Recording Addition on a Hundred Chart
Make no mistake—the standard algorithm remains the goal for multi-digit addition and subtraction. But research and experience show that introducing students to alternate strategies first helps build the deep understanding they need to make sense of the algorithm when it is introduced. These strategies don’t replace the standard algorithm—they lay the groundwork for it.
In this post, we’ll explore how using a hundred chart to record addition can help students develop important reasoning skills around multi-digit computation that will support their long-term mathematical understanding. You might also like these posts: Adding on a 120 Chart, Exploring Addition Strategies, and More Mental Math Strategies.
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We’ll get to a pencil and paper freebie in a bit, but let’s talk about introducing the strategy using a 120 chart. We teach the patterns on the hundred chart—1 more, 1 less, 10 more, and 10 less—for a reason: they’re foundational for understanding place value. And they become especially useful when students use the chart to add and subtract. Think for a minute how you’d use the hundred chart to add the numbers 34 + 28.
Chances are, you used something similar to one of these methods:
- Start on the number 34. Count on 28 to get to 62.
- Start on the number 34. Jump down two rows to 54. Count on 8 more to get to 62.
- Start on the number 34. Jump down one ten to 44 and another ten to 54. Add 6 to get to 60. Add another 2 to get to 62.
- Start on the number 34. Jump down three rows to 64. Come back 2 to 62.
- Start on the number 34. Move ahead 6 o get to 40. Jump down two rows to get to 60. Move another 2 to get to 62.
- Start on the number 34. Count on 8 more to get to 42. Jump down two rows to get to 62.
Notice that there are many ways to solve this problem using the same tool. Our goal is to support students in using strategies that make sense to them while gently guiding them toward more efficient methods. For example, if a student is counting on by ones to move 28 spaces, it’s a great opportunity to meet with them and explore how the hundred chart patterns can help make their counting quicker and more efficient.
I wanted to come up with a way for kiddos to show their thinking on paper—something they could use for independent practice after we’ve done plenty of whole-class work. So I created this little freebie for showing addition on a hundred chart. One version has numbers included, and another leaves the number spaces blank so you can add your own.
I also made two more versions with space for kids to show their thinking on an open number line, like in the photo below. There’s no single “right” way to show the work, and that’s the beauty of it!
In my example, I jumped down 20, split the 8 into 7 and 1, used the 7 to go from 73 to 80, then added 1 to get 81. Another student might split the 8 first, use the 7 to go from 53 to 60, jump down 20 to 80, then add 1. Someone else might jump a friendly 30 from 53 to 83, then go back 2 to land on 81. All strategies are valid, and the more we see, the more flexible our thinking becomes.
You can grab your free download here! And check out this post to see how to record these strategies on an open number line.
This is perfect for my upcoming lessons!!
Beth
Thinking of Teaching
Oh good!! Glad the timing worked out so well. 🙂
Love this!!! Thanks for the freebie:) -Jill
My pleasure! 🙂
This is great. Loved how you used the open number line to show thinking.
Love the open number line!
Thank you! What a great concept.
I love this! I am always looking for ways to help my kiddos explain/show their thinking in math! Thanks so much for the freebie! I can’t wait to try it with my kiddos! 🙂
Thanks, Hilary! I’m with you–kids need to be able to explain their thinking in lots of ways, verbal and written.
Thanks for the sharing! I love the concept to easily help give a visual for the addition set…
Thanks, Heidi!
Teaching this tomorrow to be exact in my Envision lesson, thank you! This will be great to reinforce the lesson and to be used for practice. Thank you very much!
Well, how perfect is that? 🙂
I’m going to share this with my 2nd grade teachers. I’m sure they’ll love what you have to share.
❀ Tammy
Forever in First
Great!
Donna,
I am curious if you would use this with fifth grade students who still rely on their fingers to add. I would like to know your thoughts.
Thanks
Dianne
Absolutely!! Kiddos counting on their fingers in 5th grade need all the number sense instruction they can get. I would even work with them on strategies for basic facts. Check out this post: http://mathcoachscorner.blogspot.com/2012/05/it-all-adds-up.html
Thank you soooo much for your resources and ideas! In my 3rd grade classroom, we use the addition strategies you’ve been sharing recently. I’m big on helping the students understand how numbers work and on using mental math strategies. I was wondering if you have any ideas how to bridge the gap with parents’ “old” ways of doing procedural addition/subtraction strategies. I’m having a difficult time this year with my students insisting that “my mom said I have to carry the one” rather than using place value, compensation, friendly numbers, etc. and vise-verse with subtraction/borrowing rather than using a number line or counting up. I guess my question is how do I “teach” and/or share these strategies with my families in a positive and effective manner so that I can get them on board with the math their students are doing successfully in class and then going home and getting so confused with their parent’s reteaching??? Or, how do I embrace these methods in the classroom as well to help my students understand what their parents are teaching them? Thanks so much for any advice!
kstokes5@columbus.rr.com
I hear this so often!! Unfortunately, we have to educate the parents along with the students. I would suggest communicating with them the research behind using multiple strategies and share with them what some of the strategies are. Maybe a parent night or a sheet you send home? As for the traditional algorithm, we teach it along with the other strategies. The idea is for the kiddos to have a variety of tools, and it’s just another of the tools. Hope that helps some!
