- Episode Highlights
- Transcript
Subtraction often becomes a stumbling block not just for students, but for teachers trying to figure out how to move beyond memorization and speed drills in their instruction. So what does it look like to teach subtraction in a way that builds true fluency?
In this episode, we continue our fluency series by exploring what makes subtraction uniquely challenging, and how students gradually move from early counting strategies to more efficient, reasoning-based approaches.
You’ll hear how subtraction fluency develops over time, why memorization falls short, and how to help students build flexible, lasting understanding while still honoring where they’re starting. This episode sets the stage for a deeper, more meaningful approach to subtraction within 10 and 20.
Hello, Meaning Makers! I’m excited to continue our discussion about operations by moving on to subtraction strategies.
Today, we will review the meaning of fluency, discuss the grade-level expectations for fluency with subtraction in the primary grades, and introduce appropriate strategies for solving subtraction facts within 10 and 20. Let’s get started!
What Does Math Fact Fluency Really Mean?
It’s crucial that we as teachers understand what it means to be fluent with math facts, so even though we already discussed fluency in a previous episode, it’s definitely a topic worth returning to.
Despite the historical emphasis on speed when it comes to math facts, fluency is NOT just about speed and correctness. It’s an intricately woven combination of four components: accuracy, efficiency, appropriate strategy use, and flexibility.
Now, speed and correctness do play a role, as we want students to solve math facts in a reasonable amount of time and arrive at the correct answers. However, that ability is developed over a long period of time as students have rich, meaningful experiences working with a variety of strategies for addition and subtraction.
As students progress from using counting strategies to using reasoning strategies to solve math facts, they learn to choose appropriate strategies given the problem, and be flexible in how they use them.
Why Memorization Isn’t the Answer
It’s imperative for students to use strategies to solve math facts as opposed to relying on memorization. Have you ever stopped to think about just how many math facts there are?
If you consider all four operations, there are hundreds of math facts for students to learn. It’s impossible to expect students to memorize all of those facts during their time in elementary school from kindergarten to third grade and then retain them all beyond that.
Not to mention, memorization does not even guarantee that students truly understand the meaning of the operation.
Real-Life Fluency Analogy
Let’s connect this to our adult lives for a second. There are things that you as an adult have committed to memory – think about how they got there in your memory. How did you become fluent? For example, you probably can drive from your home to work without using a map or GPS. But how did that happen?
Did you study a map and memorize the street names and the places to turn before leaving your house? No. You drove that route over and over again, using the map as a tool while you were learning.
Maybe you even tried multiple routes and decided which one was the most efficient. Maybe you even were flexible with your route and took a detour to run an errand on the way home from work – do you see where I’m going with this?
You didn’t stay home until you had the route memorized. The route became committed to your memory BECAUSE of the many experiences you had driving it.
This analogy parallels the journey we want our students to take with math facts. You can look at math facts on flashcards and try your hardest to memorize them, just like you can look at a map and try to memorize the directions, but until you practice using strategies to solve math facts, or get in the car and experience the route for yourself, those facts, just like those directions, don’t mean much.
Grade-Level Expectations for Subtraction Fluency
It’s important to remember that fluency is a year-long goal. As you might recall from the first podcast episode about addition strategies, according to the Common Core State Standards, first graders are expected to add and subtract within 20, but fluency is only expected within 10 by the end of the year.
In second grade, students continue working within 20, and they are expected to demonstrate fluency with all addition and subtraction facts within 20 by the end of the year.
Let me repeat that—in first grade, fluency is only expected within 10, and that’s not until the END of the year.
It is IMPERATIVE that we take our time with this standard and give students plenty of meaningful experiences adding and subtracting within 10 and 20. And I’m sure it goes without saying—subtraction facts are more difficult than addition facts. Therefore, those meaningful experiences are crucial.
Subtraction Strategies Within 10 and 20
Let’s take a look at strategies students use when subtracting within 10.
Count – Count – Count Subtraction Strategy
The most basic addition strategy students use is “counting all” where they literally count every number to find the answer. There is a similar beginning strategy for subtraction called “count – count – count”.
It’s easiest to explain with an example, so I’ll use the problem 8 – 3. With this problem, a student would count out 8 fingers (1, 2, 3, 4, 5, 6, 7, 8)… count off 3 fingers (1, 2, 3)… and then count the number of fingers left (1, 2, 3, 4, 5)… to get an answer of 5.
Remember, it’s important to honor where our students are at by accepting the strategies they use. So when they are using the “count – count – count” strategy we can recognize how this strategy allowed them to act out the process of subtraction and arrive at a correct answer.
Was it efficient? No. However, it is our job to ignite the spark in our students that makes them want to find and utilize a more appropriate, efficient strategy to solve the problem.
Counting Back Subtraction Strategy
The version of this strategy for addition facts is “counting on”. With “counting back”, students are able to hold the minuend (the whole) in their head and count backward from there to take away the subtrahend to arrive at the difference (the answer).
For example, with the problem 9 – 3, students begin at 9 and count backward until 3 has been taken away… “ 9… 8, 7, 6”.
This sounds similar to the “count -count – count” strategy I just mentioned, but the difference is that with “count – count – count”, students have to count out the whole and they have to count the remaining quantity to find the difference.
With “counting back”, students begin with the whole already solidified and count back from there. They know that the last number they say is the answer.
Counting Up Subtraction Strategy
Students use this strategy by building on their knowledge and strengths with addition. They realize that subtraction is finding the distance between two numbers, and that distance can be calculated by “counting up”.
Students “count up” from the subtrahend (the number being subtracted) to the minuend (the whole). For example, with the problem 7 – 5, students would begin at 5 and count up until they reach 7, arriving at a difference (or the answer) of 2.
Think-Addition Subtraction Strategy
This strategy also builds on students’ knowledge and strengths with addition. But instead of having to count to find the difference, students use the idea of parts and wholes.
It’s important that students are already in the process of developing fluency with the corresponding addition facts in order to make sense of this strategy.
With “think-addition”, students look at the subtraction problem and think about the addition fact that uses those same numbers. For example, with the problem 7 – 3. Students would think, “3 plus what number equals 7? It’s 4!” In order to use this strategy, students must understand that two parts (3 and 4) make the whole (7).
Wrapping Up and Looking Ahead
Meaning Makers, I know it is challenging to help our students discover a need for a better strategy beyond “count – count – count”, but I’m here to support you with this!
This will be the focus of our next podcast. We will discuss how we can support our students in discovering these other strategies for subtraction, and I will also share some math tools that are perfect for helping students with their subtraction fluency development.
I’m excited to continue this important conversation with you! See you next time!
