Mathy Mama

🧠 How does place value affect the value of a number?

✏️ Write out the expanded form of the number - in fact, you don’t have to do the whole number, just the digits that you are interested in. This helps make this abstract concept more concrete!

🫨 Don’t panic! We can convert decimals to fractions, AND understand why the process works!

👉🏼 Follow along for help with elementary math topics! Hi, I’m Justina, math teacher and mom of three.
🌟 I want to help you understand the new math methods so you can help your kids with their homework!

😲 What have you forgotten about Place Value??

Place value is one of those ideas that we learn when we’re young, it becomes ingrained, and we don’t really ever think about it again. So when your students start learning about it in elementary school, there are so many vocab words you probably don’t remember ever learning!

I will be working through the 4th grade curriculum this year and sharing videos with everything you need to know to help your kids with their math homework!

🤨 Expanded Form is a really weird way of writing a number.

If you see this written on a page, it can look like a jumbled mess. Instead of trying to understand Expanded Form at one glance, work through each individual part of the number and the Standard Form will fall into place.

Moving back and forth between Standard and Expanded Form helps our kids to focus on each digit in a number and understand its value. This will help them as we move into decimals this year. It also lays the groundwork for scientific notation and exponent rules in later years.

This year I will be working my way through the 4th grade math curriculum, creating videos as we go. I will also be reposting my 5th grade math videos.

What other topics would you like to see me cover?

🤔 How many zeroes should your answer have?

Instead of jumping straight to the "rule" with your kids, take a few minutes to investigate WHY the rule exists!

When the rules are built on understanding, they stick better! We should be looking to help our kids develop their math reasoning skills, not just memorize steps.

👉🏼 Follow along for help with elementary math topics! Hi, I’m Justina, math teacher and mom of three.
🌟 I want to help you understand the new math methods so you can help your kids with their homework!

🫣 I said yesterday was going to be my last division video, but then I remembered I had this video, I think it wraps things up well!

As an Algebra teacher, I did not allow my kids to do KCF. Even before common core was a thing, I was a huge believer that true learning comes from understanding, not tricks.

I wanted my high schoolers to use the proper language for what we were doing - “To divide be a fraction, you multiply by the reciprocal.”

We said that phrase over and over again until they could say it in their sleep.

In high school, I wasn’t worried about WHY we multiplied by the reciprocal. At that age, it should be a math operation that they just know.

5th and 6th grade is the perfect time to wonder why. Don’t start by telling them to “multiply by the reciprocal”. Instead, help them to see that dividing a fraction strip into thirds creates a group of 3.

Then, give them a problem that makes the picture annoying.
50 ÷ ⅔?
Nobody wants to draw that!!

Look for the patterns, then generalize it. Because once you’ve seen the patterns, and understand where the rules come from, you have the tools to tackle any problem.

Thanks for joining my these past few days for this series on fraction division!

School starts in about a month - what would you like to see next?

Let me know in the comments!!

I also have an idea floating in my brain about a multiplication review activity to post this week - I need to see if I can recruit one of my kids to help me with this one.

I never realized there were two different ways to think abut division until I started studying elementary math. My mind always pictured Sharing Division.

You don't need to understand the difference in order to solve a simple division problem. 15 ÷ 3 will be 5 no matter what.

But when you try to do 12 ÷ ½ and think about sharing with half of a person...things get a little weird.

That's when Measurement Division can really shine. In my next video, I'll show how we can do this fraction division with physical objects.

How can we visualize a fraction divided by a fraction?

It took me a minute to wrap my head around this one - and through this process I gained a deeper understanding of division 😮

I was taught to do this problem by multiplying the the reciprocal - and I was GOOD at it. I could KCF with the best of them. But I never stopped to think about why it worked - and if I ended up with a nonsensical answer, I would have had no idea.

There is power in being able to visualize a math problem. It lets you more easily apply those strategies to the real world.

We won’t ask our students to do this forever. They NEED to know how to multiply by the reciprocal. But if we start with hands on and visual approaches, students will have a broader understanding of the math world around them.

Did you know that there are two ways to think about division?

Think about the problem
12 ÷ 4

Sharing Division: I want to share 12 cookies with 4 people. How many cookies does each person get?

Measurement Division: My string is 12 inches long and I’m going to cut off 4 inch pieces. How many pieces will I end up with?

They are both division problems, and they both have the answer of 3, but they create very different images!

When dividing with fractions like in this video, it is helpful to imagine measurement division (creating pieces that are ¹/₄ units long).

If you try to imagine sharing division, you would be sharing 3 cookies with ¹/₄ people 🤔

(Disclaimer: Sharing Division is actually called Partitive Division, but unless you’re teaching elementary school I don’t think it’s important to know that name)