Math manipulatives are an essential part of elementary education. For years my go-to manipulatives were base 10 blocks, fraction tiles, and pattern blocks. I used them with place value, subtracting whole numbers, and pretty much every fraction concept, including when I taught students to subtract mixed numbers. They did help my students learn, but these hands-on resources caused a lot of frustration. Not only did they take a lot of time to pass out and collect, but half of them would also wind up on the floor! Oh, and the noise…can we please make all math manipulatives out of foam? I soon discovered a much better resource that would end my frustrations for good.
The Magic of Unifix Cubes
In 2018, I attended Greg Tang’s conference and learned about the magic of unifix cubes. While I had these manipulatives in my classroom, students only used them during indoor recess. Unifix cubes seemed more appropriate for primary students than for 4th graders. However, my mindset changed when I discovered how Greg Tang implemented them with upper elementary skills.
For starters, unifix cubes are SUPER EASY to distribute and collect. I love how simple they are to assemble, and because of this, they are much less likely to end up on the floor. I’ve incorporated them when teaching prime and composite numbers, multiplicative comparisons, improper fractions, and mixed numbers.
My favorite skill to pair unifix cubes with is subtracting mixed numbers with regrouping. The first time I used them with this lesson, I was SHOCKED! My students actually understood what they were learning, and they were having FUN!
We then progressed to solving problems without manipulatives, and they still understood the concept. I’m not kidding…this strategy is PURE GENIUS! I wanted to give Greg Tang a gigantic hug and thank him for sharing his brilliant ideas.
So, how exactly do these manipulatives work with mixed numbers?
Step by Step: Subtract Mixed Numbers
To begin, have students model the mixed number or whole number they are subtracting from with the unifix cubes (see examples). For instance, if the denominator is 5, that means each whole is 5/5. So 2 and 4/5 would have two groups of 5/5 on the whole numbers side, and 2/5 on the fraction side. This is an important concept for 4th graders, so the first step alone is extremely beneficial!
Next, it’s time to subtract the fractions. With this strategy, students will see why they need to regroup. If they have 2/5 on the fraction side of their model, they can’t take away 4/5. By moving one whole over to the fraction side, they will understand why the 2/5 changes to 7/5. This is the most difficult step, and the unifix cubes make this crystal clear.
Finally, students subtract the fractions and whole numbers. Make sure to use a variety of denominators to reinforce how they affect regrouping. It’s also important to practice subtracting fractions from whole numbers (example 2). Students often struggle when there isn’t a fraction to subtract from.
Below is a video from start to finish with yet another example. This is from my Subtract Mixed Numbers with Regrouping PowerPoint lesson.
Resources to Get You Started
Are you ready to get started teaching with unifix cubes? I know you are! The work mat used in the examples above is FREE and ideal for your whole group lesson. Laminate or place the work mat in sheet protectors for repeated use.
Task cards are my go-to math resource because of their versatility. Whether used as a daily warm-up, practice for small group centers, or posted around the room for a gallery walk, task cards are effective and easy to use. The first set includes images of the unifix cubes to reinforce the whole group lesson. The second set is less guided without the models. The PowerPoint Lesson includes printable and digital activities to use in math centers.
What Teachers are Saying
Below are reviews from teachers who have used these task cards to teach students to subtract mixed numbers.
Brittanie: “I downloaded your free template using these unifix cubes and used it with my summer school students this year. They instantly made the connection and understood it better than they did during school. They were all saying things like “this makes so much sense now” or “this is so easy this way”.
Allison: “While teaching fully remote 5th graders, I knew subtracting mixed numbers with regrouping was going to be a challenge. However, this visual was key in helping be able to clearly explain and model the process and then have students practice using the manipulatives as well. Very well done and excited to use it with students in person for next year.”
Amanda: “My kids were so stuck on this until I used this resource! Next year I am going to start my unit with this! Thank you!!!”
It looks like I’m not alone in my love for this strategy! But, did you know that subtracting with regrouping isn’t the only skill they work well with? In Episode 26 of Elementary Math Chat, I share 4 other skills you can teach with unifix cubes.
This episode will make you love unifix cubes even more, so listen using the link below or through your preferred listening app!
https://krejcicreations.com/episode26
Until next time,
Happy Teaching!
P.S. If work mats are your thing, read this BLOG POST!