This page includes strategies you can use to support your student's ability to develop computational fluency for addition and subtraction facts. As you read the interventions below, consider which strategy is best aligned with your student's strengths and needs across whole-learner domains.
Explicit Instruction
If you are intervening to support your student's ability to solve problems fluently, you should start by explicitly teaching the skill. This sounds like:
Activity A: Develop Understanding
If your student is struggling to solve single-digit multiplication and division facts, the first way you can intervene to support his understanding is by helping him develop his conceptual understanding of the big ideas behind the fact set (O'Connell & Sangiovanni, 2011). To do this, the teacher reads a piece of literature that reviews the big ideas of previously taught math facts and helps the student begin to explore the target fact set. For example, if a student was learning about x5 facts, the teacher would read Count on Pablo, a story about a boy and his grandmother selling vegetables at a market.
Develop Understanding In Action
Read the PDF below (O'Connell & SanGiovanni, 2011), which shows how a teacher would teach this intervention to a student who is learning to multiply and divide by 5. As you read, consider how this literature connection helps the student develop understanding of x5 facts.
O'Connell, S. & SanGiovanni, J. (2011). Mastering the basic math facts in multiplication and division: Strategies, activities, & interventions to move students beyond memorization. Portsmouth, NH: Heinemann.
Activity B: Explore the Class of Facts
Once your student has built understanding about the class of facts he is learning through reading literature, he is ready to practice using this fact set. In this intervention (O'Connell & Sangiovanni, 2011), a teacher engages the student with interactive activities that explore the class of facts he is learning. For example, if a student were learning about multiplying by 5, the teacher might use the following activities:
Explore the Class of Facts In Action
Read the PDF below (O'Connell & SanGiovanni, 2011), which shows how a teacher would teach this intervention to a student who is learning to multiply by 5. As you read, consider how this intervention might look if used to teach the other number facts.
O'Connell, S. & SanGiovanni, J. (2011). Mastering the basic math facts in multiplication and division: Strategies, activities, & interventions to move students beyond memorization. Portsmouth, NH: Heinemann.
Activity C: Build Automaticity with Cover-Copy-Compare (Multiplication and Division)
Once your student has developed conceptual understanding about a class of facts, he can practice Build Automaticity with Cover-Copy-Compare (Powell, 2011). This intervention strategy builds fluency with a class of facts, for use once a student has learned a reasonably efficient strategy appropriate to that class. The Evidence Based Intervention Network at the University of Virginia created the following brief to explain this strategy in more detail. As you read, consider why this strategy supports fluency.
Powell, S. (2011). Intervention Name: Cover, Copy, and Compare. Columbia, Mo: The Evidence Based Intervention Network, The University of Missouri. Retrieved from http://ebi.missouri.edu/?page_id=805
Now, watch Ama Awotwi implement this strategy with her intervention student.
Build Automaticity with Cover-Copy-and-Compare in Action
As you watch, consider: How does this strategy increase at-bats to help develop computational fluency?
Activity D: Build Automaticity with Math Games
Another activity to use once your student has developed conceptual understanding of a math fact to build automaticity involves math games. In this intervention (O'Connell & Sangiovanni, 2011), a teacher first models how to play games, and then allows the student to practice with a partner. Such games include:
Build Automaticity with Math Games In Action
Read the PDF below (O'Connell & SanGiovanni, 2011), which shows how a teacher would use this process to teach a student who is learning to multiply and divide by 5. As you read, consider how this intervention might look if used to teach the other number facts.
Building Automaticity Division
O'Connell, S. & SanGiovanni, J. (2011). Mastering the basic math facts in multiplication and division: Strategies, activities, & interventions to move students beyond memorization. Portsmouth, NH: Heinemann.
Activity E: Connect to Division
Once your student has developed automaticity with multiplying the given math fact, he is ready to learn how the fact is connected to other operations, such as division. In this intervention (O'Connell & Sangiovanni, 2011), a teacher reads literature that connects multiplication to division, asks questions about the story, and engages the student in activities that allow the student to see how the two operations are related.
Connect to Division In Action
Read the PDF below (O'Connell & SanGiovanni, 2011), which shows how a teacher would teach this intervention to a student who is learning to multiply and divide by 5. As you read, consider how this intervention might look if used to teach the other number facts.
Connecting to Division - Multiply
O'Connell, S. & SanGiovanni, J. (2011). Mastering the basic math facts in multiplication and division: Strategies, activities, & interventions to move students beyond memorization. Portsmouth, NH: Heinemann.
O'Connell, S., & SanGiovanni, J. (2011). Mastering the basic math facts in multiplication and division. Portsmouth, NH: Heimemann. Retrieved from http://www.barrington220.org/cms/lib8/IL01001296/Centricity/Domain/508/oconnellmultweb.pdf.
O'Connell, S. & SanGiovanni, J. (2011). Mastering the basic math facts in multiplication and division: Strategies, activities, & interventions to move students beyond memorization. Portsmouth, NH: Heinemann.
Powell, S. (2011). Intervention Name: Cover, Copy, and Compare. Columbia, Mo: The Evidence Based Intervention Network, The University of Missouri. Retrieved from http://ebi.missouri.edu/?page_id=805
If your student understands quantity and is able to match the right strategy to the right set of facts, but he is still making computational errors or being slowed down by computation, it's worth giving your student a work-around. In these cases, you'll want to give your student a tool that he can use to solve basic facts quickly and accurately.
Such tools might include:
Think about the following scenario, which takes place after a teacher has explicitly taught a student strategies for developing computational fluency.
Teacher: "I see that you are stuck on this problem in the 4 fact family: 4 x 4."
Student: "Yeah, I don't know the answer to it."
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. Ask the student to try the problem again. | "Can you try that one again?" |
| Medium Scaffold | Do What You Know. If a student is struggling with certain problems, have him skip the ones he cannot complete and come back to them afterwards. This will help you identify the problem types he needs additional support with. | "I can see that you are stuck. Skip this one and go on to the next one. Just do the ones you know first." |
| Highest Scaffold | Identify the Barrier. If the student continues to struggle, he may need additional support with conceptual understanding. In this case, follow the guidelines on the previous page to figure out where to intervene to support his conceptual understanding. | "I can see that you are stuck. Let's see what else I can help you with before we practice this again." |
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 | Start small. If a student struggles to complete problems fluently, give him just a few problems to build automaticity with (such as one number family), and then add on. | "Let's practice building fluency with the 4 number family only." |