Just like crawling, walking, and running are all developmental stages, there are also developmental stages for math fact mastery. Students move from one developmental stage to the next until they master their addition and subtraction facts.
It’s important to know what the stages of math fact mastery are. Then you can identify what stage students are in and help them get to the next.
In this blog post we will go over each stage of math fact mastery and how to help students get to the next and ultimately, get to math fact mastery.
But first, I want to make sure you know about my free workbook for teachers: The 7 Steps to Ensure Math Fact Fluency. In this workbook, I give you actionable steps to help students get to know their math facts fluently. Download yours free here.
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The 3 Stages of Math Fact Mastery
When you understand the stages of math fact mastery, you can help students move from one stage to the next.
In the first stage, students use counting strategies. You can know students are in this stage if they are using blocks or counters. For example, for the equation 3+5, they count out 3 counters, then count out 5 counters, then count out all of the counters.
When students need math fact mastery help, I also go back to the basics. We work on counting strategies and make sure they are really solid with those.
Students are also in this stage if they use their fingers. They may even use the Counting On Strategy or the Counting Back Strategy by using their fingers or verbally counting on or back. These are a good strategy for students who have been using counters to move on to something less concrete.
However, some students struggle with the counting sequence, so using the Number Line Strategy can help students with the sequence and move on from the counting stage.
On the road to math fact fluency, students need to master addition and subtraction using a number line.
Help students in this stage with Counting On Task Cards, Counting Back Task Cards, Number Line Addition Task Cards, and Number Line Subtraction Task Cards. Find the Bundle of all the strategies here. Teaching online? Find the digital version here.
For students to learn each math fact, working with fact families as a reasoning strategy is a great plan!
In the second stage, students use reasoning strategies to add and subtract. This means students use known facts to help find unknown facts. Let me give you some examples.
Students can use doubles facts to find near doubles facts. Our brains love double facts because they are a novelty. And because of that, they are easier to memorize. If students know 7+7=14, they can know 7+8=15 because 15 is one more than 14. To learn more about how to teach doubles facts, read this blog post here: What are Doubles Facts?
We know students are getting close to the mastery of math facts when they can use known facts to quickly find unknown facts. The doubles fact strategy is a great way to do this.
Another example is using fact families. Facts are related to each other. If students know one addition fact like 7+4=11, then they can know 4+7=11. Then can also know the related subtraction facts like 11-4=7 and 11-7=4. We do need to help students see these relationships and patterns, that is why I use fact family triangles to help students practice these. Find the ones I use here.
Students can also decompose numbers and facts to help them become facts they know. They do this with the Make Ten Strategy. If a student comes across a fact like 8+4, they can think of it as 8+2=10 and two more is 12. So 8+4=12.
For math facts to master, we want students to learn facts of 10 first. From there they can use reasoning strategies to find other facts quickly.
They can also do this with subtraction, if they come across the fact 13-5, they can think 13-3=10 and 2 more is 8. So 13-5=8. To learn more about the Make Ten Strategy, read this blog post here. Find the Make Ten task cards I use with my students here.
Math Fact Mastery
After practicing these strategies and becoming proficient in them, students come to the third stage of math fact mastery, which is mastery! This means students are able to produce fast, accurate answers to math facts. They can produce answers in about 3 seconds or less. This means they can still use thinking strategies, but they can do so quickly in their heads.
You can get students lots of practice with math fact fluency worksheets that are fun and engaging.
Students just need lots of practice to get to this stage. I like to make this fun for students. I have them play with games. My students love playing Math Facts Old Maid, Math Facts Go Fish, and Math Facts Memory Match in my classroom. Find my bundle of math fact games here.
Math fact fluency games help students apply the reasoning strategies you have taught them in a natural way.
I also like to set out fast finisher math fact worksheets for students. These are engaging worksheets that are fun for students. Students love to solve Math Fact Riddles. They love to find certain facts in my I Spy Math Fact Worksheets. Find the year long bundle here. Teaching online? Find my digital fluency activities here.
Following a math fact fluency program can be helpful when students are on their way to math fact mastery. Part of that program should include fun practice opportunities like these Math Fact Riddles.
As students move through counting strategies, reasoning strategies, and as they get plenty of fluency practice, they will move to math fact mastery.
For more tips to getting students to math fact fluency, download my free workbook: The 7 Steps to Ensure Math Fact Fluency. Download it here.
