The Path to Unitizing

By on Aug 10, 2015 in Blog, Blogs about Subitizing and Unitizing | 0 comments


Do your students still use their fingers or count manipulatives to solve simple math problems? Our goal as teachers is to provide math experiences in which students understand numbers and their relationships in order to solve problems using non count-by-one strategies.


Robert J. Wright, et al., 2012, in the book, Developing Number Knowledge, states:


"It is critical that students' early arithmetical thinking progresses from being based on counting by ones to being based on structuring numbers.” 


Here are some examples of students’ strategies for solving simple addition facts. Notice the valuable information you can get by having students explain their strategies in writing. Who is still using count-by-one strategies including counting on and who is using non count-by-one strategies?


We want to help our students achieve the developmental milestone of unitizing. Unitizing can be described in a variety of ways. Many definitions of unitizing in math refer to the place value understanding that ten ones can also be thought of as a unit of ten. Unitizing is also described as the understanding that numbers can be organized into groups and these groups can be counted as units.


Robert Wright discusses “unitizing of parts and wholes: combining smaller numbers to make larger numbers, and partitioning larger numbers into smaller numbers.”


Kathy Richardson (2012) in her book, How Children Learn Number Concepts, states: “Children reach a deeper level of understanding of ten as a unit if they first work with various smaller groups. Forming and counting smaller groups helps children focus on the processes of grouping and regrouping, make the appropriate generalizations, and provides a foundation for understanding base ten.”


We can provide students with rich experiences with numbers that will help them travel down the path to developing a strong ability to unitize.


I have created a Math Path to help teachers understand the learning progression of structuring numbers (combining and partitioning numbers to 20).


Math Path for Structuring Numbers up to Ten:

  • Subitizing
  • Combinations of 5
  • 5 and Some More
  • Doubles to 10
  • Near Doubles to 10 (plus or minus 1)
  • Combinations of 10


Math Path for Structuring Numbers up to Twenty:

  • 10 and Some More
  • Doubles to 18
  • Near Doubles to 18 (plus or minus 1)
  • 9 and Some More
  • Combinations of 20


By using appropriate tools, students can develop a strong understanding of numbers and their relationships.

These are some of the tools I use:



I also use the materials in the Teacher Toolkit and the Multiplication Decks.


Click on the image below to learn more about the Teacher Toolkit.


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Click on the image below to learn more about the Multiplication Decks.


multcontents.jpg #7


You can find many ideas and activities on our website to help students develop non count-by-one strategies and move them along the path to unitizing. Check out my blog and the pages under the Ideas tab, especially the Intervention page that includes many videos of activities.

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