# How Children Learn Number Concepts: Number Relationships

### 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.

#### 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.

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

In the introduction to Chapter 2, we are reminded that when children first learn to count, they are simply labeling the items they are counting.  To move forward in their mathematical understanding, they must realize that larger numbers contain smaller numbers.  Interesting that throughout this chapter Kathy never uses the words compose or decompose, yet that is exactly what she is talking about.  She uses the example that 4 is contained within 6.

Ah, comparing numbers.  From my own experience, I knew that how many more was a difficult concept, but I felt validated when I read it in print.  Big ah ha moment in this chapter–when you ask a child how many more? they are often answering the question how many in the group with more?  I always knew it was a common mistake to simply state the number in the bigger group, but now I feel like I know why.  Another key idea that we need to keep in mind is that this task becomes more or less difficult depending on the size of the numbers used and the differences in those numbers.  So a child might feel comfortable determining that 7 is 2 more than 5, but might struggle with the difference between 6 and 11.  Also, and I think we knew this, children are able to compare groups that are lined up before they can compare groups that aren’t lined up.

Are you loving this book?  It lays out a crystal clear math trajectory, so to speak.  And what an amazing diagnostic tool!  With simple, quick tasks, teachers can pinpoint exactly what phase each student is in and can tailor instruction to each individual student’s needs.

Here’s the checklist for the phases in Chapter 2.  Next week, Understanding Addition and Subtraction.  Have a great week and happy reading!

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

1. I think I have this book! If I do,, I’ll link up. Your major haha moment was mine too (from your post). I always wondered why so many kids told you “how many more” was the actual amount in that group.
Thanks!
Barbara
Ruby Slippers

• I know! It’s so nice when one of life’s little mysteries is solved.

BTW, it should be a “You know you’re a teacher when…” when you say you THINK you have this book. Ha ha. I do that all the time. “Hmmmm, that book looks so familiar. I think maybe I own it!”

Donna

2. Hi Donna! Again, I thought this chapter was an easy chapter to read and made perfect sense! I have honestly never thought of asking a child to change a number without telling them how to change it. That is certainly a different type of skill and seems obvious, now that I see it in print, that it should be practiced before using math symbols!!!!

The “how many more” discussion really peaked my interest because my students ALWAYS have a difficult time with this concept! For the most they can do it if the two sets of objects are in nice neat rows that offer an easy comparison! I always try and relate it to words they might say to their friends… “that’s not fair I have 2 and you have 5…you have more than me!” I even bring kids up to the front of the room and act out “friend” situations that may help explain this concept. Usually, only my good math thinkers that really understand story problems and how to solve them can get this concept when the two sets are not shown in rows.

I LOVE your sheets for each chapter. Whether I am in K or 1st next year, my goal is to use this book!!!

Amy Burton

• Hey Amy,

Can’t wait to work with my teachers on this next year. I started reading Chapter 3, and it’s going to be great!

Donna

3. “For example, if you ask a child to change 7 to 4, they would count from 1 to 4 and remove the three extra counters. If they count back from 7 to 4, it signals an entirely different level of understanding.”

Yes – and we also need to teach children the Number Word Sequence for counting backward, so when children develop the understanding that 4 is part of 7, they know the correct sequence of numbers to count backward.