If you teach 3rd grade, you know that some students come to your class not knowing their basic addition and subtraction facts. And in 4th and 5th grade, there are students every year that lack mastery of ANY of their basic math facts—addition, subtraction, multiplication, and division. How does that happen, how can we prevent it from happening, and how can we help students who come to us without fact mastery?
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First off, let’s get it on the record—we still want our students to have automaticity with their basic facts. What’s changed is the approach we take to achieve that goal. We have moved away from learning facts through rote memorization and toward a strategy-based approach. We even see it written into the standards:
What do the standards say?
Let’s talk a little more about the standards. Students have three years to master their addition and subtraction facts.
So, in theory, they should come to 3rd grade having mastered their addition and subtraction facts. We’ll talk in a minute about why that doesn’t always happen. Unfortunately, students don’t get the luxury of three years to master their multiplication and division facts—it’s all supposed to happen by the end of third grade! Before they can tackle their basic multiplication facts, students have to understand the difference between additive thinking and multiplicative thinking, and that’s a big shift. We need to provide extensive concrete and representational experiences so students can visualize what multiplication looks like. Introducing them to multiple representations is essential. You can grab this freebie for representing multiplication facts here.
Next, like addition, they should be introduced to strategies for learning their basic multiplication facts. For example, the 2s are related to the 4s. If I know that 2 x 6 = 12, then I can double that to find the product of 4 x 6, which is 24. Download this game for the 2s, 4s, and 8s, and try it with your students tomorrow!
Finally, students are supposed to master their multiplication and division facts by the end of 3rd grade. That’s a LOT in one grade level. Especially if they didn’t master their addition and subtraction facts by the end of 2nd grade. Basic facts are not even mentioned in the 4th or 5th grade standards, and we all know that if it’s not listed in the standards, we don’t teach it.
How do we prevent the problem?
I could list a bunch of reasons why students don’t master their basic math facts, but I think it really all boils down to not building ongoing fact practice into our math instruction. You don’t get good at playing the piano without consistent practice, and it’s the same with basic math facts. Mastery of facts, beginning with composing and decomposing numbers in Kindergarten, is a year-long process that requires constant care and feeding.
The most important thing you can do is build fluency practice into your daily instructional schedule, even in 4th and 5th grade. If you are using a Guided Math approach, that means designating one of your stations for fluency practice. In our book, Guided Math Workshop, Laney Sammons and I introduced the GUIDE structure for organizing math workstations (also commonly called ‘centers’). You can see that the D workstation is devoted to fluency activities. You can accomplish this without using the GUIDE structure—just designate one of your workstations for fluency.
How do I help students who lack fluency with basic math facts?
Even if we change our classroom structure to provide ongoing practice, the results will take time. So how do we help students who come to us lacking fluency? Let’s think about a 3rd-grade teacher with students lacking fluency in basic addition and subtraction facts. Or a 4th- or 5th-grade teacher with students who lack fluency with any of the operations.
First, let’s assess those students walking in the door. And that doesn’t necessarily mean timed tests. The most effective type of assessment is one-on-one. Select a few facts that will provide you insight into a student’s thinking. For example, ask What is 6 + 6? Does the student quickly respond 12? Then ask What is 6 + 7? If they don’t automatically respond 13, can they explain their reasoning? Do they see that 6 + 7 is just one more than 6 + 6?
Next, get your students practicing right away! At the beginning of the year, put addition and subtraction games into your workstation—even in 4th and 5th grade! Students love playing games, and even if they have mastered their basic facts, they might be rusty after a summer off.
Also, don’t be afraid to introduce students to strategy-based thinking. Yes, you might not be able to go back and teach 5th graders all of the strategies for addition and subtraction, but you can plant seeds that might bear fruit. If a student struggles with 9 + 5, you could ask What’s 10 + 5? It’s likely they will quickly know that it’s 15. So then you could offer Wouldn’t 9 + 5 be just one less than 10 + 5? It just gets them thinking about the relationship between facts.
Finally, when students are doing multi-digit computation problems, provide support for basic facts. We don’t want students missing multi-digit computation problems because they are guessing at the facts. Check out this post for an easy strategy for supporting multiplication facts and to download a free game.
When working on multi-digit computation problems, provide students with basic fact charts, such as the addition and multiplication charts shown below. Every time students use the chart to find a sum or product, they are actually practicing that fact. Download the charts here.
Be sure to download all of the freebies in this post and the freebies in the other posts I’ve linked to! One more tip, use this link to find posts on my blog tagged with ‘freebies’ and ‘fact fluency’ for more resources for your classroom!