Understanding Borrowing

For math, many of us know how to borrow, but how do we explain it in a way that demonstrates understanding? Sometimes what we do is so second nature that we can struggle with the “but why?” When our phones can easily do math calculations for us it is more important than ever that we have an understanding of mathematics and not just the memorization of the procedural steps. So how do you help a student to understand borrowing?

Explain Borrowing with 12 – 7

Hey #sped! I need help with a S having trouble borrowing (12-7). He’s very visual and we’ve tried cubes and base 10 blocks. Any ideas?

— Howie Hua (@howie_hua) September 10, 2017

The objective is to understand borrowing not just to find the answer.

Multiple Ways

One way to help students to move past steps to understanding is to ask them to represent it multiple ways. Can they explain it a different way? Can they visualize it? Is there another approach? Can they make a story out of it? I like to use Google Slides for this. Each slide can represent a different approach to explaining the math problem. Duplicating a slide allows you to create a mini animation to show how numbers work together.

Add Your Method

For 12 – 7 I started a Google Slides on my phone and attempted to think of a few ways to explain borrowing. How would you represent borrowing? Add a slide(s) to the presentation. Seeing how others would approach a problem helps develop creative problem solving and appreciation for there being multiple ways to think about math.

Link to Slides (add your own representation)