# Subtraction Roundup

September 18, 2024There are some videos and materials for understanding and practicing subtraction I produced over the past five years that I want to now collect in one place, with a serious question for readers: should I do more like this? Would having videos and materials organized specifically by operations or other math topics be helpful? Or is it better if I just focus on new games and lessons and curriculum?

Leave a comment if you have thoughts. Enjoy!

# Part 1: Understanding Subtraction

When it comes to arithmetic, there are always two parts:

- Understanding the operation, and
- Understanding how it works in base 10.

The videos below tackle precisely these questions for subtraction.

**Understanding Subtraction**

**Understanding Subtraction in Base Ten**

When you work in base ten, the algorithms and even the numbers themselves conceal information. (That’s part of what makes them powerful, paradoxically.) But if we *start from understanding*, we can see *why* the algorithms work, and extend them into diverse situations.

This video explain how to understand multi-digit subtraction as multiple simple subtraction problems, and how calling altering our representations of numbers makes the subtraction easy to do. It ends by connecting all of this to the algorithm, so that you can see why the algorithm works, and how it makes sense.

# Part 2: Subtraction Explorations and Practice

## Subtracting Reverses

This strange little mystery can motivate a ton of subtraction practice. The subtraction here is focused on 2-digit minus 2-digit examples. However, by coloring a hundred chart as you go, you can find really interesting patterns, many of which you may be able to explain.

If you want to take this problem to the next level, try reversing 3-digit numbers and see what happens when you take the difference!

The lesson plan is here, in our lesson library.

## Diffy Squares

There’s a lot of deep mathematics in diffy squares, and it’s possible to find strategies and solutions to “solve” diffy squares. But the best part about diffy squares is trying to beat your old record, and hitting a wall at level 7 or 8. This will give your kids an epic reason to keep doing subtraction practice. To get started, check out the video and read the PDF below.

(It’ll be a serious challenge for motivated students who know algebra to find real numbers to put in a diffy square so that it NEVER terminates. You can find a way to approach this problem here.)

## Harmonic Triangle Challenge

This challenge is meant to motivate fraction subtraction practice, and also generate curiosity as to why the fractions seem to always simplify to unit fractions. (Why?!)

Motivating this problem may require as little as the PDF below. The video is there to help too.

# Extras

The first videos above were motivated in part by a piece I wrote about *starting from* understanding, and how that can help guide math conversations at home. You can read that here.

I also have a video in our Family Math Night resource kit that touches on subtraction. It’s below.

Yes – I appreciate having the information organized by topic. I can see how it progresses from the basics to more advanced.

Yes, this is very helpful! I didn’t even realise you had videos. We home educate and if we could have things like this for all the different maths concepts you have, we would definitely use it. Thanks for taking the time to do this helpful post, and the videos.

We actually have a fair number of videos, in a few different categories: https://mathforlove.com/video/

Wow, this videos link looks incredible, so many to for me (and, if relevant, also the kids) to watch. Thanks for sharing. Hugely grateful.

I like the content you put out. I think more videos and content are fantastic. I think it helps support the games.

Regarding your question about how to organize materials on the website, I would suggest a both/and approach. If I am looking for a specific topic, e.g., subtraction, having all things subtractions grouped is useful. If you are looking for number operations, having the addition and subtraction clustered together might be useful. While the permutations might get too complex to satisfy all viewers, various clustering of materials could be useful in how users search. I am rebuilding my own website (formatting failed an upgrade) so I am thinking similar questions as you. On another note since we are in subtraction, and… Read more »

I also find it very useful when the information is organized by topic. Thank you for this subtraction roundup! My son just started bringing home subtraction homework and I will start using these strategies with him.

I agree with Elin. It is very helpful to have videos and other materials organized by operations or specific math topics. This organization makes it easier to see how math concepts progress from one to another.

Having them structured this way also helps in selecting appropriate games and rich tasks for the corresponding concepts.

Thanks a lot, Dan, for putting this together.