An Addition Algorithm

Posted on August 23, 2011. Filed under: Assessment, Common Core, During the Guided Math Lesson, Elementary math, Guided math, Manipulatives | Tags: , , , , , , , |

The New Math Common Core states that children will understand how to “add and subtract (depending on the grade level the number range varies)…using strategies and algorithms based in place value, properties of operations and/or the relationship between addition and subtraction.”

We have to really think about what does this mean in action? How does it look in the classroom?  How do we get fluent as a teaching community ourselves, so that we can teach this way.  I think one way to start is to have grade level discussions about how to operationalize this.

I do think that we should use small guided math groups to discuss different strategies because you want to give the students a chance to talk about their thinking.

Here are some examples of teaching partial sums.



What do you think of the way the teacher frames the method?

How does it make it more student friendly by saying we are going to “break-down” the parts. 

What do you think of the way that the teacher uses different colored pencils to highlight the parts of the problem?

In this next video notice how Eli is solving the problem by drawing out the base ten blocks.  What does this tell us about his understanding of place value?

Now look at this video of a teacher using technology to teach the partial sums method.

How does this instructional strategy of representing it differ from using the concrete base ten blocks?  Do you see how it clearly shows the relationship of place value while moving towards just the abstract representation – but using the pictures as the ongoing scaffold.

Look at these next two videos:

Video 1

Video 2  

What do you notice about the way that the teacher is talking about the numbers?  Notice how he says “5 tens or 50 ones.” Also notice the very step by step process that he uses to scaffold learning of the strategy.

Here is a Partial Sums Poster.

I wanted to share these videos because they offer different perspectives and nuances on teaching this algorithm.

Happy Mathing,

Dr. Nicki






Partial Sums Poster

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3 Responses to “An Addition Algorithm”

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Dr. Nicki,
I look forward to your blog enteries and always find them very helpful. I just want to thank you for all of your hard work.

You seem to accept that teachers should respect, be answerable to, and accept whatever the Common Core Standards say. I’m much less sanguine about them and wonder if your readers have considered questioning the notion that the “gods” of mathematics have spoken and we mortals have no choice but to obey. For that matter, I wonder if you’ve considered that notion yourself.

Hi Mike,
I think you raise a great issue. I think we should always think critically about the standards. Along with that, we all know that the standards are coming! Everybody except Alaska and Texas has signed up to implement them. So, I think we have to really talk about what that looks like. We have to consider how do we effectively implement them given that they are here to stay for a while. I also really like a great deal about the new standards. I think it is great how they are based in the research. I don’t think we talk about math research enough and so to see standards that tie directly to the research is exciting.

Happy Mathing,
Dr. Nicki

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