, this problem was very challenging. Students must remember to rename multiple times, and then subtract the correct place values. 

It is interesting to see how some students excel at addition, but struggle with subtraction and vice versa. For some, it is easy to add, but for others taking away makes more visual sense. 

Even I struggled with this at first. I had to remember the simple operation of regrouping and then subtracting in order to arrive at the correct difference. 

These multi-step problems are new to our 4th Graders. They must learn the steps in order to become confident with them. Over time, I believe they will with the proper routine and structure.