Play-by-Play: Dividing Fractions When Key Math Tools Are Missing /4
(Part 4 of Catching Up in Math—A Real-Time Example)
New to TimeTrek? This is the final post in a series on catching up in math. You can find links to the whole series at the bottom of this page or start at Part 1 here.
Welcome to Part 4 of The How-To Guide for Catching Up in Math. Curious how it all comes together? This post is an walkthrough example of what a math lesson might look like. Keep in mind this is simply a snapshot of what’s possible and so much of how each lesson will go is determined in the moment. Let’s get started.
Imagine your child sits down to work on Dividing Fractions. They’ve already studied the lesson and moved on to the practice problems. The first question says:
✏ "Solve: 2/3 ÷ 1/4"
They correctly rewrite it as 2/3 ÷ 1/4 → 2/3 × 4/1 and multiply across to get 8/3.
They stop and look at the problem.
🗣 "Okay, I'm done."
You glance at it. They got the right answer, but forgot to simplify at the end. You ask:
🗣 "Can we simplify this?"
They hesitate. "Uhh... I don’t think so."
This tells you they aren’t fully recognizing the need to simplify fractions or understanding why we simplify in the first place.
1️⃣ Make Math the Priority
✅ You’re starting with math first today, keeping lessons consistent so that progress can build and skills stay fresh.
🗣 “Let’s start by figuring out if our answer can be simplified, then we’ll come back to dividing fractions.”
By focusing on math first, you ensure it doesn’t get pushed aside and that foundational skills are reinforced daily.
2️⃣ Connect Every Lesson to What They Already Know
Before starting, you connect today’s lesson to what they already know.
🗣 "Yesterday, we multiplied fractions. Today, we’re doing division, but notice the difference is we flipped the second fraction first - that flipped fraction is called the reciprocal."
By framing today’s lesson as a continuation rather than a new, separate topic, you make it feel more manageable. By referring to the topics by their math terms, it gives your student a name to use in solidifying this skill as a math tool. Make sure they’re writing down any math terms introduced for easy reference later.
3️⃣ Layer in Missing Skills Instead of Dropping a Grade Level
Now you focus on the gap: Simplifying fractions.
🔹 Quick Intervention
They pause when asked if 8/3 can be simplified. You guide them through the process:
🗣 "Simplifying means finding an easier way to write a fraction. We do this by looking for common factors. What numbers go into 8?"
✅ Step 1: Find common factors.
🗣 "What numbers go into 8?"
✅ It takes a few minutes, but they say: 1, 2, 4, and 8. You take note that there are likely gaps in multiplication tables, but do not interrupt to address it at this moment.
🗣 "What about 3?"
✅ They say: 1 and 3 - it’s a prime number.
🗣 "Good! and since 3 doesn’t go into 8, do they share any factors other than 1?"
❌ Nope.
🗣 “Since 8/3 is already in simplest form, you can move on to writing it as a mixed number.”
✅ 8 ÷ 3 = 2 remainder 2 → 8/3 = 2 2/3
You take note that your student will need some long division practice - since they know the steps but had some difficulty determining the remainder.
🔹 Immediate Practice
Now that they understand simplifying, you reinforce the skill with three quick examples:
✅ 5/10 simplifies to 1/2
✅ 9/4 converts to 2 1/4
✅ 20/16 simplifies to 5/4 which then converts to 1 1/4
They start recognizing common factors more easily. If this is not the case, you may choose to return to the full formal lesson on simplifying fractions in their math curriculum.
🔹 Return to the Lesson
You have them apply what they just learned with another division problem:
✏ Solve: 6/8 ÷ 2/3
They correctly rewrite it as 6/8 × 3/2, multiply to get 18/16, and immediately recognizes the need to reduce to 9/8 and covert to a mixed number 1 1/8.
This reinforces both dividing fractions and simplifying. If they’re still not getting it or if they need more practice, it’s okay to move on to practicing dividing fractions since they understand the division well and will be able to continue practicing simplification throughout the lesson.
4️⃣ End the Session on a Positive Note
Today we learned:
✅Dividing Fractions - which is just like multiplying fractions except you multiply by the reciprocal
✅Simplifying Fractions - reduce to simple form and convert improper fractions to mixed numbers.
Today we realized you could use some practice in:
✏ Using multiplication tables to determine the Greatest Common Factor.
✏ The steps to long division (it gets complicated when the numbers are longer!)
🗣 “That was tricky at first, but you figured it out! How do you feel about dividing fractions now?”
If they feel confident, you ask: 🗣 "Awesome! Do you want to do a couple more tomorrow, or are you ready to move to something new?"
If they’re unsure, you adjust: 🗣 "That’s okay! We can practice a few more tomorrow before moving on. Do you want to try some word problems next?”
You let them help decide the next step, giving them ownership over their learning. You can guide the decision, making sure not to move on unless you’re confident in their new skills or have a plan to work them in later.
🗣 "Great work today. Go take a fun break before we do Language Arts - you earned it!"
Final Takeaways from This Lesson
✅ Math stayed the priority - It was tackled first and is reinforced daily.
✅ The lesson was connected to what they already knew - to make it feel like a continuation, not a new challenge.
✅ A foundational skill was addressed naturally - They strengthened simplifying fractions without having to go back a lesson unless completely necessary. You made note of skills that could use sharpening.
✅ The lesson ended with confidence - letting them participate in setting up tomorrow’s lesson and keeping motivation high.
In Review (Still with me?)
Even though the lesson may have taken longer than anticipated, you tackled everything that came up. Along the way, you addressed gaps immediately - helping your child build confidence and stay on track instead of continue to build on top of missing skills.
This dynamic approach of identifying gaps and filling them as they arise allows your child to master the concept without feeling overwhelmed or “behind.” This strategy can be introduced in virtually any math where a student is having difficulty connecting past material to the current lesson.
Not Great at Math? You Can Still Teach It!
Worried that your own struggles with math will hold your child back? You don’t have to be a math expert to teach math effectively. You don’t even have to be all that good at it even. The key is focusing on problem-solving, recognizing patterns, and using the right tools - just like your child is learning to do. Grab a good resource (I recommend this one for 5-7th grade, maybe also this workbook to follow along if you need more practice).
📌 Need more tips? Check out my article on teaching math when you’re not a math person for practical ways to teach math confidently, even if it was never your strong suit!
Thanks for reading! This is where I share general insights and strategies from my own family’s experience and from working with other homeschoolers. Every child’s journey looks different, but these principles can apply across the board. If you’d like to see more, follow along on 𝕏 TimeTrekFam for daily updates and general shenanigans and click below to subscribe for free on Substack for the real content!
