Math Interventions

One skill that a student will acquire as he develops his understanding of quantity is subitizing. Subitizing is the ability to instantly represent a number without having to count it (i.e., a student can look at four cubes on the table and tell you there are four cubes without counting them).  This skill is considered more basic than counting. This page includes intervention strategies that you can use to support your students in this area. As you read, consider which of these interventions best aligns with your student's strengths and needs in the whole-learner domains.

Explicit Instruction

If you are intervening to support your student's ability to subitize, you should start by explicitly teaching the skill. This sounds like:

• Explain the Skill/Concept. Define subitize, and explain the activity. ("Subitizing is the ability to quickly look at group of objects and identify how many there are without counting them." "Today, we are going to learn strategies that will help us develop these skills." )
• Model Skill with Examples. Think aloud about how to use subitizing.  ("Let's say that I have three candies on my desk. If I look at them quickly, for one or two seconds only, and then close my eyes, I should know that there are 3 candies, without counting them. I know that I can subitize if I look at the objects, then close my eyes, and I can tell you how many there are.")
• Model Skill with Non-Examples. Think aloud about counting, which is different from subitizing. ("What if I looked at those candies, and instead of knowing there were 3, I had to count them. 1, 2, 3. This is counting, not subitizing. It's okay to count when there are a lot of objects: like, if I put a whole handful of candies on my desk,  I'd have to count them because that number would be too big to hold in my mind. However, when we are working with just a few objects, it's important that we can understand how many there are without counting them. This skill will help us as we learn to count later.")
• Practice the Skill. Engage in one or more of the activities below to practice the skill with your student, providing feedback as necessary. ("Now you try. I'm going to show you...")

Activity A: Small Collections
If a student in the primary grades is unable to subitize a small number of objects (such as 1-3), support his ability to instantly represent them by teaching Small Collections (Clements & Samara, 2009). This intervention strategy helps a student learn to identify numbers in groups, and then visually represent that number himself. In this strategy, the teacher lays out a small collection of objects (such as blocks or cubes) and shows the student the blocks for one to two seconds. Then he uses his hand to cover the blocks. The teacher then asks the student to make a group that has the same number of blocks. After he is finished, the teacher shows his own group of blocks and asks the student if the groups have the same number. Then, he asks the student to name that number. 

Small Collections in Action
Teacher: I'm going to show you a group of cubes for a few seconds. Ready? (Teacher shows 3 cubes and then covers them with her hand.) Now, can you make a group with the same number as you saw?

Student builds a group of 3 cubes, and teacher lifts hand to show her 3 cubes.

Teacher: Do we have the same number of cubes? (Student nods.) How many cubes are there?

Student: 3.

Activity B: Snapshots
For a student who is able to subitize small groups of numbers (1-3) but unable to subitize larger numbers (up to 10), teach him Snapshots (Clements & Samara, 2009). This intervention strategy helps a student to identify groups of numbers up to 10. In this strategy, the teacher lays out the number of objects that she is trying to teach the student to subitize (such as 5), shows the objects for one to two seconds, covers the objects with her hands, and then asks the student to name the number. Then, the teacher moves the objects around in a different formation, covers them, and asks the student to name the number again.

See below for an example of formats used to subitize 4 (left) and 5 (right):

Clements, D.H. & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge.

The teacher continues to move the objects around, in progressively different formats, until the student is able to recognize multiple formats of that number. At this point, the teacher can teach the student to subitize a new number, and can start to show the student a different number of objects (4 instead of 5) each time.

A similar, but more challenging, approach to Snapshots is to show an amount of objects (such as 5) and have the student match the number of objects to the correct number card (a number card that says 5).

Snapshots in Action

Teacher: I'm going to show you a group of cubes, and you're going to tell me how many there are. Ready? (Teacher shows 5 cubes for two seconds and then covers them with her hand.) How many?

Student: 5.

Teacher: Now, I'm going to move around the cubes, and you'll tell me how many there are. (Teacher moves cubes into a different formation, shows them for two seconds, and then covers them with her hand.). How many?

Student: 4....wait, no 5. 

Teacher: I'll show you again. Ready? (Teacher shows same formation.)

Student: 5.

Activity C: Subitizer to 20
If a student is able to subitize objects to 10, but struggles to subitize objects to 20, teach him Subitizer to 20 (Clements & Samara, 2009). In this intervention, the teacher puts objects together in groups of 5, shows the student these objects for one to two seconds, covers them, and then asks the student to name how many objects there are all together.

One helpful resource to use when teaching this strategy is ten-frame template. Click here for a ten-frame template. This ten-frame template can be used to help students conceptualize groups of 5, as well as to help students identify objects that are less than 5 by subitizing the empty squares.

Subitizer to 20 in Action 
Teacher: I'm going to show you a ten frame, and you'll subitize how many there are. Ready? (Teacher shows a ten frame with 5 squares filled in and then covers it with her hand.) How many?

Student: 5. 

Teacher: Great, now we'll try a new number!

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Think about the following scenario, which takes place after a teacher has explicitly taught a student strategies for subitizing.

        Teacher: "I'm going to show you a small amount of objects for one second, and then I
        want you to tell me how many there are. Ready?"
        Student (after teacher covers the objects with her hand): "Wait! I didn't have time to
        count them!"

In such a case, what might you do? 

When you are planning your lessons, you should anticipate that your student will make errors throughout. Here are a series of prompts that you can use to respond to errors. Keep in mind that all students are different, and that some students might respond better to some types of feedback than to others.

Level of Support	Description of Scaffold	Script
Smallest Scaffold	Try Again! Tell the student that he shouldn't attempt to count the objects this time, and show the student the objects again.	"This time, when I show you the objects, don't even try to count. Ready?"
Medium Scaffold	Back it Up. If a student is struggling, back up your process. Take away one of the objects, or start with a small number, such as one or two, and ask the student to try again.	"Let's try again. Now, see if you can figure out how many there are without even trying to count."
Highest Scaffold	Model. If the student continues to struggle, model the process of subitizing, starting with only one object.	"I can see that you are stuck. I'll show you how I glance at the objects and guess how many there are."

If your student struggles to meet your objective, there are various techniques that you might try in order to adjust the activity so as best to meet your student's needs. 

Activity	Description of Strategy	Script
All Activities	Make it Interesting. If you find that your student is unable to subitize small numbers even with practice, try to use objects that will engage the student's interest, such as pieces of candy, or toys.	"Let's try to subitize with a new object! Ready?"
All Activities	Draw It. If your student continues to struggle, try this: instead of using objects, have your student draw a circle on a piece of paper. Then, use that drawing to subitize, and have the student add circles until he can subitize up to 5.	"I'd like you to draw one circle. Now, I'll cover it, and I want you to tell me how many you see."