How Children Learn Number Concepts: Numbers as Hundreds, 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.

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.

Use the links to step through the entire series of posts:

Chapter 1, Understanding Counting
Chapter 2, Understanding Number Relationships
Chapter 3, Understanding Addition and Subtraction: Parts of Numbers
Chapter 4, Understanding Place Value: Tens and Ones
Chapter 5, Understanding Place Value: Numbers as Hundreds, Tens, and Ones
Chapter 6, Understanding Multiplication and Division

“When children can think of hundreds, tens, and ones flexibly, it is not a big leap to add or subtract.”

While many of the concepts in this chapter mirror those in Chapter 4, Richardson points out that working with numbers to the thousands adds another level of complexity that may be difficult for some kids. At this stage, they have to hold more and more in their head as they work with larger numbers.

A couple of points stood out to me in the introduction to the chapter.  On page 118, Richardson talks again about reorganizing numbers.  Every time I hear that phrase, I like it more.  On page 119 she points out that students should not trade one type of block for another at this stage.  Instead, they should simply reorganize them, for example, grouping 10 tens together to make a hundred.  I found that really interesting since trading is a big part of most place value instruction.  Something to keep in mind.

Fascinating, isn’t it, that the work related to combinations for 10 in Kinder and 1st  is foundational for understanding hundreds and thousands?  It’s critical as students work with larger numbers that they are as fluent with parts of hundreds (30 + 70) and thousands (300 + 700) as they are with 10 (3 + 7).  Very cool.

A final thought–at least three times in this chapter, Richardson mentions that learning place value takes time. I wonder how much time we typically spend on place value in 1st, 2nd, and 3rd grade, especially in relation to the time spent teaching multi-digit addition and subtraction.  And I wonder how well we make the connection between place value and addition and subtraction.  I’d love to hear your thoughts on what changes you see yourself making in the classroom based on what you’ve read so far.  What were your big ah ha’s?

We’ll wrap up next Monday night with Chapter 6.

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


  1. Amy B

    While I don’t teach numbers this high, it was interesting to connect how the student’s understanding of 10 can help them when working with number later in higher grades. Next year, I also plan to introduce my students to place value even though many may not understand it! I will be using unifix cubes when counting up the days of the week. Once we reach 10, we will make a tower of 10 etc…I have already at the end of this year tried to make sure I took my lessons thru CRA steps. I think they are so important and can’t believe I have always been doing it before. Moving to kindergarten next year will allow me to see my students move through the stages of counting. I have enjoyed this book so much, especially the first 2 chapters!
    AMy Burton

  2. lcooney

    My ah ha’s keep coming up the same. I need to take more TIME. My kiddos need more time to work on the place value and number concepts. Love the book and your blog!


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