by C. Elkins, OK Math and Reading Lady (updated post on 8-12-17)
The term “subitize” means to recognize quantity without counting. It is a concept recently added to the new OAS (Oklahoma Academic Standards). KG students should be able to “recognize without counting the quantity of a small group of objects in organized and random arrangements up to 10.” For first graders, the quantity is increased to 20 of “structured arrangements.” Subitizing is an important pre-requisite skill to learning addition and subtraction number combinations or number bonds.
Suggested items for the teacher to present this concept:
- Dot cards
- Ten frames and 2-color counters or tiles
- Dot dice
- Tally marks
- Number Talks: Helping Children Build Mental Math and Computation Strategies by Sherry Parrish 2010 (mathsolutions.com)
- Subitizing Flash Cards by Liv To Teach ($3) http://www.teacherspayteachers.com
- Giant Magnetic Ten frame: Nasco (www.enasco.com) item # TB25547T for $19.50 or www.Lakeshorelearning.com for $19.99 item # PP939.
Teaching Ideas: Most KG and First grade students can recognize quantities of 1, 2, or 3 without counting, so I will focus on 4 and up.
Using Ten Frames:
- Provide each student with a blank ten frame. The teacher needs one to model with (large magnetic one is great, or use your document camera and projector).
- If you are working on the number 4, model for students one way to show 4 on a ten frame. Suggestion: Show them 4 across the top row will leave just one empty spot, because when the whole top row is filled, there are 5.
- Another suggestion to model: Place 2 on top and 2 on bottom (to form a square). This will start to reinforce that 2 and 2 make 4.
- Have students show these same representations with their ten frames.
- Direct students to show other ways to make 4. See possible examples in the pictures. Ask, “How many different ways can you make 4?”
- You could record their discoveries on an anchor chart or poster. If needed, students could record their responses using mini ten-frame templates on a worksheet.
- When ready for other quantities, repeat this procedure (see pictures for 5 and 6 as examples). Build on the known quantities and arrangements to learn the new.
Using Dot Cards
- Have sets of dot cards available for use. They can be on five or ten-frame cards, or presented in other structured arrangements (see pictures). These are available commercially or you can make your own with dot stickers.
- With your students in close proximity, quickly show a card and then cover it up. The idea is to see if students can determine the quantity without physically counting the objects. Ask them, to give a signal (such as thumb up) when they have a quantity in their head. Then randomly ask students, “How many did you see?” Observe students when you flash the card to see who is trying to count them, who responds quickly, etc.
- Don’t forget to ask, “How did you know?” This is a very insightful question. If you showed 6, did the student see the 3 and 3 arrangement? Or did they see 5 and 1 more? Or maybe 2, 2, and 2. This shows students are on their way to subitizing!
- Consult the book, Number Talks, for a much more in-depth view of this practice. Some number talk videos are also available to view on youtube.com.
Morning Meeting / Calendar Time / Work Stations
Reinforce the concepts you have worked on during your daily morning meeting throughout the year. Utilize other visuals to practice subitizing (such as dot dice, dominoes, tally marks, or finger-counting pictures to 10). There are many visuals available on Pinterest and at TPT if you put “subitize” as your search. I listed my favorite above (Liv to Teach). If you work on a number of the day, students could be responsible for posting a visual picture of the quantity with these different representations.
With subitizing cards at work stations / centers, students can match numerals to quantities, flash to their friends, or repeat the activities you modeled with them on their own (How many ways to make 7?). Here are some more tips on helping children build on their knowledge to subitize larger quantities:
Four: in a row, in a square (so they see 2 + 2), with 3 in one row and 1 in another, in an L shape, etc.
Five: With a dice, the 5 are arranged with a square (4) with 1 dot inside — so then they relate 5 as 4 + 1 or 2 + 2 + 1; With 5 on a ten frame, they see the top or bottom row fully filled; A set of tally marks is five, as are the fingers on one complete hand.
Six: Like on a dice, they could see it as 2 + 2 + 2 or 3 + 3 or 4 + 2; With a ten frame, they can arrange dots with a full row of 5 and one more on the second row, or with 3 on one row and 3 on the second row.
Seven: This builds on above with ten frames — A full row of 5 plus 2 on the second row; or 4 on the top row and 3 on the bottom row which helps them see that 7 is the same as 6 with one more.
Eight: Build on a ten frame with 5 in a full row and then 3 on the bottom row; or 4 on the top and 4 on the bottom; or 2 + 2 + 2 + 2.
Nine: Make sure they see that if all of the sections of a 10 frame are filled in except one is the same as nine; or the top row (5) and the bottom row (4); or they may see it as 4 + 4 + 1 more.
Ten: The whole ten frame filled in is ten; 2 hands; 2 sets of tallies, 1 base ten rod
Eleven – Nineteen: A full ten frame or base ten rod plus one of the above combinations. Do not expect students to subitize with random dot arrangements for these amounts.
Twenty: Two ten frames; 4 hands; 4 sets of tallies; 2 base ten rods.
Added Note: When students are using base ten manipulatives to make a number (i.e. 37), I teach them how to arrange their ones cubes into structured arrangements so that they and I know immediately they have made the number correctly. So in this example, their 7 ones need to be arranged in rows of some kind (5 + 2 more like on a ten frame, or in 2 rows of 3 with 1 more, or in 3 rows of 2 with 1 more). This allows the student to practice subitizing, as well as showing understanding of how the number can be broken apart. A big bonus to the teacher who is observing. I can tell at a glance if they have the number correct. I do no allow random jumbles of ones cubes any longer!!
Subitizing is such an important foundation skill to build number sense. Great article with great visual representations!
Thank you! You are absolutely right that this is such an important skill for primary students! If they can get a good grasp on this, then mastery of number combinations in addition and subtraction usually follows!
Cindy Elkins this article was so helpful preparing to teach the first standards in math. Thank you so much for your detailed explanation.
Thanks, Misty. Glad to be of help. Hope you had a good first day of school on Friday!