Strategies for Adding Strings of Numbers

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

I’ve been working with my 3rd graders on adding strings of numbers using the book 1001 Animals to Spot.  I just found out there’s a whole series of these books, so I might have to pick up some of the others.  The kids love looking at all the different animals, and we’ve had some great discussions about the animals and regions depicted in the book.

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As you can see from the picture, each page lists how many of each animal they can find pictured on the page.  During the first lesson, when I wrote the first string of numbers horizontally on my white board, I asked the students how they would go about adding all those numbers together.  One student responded that she would add the biggest numbers first.  The other kiddos agreed. Over the course of a couple of weeks, they’ve been learning that they can add the numbers in any order, and they should choose the numbers that make it easiest to add.

Let’s look at an example and some of the strategies the students have learned:

Notice that we crossed off the numbers as we used them and kept a running total of the animals. That was actually very difficult for the students (remember I pull intervention groups).  They understood combining the numbers, but didn’t understand why they needed a running total. To make it more concrete, I cut index cards in half and wrote the numbers on index cards, and we lined them up, just like the string of numbers. As they crossed off and used the numbers, we put those cards into a pile, so they could see that the numbers of animals we had “found” was getting bigger and bigger.

Click here for a copy of the strategies and here for a set of downloadable number cards. You will need to print several sets of the number cards to do activities like this, because the numbers can be repeated in the strings.

7 Comments

  1. Pat McFadyen

    Donna, I love sharing these strategies with my 5th graders, too! We definitely look for numbers that make tens, hundreds, or thousands. They seem amazed that you can add numbers “out of order” and keep subtotals. It’s great for number sense!

    Reply
    • Donna Boucher

      I agree, Pat! Many students have not learned these strategies, and they almost think it’s magic when they do!

      Reply
  2. Greg Coleman

    Great lesson! I really like how you pulled in a book to make learning more relevant. Kids love animals so I am sure this made the lesson more engaging.

    Greg

    Reply
    • Donna Boucher

      Absolutely, Greg! I even learned some new animals! 🙂

      Reply
    • Greg Coleman

      You could easily tie this into a science (animals) or social studies (habitats) unit as well. Great choice with the books!

      Greg

      Reply
  3. Margie Pearse

    I love it whenever we create moments for children to experience the workings of their minds. Our brains so naturally want to make sense out of what may look confusing. It is empowering for our little ones when they discover their natural tendency to find order in things. They are building schema for future success, and we know that experiencing success in something propels us forward.

    Love this idea! Love the interdisciplinary possibilities too!

    Reply
    • Donna Boucher

      There is absolutely nothing that compares with working with students in small groups, because of the insight it gives us into their thinking, Margie. So powerful for uncovering misconceptions!

      Reply

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