 ### How You Can Use Addition to Teach Place Value

If you are on Facebook, surely, you have seen rants about how Common Core Math is the WORST. Seemingly elaborate diagrams are drawn to add simple numbers such as 19 + 6. Students are drawing number bonds to break apart the 6 into a 1 and a 5, are circling numbers, writing new equations. All to solve a relatively simple problem.

No one intends for our students to go through all of this to solve problems such as 19 + 6 in the future. The purpose of the activity is to use the operation of addition as a tool for teaching place value, number sense, and properties of operation.

Rest assured, the procedure and algorithm will be taught further on down the line. Take a look at the standard at grade 4:
Fluently add and subtract multi-digit whole numbers using the standard algorithm.

However, prior to grade 4, let's use the operation of addition to teach and learn as much about place value as we can!

In grade 2, students are expected to:
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

So what does a "strategy based on place value" look like and how will this benefit our children and students? Take the expression 27 + 32. In the standard algorithm, you would stack the numbers, add the 7 and 2 and then add the 2 and 3. You would get a result of 59 and you would be absolutely right. Is there anything wrong with this algorithm? No!
... Unless that is you were hoping to teach place value concepts. I am going to walk you through a MUCH LONGER method. The purpose of this method is NOT to teach an addition procedure that a student would be expected to use for the rest of their life. It is to take advantage of adding to teach the concept of place value in a meaningful way.... not to mention that understanding place value allows students to be flexible in their ability to perform mental math! First, a student would decompose 27 into 20 and 7 and 32 into 30 and 2. If you were to do 27 plus 32 in your head, it is likely that this is the first step that you might take.

As adults, we flexibly break numbers apart so that we are able to do mental math. A child often thinks the number 27 just simply means "two seven" if they aren't grounded in place value.

Next, a student would be asked to put the tens together. As adults, we know that 27 + 32 is the same as 20 + 30 + 7 + 2 but a student learning the traditional algorithm learns nothing about the flexibility of numbers!

The step of putting 20 and 30 together in and of itself is a powerful step in learning about place value. Students can see that adding 20 + 30 is really as simple as adding 2 + 3. If 20 means two tens and 30 means three tens, 20 + 30 is really just putting 2 tens and 3 tens together. 5 tens = 50. More on adding decade numbers mentally HERE.

Remember those viral Facebook posts? I'm sure the comments would be running WILD right now after my last paragraph.

Yes. This is A LOT more steps.

Yes. There is significantly more opportunity for error in these steps.

Yes. Yes. Yes.
But I'm not teaching the procedure of addition. I am teaching place value concepts by USING addition and I am developing flexible thinkers who, someday, will perform mental calculations with ease.

After adding the tens together, students combine the ones together. If you are thinking to yourself "WAIT! What if the ones make a new ten?!" No worries. That's a lesson for another day and just THINK about the place value learning that will take place in that discussion!

Lastly, students combine their group of tens and their group of ones to find their total.

There is so much power in teaching place value through the use of operations.  Ignore the viral Facebook posts, trust your training, and develop students who understand not only addition but place value too!

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