Donna, love this activity and will be using in class tomorrow with my second graders. Your ideas are so refreshing and really help the kids develop their number sense. I was wondering if you have any suggestions for a fun math station for a family math night that would work on number sense, but be geared to intermediate (4-6th graders). They still struggle with their math facts and I do believe it all comes down to number sense too..Thanks!
deb
Deb,
Thanks for the nice comments about my blog! The older kiddos definitely number sense as well. Check out this post and see if that might work for you.
I love this! I am vary anxious to see my students try this so I can really see their thinking patterns. Thanks for sharing! I really enjoy reading your blog and newsletters! How do you find the time?
Thanks!
I’m an empty-nester as of August when my son left for college, so I have some time on my hands! Actually, I just love doing it, so I make time. It’s a better way to spend an evening that watching reality shows! Ha ha.
Thank you so much for sharing this Donna! I am using so many of your wonderful ideas and activities in my classroom and am so grateful to you for sharing your knowledge! I really look forward to all of your new posts!
Linda
AroundtheKampfire
My pleasure, Linda! I love knowing that I’m helping out!
These are really great activities! I’ve downloaded mine and look forward to using them. PS I’m your newest follower!
Karen
http://littlesecondgradesomebodies.blogspot.com/
Glad you find the activities useful, Karen!
This is great!!
missthirdgrade.com
Thanks for leaving some love, Courtney!
Thank you for the great tool!
You’re so welcome, Patty! 🙂
Thank you so much! My students are struggling with open number lines. This will be very helpful.
Thank you so much! My students are struggling with open number lines. This will be very helpful.
So glad you think it will be useful, Hillary! 🙂
I absolutely love this! I especially like the tie in to the number line. Great job as usual!!!!
Wow! A group comment. Ha ha. Glad that this is something you ALL can use. 🙂
Thanks for sharing your resources. This year I’m with my two kiddos at home and I do my things but it’s very tiring. Your articles and resources give me ideas to work with them, and this one is awesome. I hope to use this one soon!! Glad to follow you on facebook. Many blessings!!
It’s my pleasure, Anna! Sounds like you’ve got your hands full. 🙂
Thank you so much for the freebie! My third graders, this year, are struggling immensely with adding and subtracting and hopefully a blank one in their working files will help them to get up and down the hundred chart a little better.
What third graders aren’t, Tess? This is definitely something that they might connect to.
This is perfect for our second and third graders, thank you so much for sharing all that you do! I LOVE your site!
You’re welcome, Pam, and thanks for the sweet comment!
I really like this way to show kids’ thinking. We’ve been using the 0-99 chart in our district. Do you have this (or could you make one) using a 0-99 instead of 1-100?
I’m sorry, Michelle/Gail, but I don’t have it in 0-99.
Thank you! I am going use this with my morning work. I really want to work on number sense. More and more am I convinced this is the secret to being successful in Math.
Number lines are awesome tools! Especially open number lines. So great for letting the kiddos show their thinking.
These tools are so helpful. Thank you so much!!
You’re welcome!
Donna, your blog is my homeschool maths textbook. You rock!!!! I can’t thank you enough!!
How cool! Glad you’re finding my blog helpful. 🙂
Awesome strategy! Thanks for sharing.
My pleasure, Tori!
We use a computer program called JiJi. They have these exact types of problem that my students always struggle with. This is going to be perfect to use to help them. Thank you!!
Sounds like a cool program!
I adore these sheets. This is how I teach Double digit addition and subtraction in second grade. They walk away with a much deeper understanding of the concept. Thank you so much!
Absolutely!! It really makes sense to them. 🙂
THANK YOU!!! I’m student teaching and I’m in my total teach! eeek! hehe and this just saved my life!
I started with my 100th chart by adding and now I’m introducing open number lines,so this links perfectly:)
Thanks a million!
-Kat
Thank you very much for sharing these pages. It brightens my weekend and makes me look forward to teaching again on Monday.
What a lovely comment! Thanks so much. 🙂
Just what I needed!! Thank you!!
Thank you so much! This will be perfect for my first graders!
oooooo, can’t wait to use this! love it. thanks for sharing clever lady!
I love this idea, I think it will help my 9 year to better grasp the idea of how skip counting can be so helpful in mental math.
Thank you for this freebie! It will come in handy for all ability levels in my classroom!
Thank you! I have some mathemagicians in my first grade class who are going to love this!
I would like to thank you for this great resource. It had helped my students to become more efficient in their math skills. The sheet is helpful because of the setup of the sheet. Students can see what they are doing on one page.
I love this! I was doing a Google search & this was exactly what I wanted. Thanks!!!
I love this! Thank you for taking the time to make this!
This is a wonderful resource! Thank you for sharing it with us.
Love this resource! I know it’s been a few years, but would you be able to make the same thing for subtraction? Or make a sheet with no equation on the top so it could be used for either addition or subtraction? Thanks so much for sharing your awesome resources with us!
I love this worksheet! My kids really liked the strategy as they have a 100 chart right on their desk. I am looking for some subtraction worksheets with the same strategy do you have any?
I don’t have any subtraction sheets, but you could use the same strategy using the little 100 charts.
I would love to see a subtraction resource like this as well. This is perfect for my second graders!