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December 19, 2017
Using Quick Images to Promote Multiplicative Thinking

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 see "how many." It can also be an effective way to move students' understanding along the multiplicative framework (e.g., from counting by ones to equal groups) or to use a visual model to focus instruction on specific concepts or properties. The basic structure of the routine is described below and shown in these  short videos  of Beth doing Quick Images in a third grade Philadelphia classroom. 

Basic Activity for Quick Images:
  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. Also listen for unanticipated or unique math ideas or strategies that students are thinking about that would be worthwhile to share.
  4. Ask students to share how many dots there are and how they saw it. Write equations to represent their thinking and explicitly connect student strategies to each other and to the model. 
The example below shows how you can use equations to record and connect student explanations to standard notation.  ("I saw 8 groups of 4" is recorded as 8 x 4) and also to show how the equations are related to each other and to the model. 
Action Item

You can get started by downloading these  Examples of Quick Images. Think about what concepts can be highlighted with each image (e.g, connecting equal groups to the array model, the commutative, or distributive property). After deciding what concept you want to focus on, try the Quick Image with your students. What different strategies did they come up with? What is another image you could use to build on and extend their thinking?
 
Doing this activity on a regular basis will help your students build multiplicative understanding. You can make up your own images, but there are also a number of internet sites where you can find more examples. (Search for Quick Images or Dot Patterns). 

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.