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I fell in love with Backwards Math in 2013, when I first saw it. I have no idea who to credit, but they made my second graders and me very happy. The way that I first saw backwards Math was similar to this:

"The answer is 22 stickers. What is the question?"

I loved seeing my students think creatively to come up with real world situations and I loved seeing how excited and proud they were to share their situation. From there, I decided to create Backwards Math equations and incorporate it into their daily routine. The creation looked something like this:

______ + ______ = 75


______ - ______ = 75

On Fridays, we were really feeling ourselves and they did problems like this:

______ + ______ - _______ = 21

This was one of our favorite routines in Math. I really loved it for so many reasons.


1. It is already differentiated! Students could choose whatever numbers equals the answer. In reality, they could choose that number plus zero and be accurate. However, my experience in my classroom is that students rarely do. Students want to come up with an impressive equation. It was normal for me to see students truly push and get hung up thinking of other numbers to fill the blanks, even though they already knew several numbers that could fill the blanks. Trust me, if you create an environment of high expectations students will not try to take the easy way out and do the bare minimum. They will push themselves!

2. Students were able to be creative. Their is joy in students getting an answer correct, but I've found greater joy in seeing how my students can creatively come up with something that is correct...ON THEIR OWN. The top is off with Backwards Math. Many times, I have been genuinely impressed by the things they come up with. It gives me so much information about how they think. That was something that I standard answer to an equation could not give me.

3. It gave me valuable data on the child without the traditional form of an assessment. Students were free to choose whatever numbers they wanted to fill the equations. Over time, I could notice patterns in the numbers students chose regularly.

The Breakup:

As much as I loved Backwards Math, for some reason for years I stopped using it consistently. I knew the good outcome from it. I knew the positive changes that it made. I knew how it was already differentiated. However, for some reason I did not have a place for it in my daily Math routines over the years. I would occasionally use it, but it wasn't a daily routine. I would continuously tell myself that I would find a strategic way to incorporate it back in. And then one day, after repeatedly trying to deepen my fourth-graders understanding of division. I realized that Backwards Math was exactly who I needed back in my life. I first started using it again with division, then I incorporated into our fractions.  


Backwards Math is back in my life, but in a much more strategic way. Nothing is wrong with the way Backwards Math was, but I also made a couple of changes to extend my fourth graders thinking even more. Some examples of how I do this is:

_____ + _____ = 6/10

After students answer I might add a "rule":

  • That one fraction has to be greater than half. In that particular case that means that it should be 5/10 + 1/10.

  • The addends must be the same. In that case, it means it should be 3/10 + 3/10.

  • One addend must be equivalent to 1/5. In this case, students would need to have one of the addends as 2/10.

These are just examples of how I push students' thinking towards a certain direction after they have already created their first one and proudly shared out their different ways. There are many "tweaks" that can be made or quickly added to Backwards Math to push your students thinking!

So, I encourage you to make Backwards Math a daily routine in your classroom.


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