### How It Works

**Welcome** to Math That Makes Sense: How to Teach Elementary Arithmetic. I originally taught this course live at the Well-Trained Mind Academy to a group of about 15 parents, in the fall of 2016. It was a joy to teach them and see their commitment to giving their kids a great math education! Now, I’m thrilled to be able to provide all the course videos for free, right here at my website.

If you’d like to **take the whole course**, you’re welcome to do so! There are eight 90-minute videos that cover all of that cover all of elementary arithmetic, from preschool number sense to multi-digit multiplication and division. Each video is on its own page, so just click the title to go right to that video. Start at the beginning and watch the videos in order. Bear in mind that the original students used a textbook (and even completed homework!), but you don’t need the textbook to be able to learn from the course. (If you’d like to buy the textbook as a reference, you can find it at Amazon.)

Or, if you’re looking for **help on a specific topic**, you can just go straight to the matching video. You’ll see the outline of the whole course below. Just search for the topic you’d like to learn more about and go to that video. Once you’re there, you’ll find an outline with time stamps so you can go right to the question you’re interested in.

Please feel free to add your comments and questions to the page for each video. I’d love to hear what you find most helpful in the classes and how you put them into practice with your own kids.

Happy Math!

Kate

### Math That Makes Sense Course Outline

Click on the titles to go to the videos. Once you’re there, you’ll find an outline with time stamps so you can easily find the information you need.

##### Lecture 1: Foundations, Early Number Sense, and Place-Value

- Foundations
- What are the key principles of quality math teaching?

- Early Number Sense
- How do young children develop early number concepts?
- What is subitizing and why is it so important?
- Why is the decimal number system so useful (and tricky)?

- Place-Value
- How do we break the concept of place-value into manageable chunks for kids?
- What manipulatives are best for teaching place-value?
- What common errors do children make with place-value?

##### Lecture 2: Addition and the Addition Facts

- Concept of Addition
- How do children learn what addition means?
- What are the properties of addition, and why are they important for kids to know?

- Addition Facts
- What are the most effective ways to teach the addition facts?

##### Lecture 3: Subtraction, the Subtraction Facts, and Mental Math

- Concept of Subtraction
- What makes subtraction so hard?
- How do children learn what subtraction means?
- What are the properties of subtraction?

- Subtraction Facts
- How do we teach children the subtraction facts?

- Mental Math, Part 1
- What is the purpose of mental math?
- What are the most useful mental math techniques for addition and subtraction?

##### Lecture 4: Multiplication and Division

- Multiplication
- How do children learn what multiplication means?
- What are the properties of multiplication, and why are they important for kids to know?
- What are the most helpful “thinking strategies” for the multiplication facts?

- Division
- What are the two different interpretations of division?
- How do children learn the division facts?
- How do word problems help children understand remainders?

##### Lecture 5: Mental Math and Word Problems

- Mental Math, Part 2
- What are the most useful mental math techniques for multiplication and division?

- Word Problems
- What are word problems’ role in a quality math program?
- How do you teach children to solve word problems?

##### Lecture 6: Addition and Subtraction Algorithms (Written Process)

- What is an algorithm?
- Where do algorithms fit into an incremental teaching sequence (and why)?
- How do you teach students the addition and subtraction algorithms?
- How do you help children with the mechanics of the addition and subtraction algorithms?

##### Lecture 7: Multi-Digit Multiplication and Teaching a Great Math Lesson

- Multi-Digit Multiplication
- What are the advantages and disadvantages of the two models for teaching the multiplication algorithm?
- How do you teach the multiplication algorithm incrementally?

- 7 Steps to Teaching a Great Math Lesson

##### Lecture 8: Division and Conclusion

- Division
- Why teach long division anyway?
- What are the pros and cons of the two ways to teach long division?
- How do you transition from one-digit divisors to two-digit divisors?

- Conclusion

I just stumbled across your blog as it was linked from Pam Barnhill. So happy you exist! Can’t wait to receive your emails!

Thanks, Renee! I hope you find them helpful! Definitely let me know if there’s anything specific you’re wondering about–I love to write articles about homeschool moms’ real-life math challenges.

I stumbled here also… after Googling, “Does Singapore math have tests after each chapter”. I am homeschooling my 7 year old who adores math (while I secretly hate it and am worried I’ll mess up trying to teach him a subject I never liked) With him; and likely most kids, there is an important teaching point between, “Too easy, I’m bored…… and…….too hard, I give up” . Additionally, and very unlike myself, this kid is so adept at math that I wonder if I’m allowing him to move ahead too quickly.

And so – I like Singapore math and will certainly stick with it, but I do wish they had tests or accumulative review pages after 3 chapters or so. If nothing else, it would boost my confidence that I’m teaching well and he is retaining the material. I can always make my own up though!

As it is; I use Xtra Math online to make sure he can do a lot of quick math facts…. it’s like Kumon but free and on the couch!

Our family enjoys your “Facts that stick” books, thank you so much! Games are fun, worksheets are short and to the point and is very practical. I am looking forward to watch these videos, too!

Glad you and your kids have enjoyed Facts That Stick, Sally! Happy Math!

Thank you so much for these videos! I found and watched this course on the WTMA but my kids were kindergarten age. I so needed this refresher.

My oldest is now learning the addition and subtraction algorithms and I know multiplication is coming! I expect I will be back for a refresher again when we get deeper into multiplication and division algorithms. Extremely informative and helpful!

I’m so glad you’ve found them helpful, and that you’re now able to watch them as a refresher. Thanks for taking the time to let me know, and happy math!

Kate

I am sincerely struggling with this program, and I could not feel more stupid. Can you specifically address the issue of why I have to teach addition or subtraction in two steps, when it comes to the dividing dark line on the

10 frame? So if I asked my child what’s 4+3, you want me to teach them to make it five, and then add another two. I cannot get past this and can’t move on because I don’t understand adding an extra step. I am using first grade with one daughter, and second grade with the other daughter for the first time this year, and I’m ready to scrap all of it because I feel so stupid and can’t move on from this issue. Please help!

Check out this article (especially step 2) for a detailed explanation. If your child immediately knows that 4 + 3 is 7, you don’t need to go through any extra steps. But if she’s counting “4, 5, 6, 7” to find the answer, teaching her to visualize it in two steps will help her become automatic with the answer more quickly.

If you’d like to chat with other moms using the program about this, I highly recommend the MWC Community Facebook group. The parents there are super-supportive and very insightful.

Happy Math!

Kate