# How Children Learn Number Concepts: Place Value, Tens & Ones

### 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.

#### Place Value | Professional Books

Thanks for joining me for Book Study Mondays!  We are doing a virtual book study of Kathy Richardson’s book, How Children Learn Number Concepts.

Which brings us to Chapter 4, Understanding Place Value: Tens and Ones.  Richardson packs a lot of information into this chapter.  So much so, in fact, that it’s divided into two sections:  (1) Learning the Structure of Two-Digit Numbers and (2) Learning to Add and Subtract Two-Digit Numbers.

I absolutely love the way this chapter emphasizes over and over the connection between place value and the operations of addition and subtraction.  This is such a common breakdown in mathematics instruction in many classrooms.  Teachers teach multi-digit addition and subtraction with no reference to place value, and they don’t understand how important it is for students to understand place value prior to attempting multi-digit operations.  After reading this chapter, it should be crystal clear how integral place value is to truly understanding the process behind multi-digit addition and subtraction.

As with other skills, Richardson reminds us that students can appear to know more than they do.  Just because a student can identify the digit in the tens place of a number, it doesn’t mean they understand what that digit means.  To demystify the concept of place value, students need lots of opportunities to group objects into groups of tens and count those groups.  Translation?  They need lots of concrete practice composing and decomposing numbers in different ways.

As I read the critical phases related to understanding the structure of tens and ones, I noticed how well aligned the 1st-grade common core standards are with the phases outlined by Richardson.  It’s all in there: understanding that a ten is a bundle of ten ones, understanding the structure of the numbers from 11-19, counting tens, mentally finding ten more and ten less, and subtracting multiples of 10. This chapter is an excellent resource for teachers trying to understand and implement the CCSM.

We are reminded that knowing the parts of numbers to 10 supports an understanding of place value.  Students who still don’t know parts of numbers should continue working on that skill as they move forward with place value.

Up next is adding and subtracting two-digit numbers.  This section makes my heart sing!  I love the use of ten-frames to show how numbers can be “reorganized.”  Isn’t that a much friendlier term than “regrouping.”? The pictures and captions Richardson uses make the concept very clear.  But what’s also clear is that teachers need to be working in small groups or individually with kiddos to truly assess their understanding of the phases.  Take, for example, the activity on pages 98-99.  Unless the teacher interacts with the student while doing that activity, there’s no way to determine how the child arrived at the answer of 13.  And it’s how the child did it that indicates which phase they are in.  Moving to larger numbers, the examples on pages 104-110 show how vital it is that children have the opportunity to discuss their strategies.

As the chapter wraps up, there’s a final reminder that models help students make sense of the math they are doing.

Checklist, Word document (editable)
Checklist, PDF (better formatting)

1. Okay…I think I will probably go broke because of this blog and wanting to get all the books you recommend. I bought Mastering Basic Math facts and am well into it, and I am thinking of getting this one now! I have kind of adopted you as my very own math coach, as my school doesn’t have one!!

• I know what you mean, but you NEED this one. This book, together with the Mastering books, are a great foundation. Thanks for adopting me. 🙂

• Do you come to schools? I think you are awesome and I would love for you to come to my school and speak. We are in the Houston area:)

• Yes, thank you for contacting me via the Speaking Engagement page. 🙂

2. I adopted her a long time ago!!! You are great Donna! I have to say I have only gotten to read about 2 pages of chapter 4…end of the year stuff catching up with me! I will definitely read the posts on here and catch up by next week!!!! 2 more days!!!!
Amy Burton

• Hey Amy! Yes, Chapter 4 is long, but good!! Enjoy your last 2 days. You’ll have PLENTY of time to catch up soon! 🙂

3. Lots of information in chapter 4! She has such a good way of explaining how kids think. Makes me think of my kids and where they are at while I am reading. I teach in a small rural school grades 1 and 2. I am thinking of some I need to spend some time with in 2nd before they move on to some new concepts.

4. Lots of information in chapter 4! She has such a good way of explaining how kids think. Makes me think of my kids and where they are at while I am reading. I teach in a small rural school grades 1 and 2. I am thinking of some I need to spend some time with in 2nd before they move on to some new concepts.

• That’s the beauty of this book! You can pinpoint the phases of your kiddos. I’ve been the same way while reading–I just want to be in a classroom trying this stuff out on the kids. 🙂

• It is once again available on Amazon!