*How to teach an excellent homeschool math lesson and make the most effective use of your teaching time–in 6 easy steps!*

I try to make sure my kids do *some* math every school day, but it can be hard to squeeze in if we have a field trip or family in town visiting. Those are the days when I just whip out a Kumon workbook and tell the kids to go do a page. Something is always better than nothing!

But on days when I teach a full lesson to my kids, I try to use these steps to make the most effective use of my teaching time. Teaching an excellent homeschool math lesson doesn’t require expensive manipulatives or even a curriculum. With intentional teaching, even a free worksheet off the internet (or that Kumon workbook) can be the foundation of a great math lesson.

Whether you use a full-blown math curriculum or like to create your own materials, here’s how to teach an excellent homeschool math lesson and make the most of your math time.

### 1. Do a quick mental math warm-up.

Asking just a few mental math questions prepares your child’s brain for math and gives some quick oral practice. Addition and multiplication facts are always great for this.

### 2. Tell your child the goal of the lesson.

For example, “Today you’re going to practice adding two-digit numbers.” I often forget to do this, and I’m always surprised how much it helps when kids know what they’re supposed to focus on.

### 3. Connect to what your child already knows.

Encourage your child to think about what she already knows about the lesson topic. For example, “What are two-digit numbers? What do you already know about adding them?” When children connect new learning to old learning, they’re much more likely to remember the new concepts. This builds confidence, too—even adults feel more confident tackling a new subject when they feel like they already know something about it.

### 4. Use pictures and manipulatives to illustrate the new concept.

Manipulatives (concrete objects) don’t have to be fancy. Everyday items from around your house work great, and you’ll be amazed at what you can print or make out of paper.

### 5. Focus on the “how”* and* the “why” to develop understanding.

Instead of presenting the lesson as a process to be memorized, encourage your child to think about why each step works. Take this addition problem, for example.

For this problem, you might ask questions like:

- Why can’t we just add the 9 to the 3?
- Now that we’ve added the 9 and the 5 to get 14, what should we do? Would it make sense to write 14 in the ones-place?
- Does your final answer make sense? Why or why not?
- How would the answer have changed if the problem were 29+36? What about 30+ 35? Do you have to redo the whole problem to figure this out or can you use the answer you already found to make it easier to figure it out?

You don’t need to do this with every single problem, but questions like this can be very helpful to slow a child down and help her think deeply when she’s wrestling with a new concept.

### 6. Correct your child’s work right away.

If possible, correct your child’s work as soon as she finishes. That way, she can correct any mistakes right away, and it ‘ll give you a sense of whether to move on to the next lesson tomorrow or review this topic. (Even better is if you can check the problems *while *your child is working, to make sure that she’s not making the same mistake over and over. But that can be hard to pull off when you have other children to teach.)

You have a lot to pack into your homeschool day. Whether you have an hour or just a few minutes for math, you’ll make the most of your math time when you follow these steps.

Happy Math!

Thanks for these reminders and pointers! We are entering uncharted waters with a first grader who ”doesn’t like to do hard things” so I have to approach things from either a very practical way or game-style to keep her engaged. We have Singapore 1A but I anticipate needing to augment with LOTS of oral work and gaming. Thanks for all you do – I really appreciate your blog and newsletter, and we will be working with Addition Facts that Stick as well:)

Thanks so much for commenting, Laura. Best of luck as you get started with your first grader–it sounds like you have a great approach mapped out. Happy math!

This is a useful list of items to think about as I am preparing to teach. Thanks for sharing it.

I’m interested to know your thoughts on how much “help” you should give to elementary aged kids with their “independent ” work after (or before) a lesson. Could you share your opinions?

I have listened to experts of other “subjects” recently say that you cannot give a child too much help on writing assignments. Do you believe the same holds true for math?

What an interesting question, Jennifer! In my opinion, there’s no cut-and-dried answer. It depends a lot on the personality of the child you’re working with and the nature of the work they’re doing. It also depends on what kind of help you’re giving.

Off the top of my head, I can think of three situations where I tend to give lots of help:

1. When a child is working on a very challenging problem, and I’m acting as a problem-solving partner. We bounce ideas around, try things, and chat about possibilities. I often have done this with the “double-star” challenge problems in Beast Academy or when my son has been stuck on a tricky puzzle.

2. When a child is having an off day and just needs someone to sit at their elbow. “Great, you solved problems #6! Now go on to #7!” (This kind of help, while sometimes necessary, makes me want to poke my eyeballs out, so I only use it sparingly.)

3. When a child is at the beginning of an assignment, and I hover a bit to make sure that they’re on the right track. I want to prevent them from practicing something incorrectly. But if they’re having trouble, I don’t sit at the elbow through the whole assignment–I back things up and reteach. The point of the assignment is to practice what you have learned, not just to get the answers right because your mom has guided you through every single problem.

In general, I believe that elementary math is a wonderful opportunity for children to learn to work independently, without a lot of help. But there are times where some more focused help is definitely appropriate.

I just watched your “how to teach subtration facts that stick” video on Youtube. The ten frame immediately made me think of an abacus. It separates the counters but does not have place value. This seems like a good way to lead in to learning to use an abacus for arithmatic.

Learning arithmatic with an abacus is very successful in developing fast mental maths but I am not sure whether it might help or hinder mathematical understanding. On the one hand it is quite a good mental model to have, on the other hand I worry that it will remove the insentive to have any other mental models. Do you have any thoughts on this?

Hi Casper,

Yes, the ten-frame is very similar to an abacus. Both organize the quantities so that we can immediately perceive how many there are without having to count one-by-one. With either one, the goal is for children to gradually move from actual physical representations to a visual model in their heads, and then finally to move from their mental abacus or ten-frame to working fluently with the numbers and symbols on paper.

That said, I don’t suggest that families only use the abacus or ten-frame, especially for developing place-value understanding. Using more than one mental model helps kids think more flexibly about numbers, and it also forces them to think more deeply about the numbers. (For example, dimes and pennies require children to think about place value in a completely different way than when they’re using the abacus. With dimes, you can’t see all ten cents. You have to remember that its value is ten and add on from there.)

Thanks for a great question! Happy Math!

Kate

Kate,

I work with home school families through a charter school as a teacher and this is the perfect article to help them work with their children. Would it be OK with you if I share it and link to your site? Your work is wonderful.

Thanks for all you do!

Please feel free, Wendy! Thanks for the kind words. 🙂