Some people call them number talks, but showing your students a series of problems or visuals during math and investigating the relationship between those problems is actually doing Number Strings.

I’m Christina Tondevold, The Recovering Traditionalist, and today we’re going to take a look at what are number strings and how to make them in our quest to Build our own Math Minds so we can Build the Math Minds of our kiddos.

Watch the video or read the transcript below:

Here are links to products/activities mentioned in this vlog.

Number Talks: Whole Number Computation and Number Talks: Fractions, Decimals, and Percentages by Sherry Parrish

Cathy Fosnot’s Minilessons

• Minilessons for Early Addition & Subtraction
• Minilessons for Extending Addition & Subtraction
• Minilessons for Early Multiplication & Division
• Minilessons for Extending Multiplication & Division
• Minilessons for Fractions, Decimals, & Percents

I misspoke in the video it was Cathy Humphreys & Ruth Parker who did Making Number Talks Matter

Number Strings vs Number Talks

To start off, I just want to explain the difference between a number talk and a number string.

The original number talks were by Cathy Humphreys and Ruth Parker and they described number talks as one problem or one visual where you talk about all the different ways kids see it, think about it, solve it, etc. On the other hand, a Number String is typically a series of problems or visuals that are related in some way.

People tend to interchange number talks and number strings because there was a book called “Number Talks” that really showed number strings. So I just wanted to clarify that before we get started. If you want to dive deeper into the difference between number talks and number strings, I have a video that you can check out here.

Number Strings and Helper Problems

A Number String is a series of problems that are related in some way and typically, there is what I like to call a ‘helper problem’ that goes along with it. Cathy Fosnot’s Mini Lessons is where I first learned about number strings and I put some links to those mini lessons right under the video above.

So, there is a helper problem that is typically something your students will understand quickly. Then, you show a problem that relates to that helper problem and discuss what kind of relationships kids are seeing. You don’t want to point them out. Instead, you want to be asking questions and getting the kids to talk about the relationships they see. I usually like to start out with visuals first because that’s where most kids will need to start.

After the helper problem, you give them a problem that’s a little bit harder but relates to the helper problem. Then, you’ll give a similar helper problem, and then another one that relates to that.

For example, our text books try to teach us ‘doubles + 1’ for addition. In other words, use the double and chunk out the 1. So if it’s 6 + 7, just think about that as 6 + 6 and add 1 to what you get. The issue is, a lot of kids don’t see how 6 + 7 relates to 6 + 6 even though we do a couple lessons from the text book.

So, you can create visuals that show a 3 + 3, then a 3 + 4. That’s a 3 + 3 + 1. With the visuals, you’re helping them see the numbers within the doubles. You could show a 6 + 6 and then a 6 + 7 visually to help them see the 6 within the 7.

So you’re starting with the 6 + 6 helper problem, then you’re showing the double + 1 afterwards. Then you just keep showing problems in that order. Double, then double + 1. After you have done that for awhile, then you might start by showing the double + 1 without showing the helper problem first.  That is kind of the typical make up of how number strings work.

Number Strings Can Be Images or Symbols

Number strings can be with images or abstract symbols. Here’s some examples from a slide deck that we have created for our members of the Build Math Minds PD site.

This one is showing a visual using ten frames and a popular multiplication strategy.

I start by showing 10 groups of 4, then 9 groups of 4:

Then, we have a discussion about what the kids observe. We could then do the same process with other problems. Like 10 groups of 6, then 9 groups of 6.

10 groups of 3, then 9 groups of 3…

You could then finish the number string by showing one without a helper problem like 9 groups of 5 and ask them, “based on what we’ve talked about in this string, whats a way that we could think about this problem to help us out?”

Now, not everyone in your class is going to come up with it. But that’s why we need to do number strings A LOT in order to see those relationships.

Again, we don’t have to just use images in our number strings. Here’s an example where we write it out in words instead.

I’m still using ‘groups of’ to remind them that multiplication means groups of and I want to illicit that visual that we have used before. You can even move into strings that are even more abstract like this one.

And again, maybe you show some without helper problems depending on where your students are at with it. But always start with a few helper problems.

Number strings are a great 5-10 minute activity you can do with your students to help them look for relationships between different visuals or problems.  This is one of the best ways to help your students discover strategies for addition, subtraction, multiplication, and division without you directly teaching those strategies.

Conclusion

You can find pre-made number strings just by Googling but I want to encourage you to try out making your own based upon what you see your students needing and connections & relationships you want to help them build.  For those of you who are members of the Build Math Minds PD site, we have a more in-depth video for you about number strings and a bunch of pre-made strings for addition, subtraction, multiplication, division, and fractions…BUT they are all editable so that you can use them as we have or you can modify them to be what your students need at the time.

I hope this helped build your math mind so you can build the math minds of your students.  Have a great day.

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