When Common Core came on the scene long ago there were many complaints (and still are today) regarding the invented strategies that teachers are to teach students in math. I heard over and over, “Why don’t you just teach them the old fashioned way (or even worse — the right way)?” I imagine you have heard that too. I found myself at a loss trying to explain to parents (and family, and friends, and…) why exactly it was “suddenly” different; though, I don’t think it was. I remember hearing in “teacher college” that everyday math (or was it still Chicago Math when I was in school?) incorporated something similar, trying to get students to think deeper about the math strategies. Nonetheless, it got me thinking: how can I understand and explain this better?

## Using Strategies or the Algorithm

**First, I researched…**

In case you are unaware, the standard algorithm in math strategies is where you line up the places and complete the problem starting on the right side with the ones, then the tens place adding in any numbers carried (or regrouping if subtracting), so on. You know, the ‘old fashioned’ way. Most kiddos can likely grasp carrying a one when adding, but when it comes to borrowing (especially with that pesky zero… Oh, the desperation that just one kiddo will get it!) it’s a whole different ball game.

An invented strategy is any of the math strategies other than the standard algorithm that does not involve the use of physical materials or counting by ones. These commonly become mental strategies over time after they have become tried repeatedly and are deeply understood. For instance, a student may choose to decompose a number or compensate. You can find examples of strategies for addition and subtraction here and multiplication strategies here.

**Then there were some differences…**

There are some major differences between a standard algorithm and an invented strategy. For instance, during a standard algorithm, students are focusing more on the digits rather than on the numbers through place value. Imagine the problem, 523+249. Students using the standard algorithm will think of 5 + 2 (digits) instead of 500 + 200 (place value numbers). When we start by thinking of the largest part of the numbers first, you are able to get a reasonable estimate then if you were to complete it based off of digits. Let me give an example. Take a problem such as 56 * 23. If you were to use an invented strategy, you would begin with the largest numbers first, being 50 * 20. If you estimate your answer, it is near 1000. This provides some sense of the size of the eventual answer in just one step. However, if you were to use the standard algorithm (just digits) beginning with 3 * 6 is 18, you then are completely unaware of the size of your answer until you reach the final step

Another beauty of using invented strategies is that there is more than one way to skin a cat (I hate that saying… I mean, who skins cats?). There are many methods or math strategies to solving the problem without having to do it just one way by carrying the one, on to the next column… *Yawn*. You don’t necessarily have a “right way” to solve problems.

There are a lot more benefits to using invented strategies. First, once it is actually understood and mastered (that’s the key — students have to understand why/how the strategy works), it is easier and faster. There are fewer errors made (research has actually proven this… Find the journal and look it up!) and students develop number sense. How many students who use the standard algorithm can actually explain why they are doing what they are doing when they do it? (Did you get that?)

When students use invented strategies, they are less likely to need reteaching. In the beginning, it will be slow and possibly time-consuming- but it pays off later once those underlying concepts are clearer. Students who use invented strategies use mental computation and estimation regularly. It creates a sense of confidence in their ability to learn math and builds their sense-making and reasoning. Finally, students who use invented strategies tend to do well on word problems by determining a reasonable estimate and eliminating multiple-choice items that are unreasonable.

So with that said, strategize!

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Kirsten says

So how do you deal with a child who is forced to use the invented method to fit CCSS but their mind works along the lines of the algorithm? I'm finding my child to be literal when it comes to math.

LisaH says

I've always heard them called "alternative algorithms" rather than invented strategies, but they have definitely been around for a while. I've been teaching for 17 years, and I learned about them in college back in the 90s! In other countries, those strategies are actually their "traditional" algorithms!

Anonymous says

In the example 56 x 23, wouldn't the estimated answer be around 1000? (50 x 20)

Tammy says

You are absolutely correct. Thank you for catching that error- guess it shows you I"m human! 😉 I have fixed it.