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December 19, 2017
Using Quick Images to Promote Additive Reasoning

Subitizing is a fundamental skill in the development of students' understanding of number.  (Baroody, 1987)

Quick images  is a 10-minute routine that can help to improve students' ability to subitize, or instantly recognize "how many" without counting. Perceptual subitizing is recognizing "how many" in a visual pattern without having to count to find the quantity (e.g., the number of dots on a dice). Adults and children can typically perceptually subitize 3 or 4 objects. Conceptual subitizing is determining the whole quantity by using a mathematical process, such as recognizing subgroups or patterns (e.g., in tens frames or arrays). 

The basic structure of the routine is described below 
  1. Show or flash the dot arrangement for 3-5 seconds. If you show it too long students will have time to count, and the goal is for them to build a visual mental image.
  2. Ask students to imagine the model in their heads and think about how many they saw and how they know. Alternatively, they could sketch what they saw on a white board. 
  3. Have students turn and talk to a partner about how many they saw and how they saw it. As they are talking, move around the room and listen to how students saw the model. Listen for 2-3 strategies to sequence and connect when debriefing the quick image.
  4. Show the image again and ask students to share how many dots there are and how they saw it. Once students are ready, you can write equations to represent their thinking and explicitly connect student strategies to each other and to the model. 
To build subitizing, it is important to only show the image for a few seconds, to discourage counting by one. Begin by just asking what they saw and how they saw it. After students become comfortable with talking about how they determined the quantity, you can represent their strategies with equations.
 
When planning, remember the stages of subitizing:
  1. Familiar designs within 5 (e.g., dice, fives frames, math hands).
  2. Unfamiliar designs within 5.
  3. Familiar designs with more than 5 (e.g., tens frames, math hands).
  4. Unfamiliar designs with more than 5.
  5. Arrays and groups where you can see all the objects.
  6. Open arrays where you see only the dimensions. 
Here is a video of Kindergarten students building understanding of number through subitizing: https://www.teachingchannel.org/videos/visualizing-number-combinations .

Action Item
  • Find and take out the dot card you made in OGAP Summer Training and plan a regular routine to practice subitizing with Quick Images. Remember you can fold the card to create different images.
  • Try using the card for Quick Images whenever you have a few minutes (e.g., when students are lined up for recess or bathroom breaks, waiting for dismissal, etc.)
  • Here are some additional examples of dot images, ten and twenty frames, and hundreds grids that you can download and use to get started with the routine. For more resources or videos, Google "quick images" or "dot cards.
Did you know?

You can access the OGAP Item Banks online in two ways: find our new searchable OGAP item bank  here ( bookmark it! ) or view the PDFs at  www.ogapmath.com/item-bank .

Also, you can access past issues of OGAP Teacher Tips by visiting  www.ogapmath.com/ogap-teacher-tips-archive.