My Students Don’t Know Their Basic Math Facts! What Can I Do?

I was recently facilitating a math professional development session for elementary teachers, and with about five minutes left at the end of the day, a teacher raised her hand and asked, “What about basic math facts? Some of my fifth graders still don’t know their multiplication tables! How are we supposed to focus on conceptual understanding when fifth graders are still counting on their fingers?!” Her complaint has been a sentiment expressed for a long time and is a recurring theme in education. 

Rather than give a quick response (as if there is a quick one), I asked the teachers to talk at their tables and share what they are already doing to help students learn their basic math facts. They were in mixed grade level groups, and I was genuinely interested in their perspectives and figured the teachers would be interested as well. 

As I circulated, participants shared a range of ideas. Some used time tests and flash cards, others had students practice using worksheets. Many used games to help students learn their facts. 

As I listened in, I reflected on what current research and educational leaders have to say about learning basic math facts. Which teaching strategies are most beneficial? Which are least helpful? In this post, we’ll explore the topic and suggest helpful activities and strategies. We’ll also advise against those practices that are not helpful, such as time tests, which mostly benefit students who already know most of their math facts and can be stressful for those who haven’t yet learned them.  

What Do the Standards Say?

The Common Core State Content Standards recommend that by the end of second grade, students should know, from memory, all sums of two one-digit numbers. The Standards also recommend that by the end of third grade, students should know, from memory, all products of two one-digit numbers. Knowing what the Standards expect is important because they serve as a guide for us to make sure that our expectations are appropriate. 

What Is Computational Fluency, and How Do Basic Math Facts Figure in?

Computational fluency refers to a learner’s ability to efficiently, accurately, and flexibly solve math computations. It’s not just about speed or automaticity. In fact, researchers have found that children build the strongest math skills through a blend of conceptual understanding, strategic practice, and reflective learning, challenging the idea that speed alone defines fluency (Melissa E. Libertus, 1 April 2025, Psychological Science in the Public Interest).

At the heart of fluency is understanding the underlying mathematical concepts and being able to choose the most appropriate strategy or operation for a given problem. For example, finding the answer to 6 x 7 quickly is important and efficient, but fluency also requires the student to understand what multiplication means. In this case, 6 x 7 can mean six groups of seven. Understanding the concept allows the learner to use this knowledge to solve 6 x 7 if they don’t know it by memory. They can use what they know (5 x 7) and then add another seven to get to forty-two (5 x 7 is 35 and 35 plus another 7 is 42). 

Understanding how learning basic facts fits into computational fluency is important. We want students to have the answer to 6 x 7 at their fingertips, but we also want them to understand what the operation means and when and how to apply it. While quickly knowing basic facts is important, just focusing on memorization isn’t enough. The goal is to develop computational fluency, of which automaticity is just one part. 

Helping Students Learn Basic Addition Facts

Following are some of our favorite activities and ideas that can help students learn their basic facts and further concept development. 

Play How Many Am I Hiding?

One of my favorite activities for helping students learn basic addition facts is called How Many Am I Hiding? In this activity, the teacher puts some cubes on a plate. She then hides some of the cubes, leaving some leftover cubes on the plate. Students must figure out how many are hiding.  

Example Scenario:

• The teacher places five cubes on a plate. 
• She verifies with the student(s) how many cubes are on the plate.
• The teacher hides three cubes and asks, “How many are hiding?”
• Student(s) respond, and then the teacher reveals how many cubes are hiding. 
• The teacher continues with the activity, hiding different amounts each time. To move onto the next number of cubes, a student must be fluent with the number they’re working with. In other words, they can’t move on to six until they’ve mastered ways to decompose five. 

I love this activity because students are working with the number of cubes at their level (or just beyond). For example, if a student can decompose numbers through 4 by memory, then they are ready to play How Many Am I Hiding? with five cubes. 

I also like the game because it helps students learn how to decompose numbers into their component parts (4+1; 1+4; 2+2; 3+1; 1+3) while helping them commit math facts to memory. A teacher might use the activity as an assessment, gauging what number facts a child should be working on during math time. 

Use Known Facts and Combinations that Make 10

Teaching combinations that make 10 is a good way to begin basic fact practice. Understanding that 10 is a benchmark number and how it functions within our number system is key for understanding place value. Students can also use the ‘Make a 10’ strategy to solve other basic facts. For example, if a student knows that 8+2 is 10, they can use this knowledge to solve 8+5 by decomposing the 5 into 3+2 (take the 2, add it to the 8 to make 10, then combine 10+3).  

Learning their doubles (2+2, 3+3, 4+4, and so on) is another way that students can use known facts to learn other basic facts (Education Week, 2023). For example, to find the sum for 6+7, a student who knows 6+6 can just add one more to get thirteen. Or, to find the sum for 9+8, a student who knows 9+9 can subtract one to get to 17. 

Play Make a Ten Go Fish

A favorite game for first and second graders is Make a Ten Go Fish. You can find the directions and materials on our website here. In the game, each player is dealt five cards and looks for pairs to make 10. If a player doesn’t have two cards that make ten, they can ask other players for a card that can help them make a 10. 

I love this game because it not only provides students with basic fact practice, but it also challenges them to find missing addends to make sums of 10. The game requires critical thinking, problem solving, and communication. 

Splat!

Speaking of missing addends, Steve Wyborney’s Splat! slide deck provides lots of basic fact practice for students. For example, a teacher shows a slide with a certain number of blue dots (let’s say five). The class counts the dots. With a click of the computer, the slide changes, showing a big black splat covering some of the blue dots. The students must quickly figure out how many dots were covered. Consistent practice with the Splat! slide deck can go a long way in helping students learn their basic addition facts.

 

Helping Students Learn Basic Multiplication Facts

Use The Multiplication Card Sort

Teachers have been using flash cards for decades to help children learn basic math facts. The Math Transformations Multiplication Card Sort is a wonderful innovation on the activity. The Multiplication Card Sort  uses the structure of flash cards, which children like, but moves the emphasis to number sense and understanding multiplication. The aim of the activity is for children to match cards with the same numerical answer, shown through different representations. Once players make a match, they must explain to their partner why the cards match. 

Cards are positioned on a tabletop, and children take turns picking them, matching up products or expressions with appropriate visual representations. Teachers can differentiate the activity by selecting cards from the deck that are appropriate for players. For example, players can play using a mix of cards that have basic facts they already know and cards with facts that they are learning. Access the cards here.  

Teach Efficient Strategies

In his article, Reconciling Memorization of Basic  Multiplication Facts with Teaching Efficient Strategies  (California Math Council Communicator, June 2008), Mark Alcorn discusses the importance of teaching third graders efficient strategies. For example, to multiply by 4 is to multiply the same factor by 2 and then double the product. Therefore, 3 x 4 = (3 x 2) x 2 = 12. Another example is 6 x 7, typically problematic for students who are beginning to put basic multiplication facts to memory. An efficient strategy to solve 6 x 7: break apart the 7 into 2 and 5 so that the problem becomes (6 x 2) + (6 x 5). Using the distributive property not only makes the problem easier but also builds conceptual knowledge for future mathematics. 

Doubles is another strategy. Once students learn 3 x 3 = 9, they can make the connection that double that, 6 x 3, is the same as 2 x 9 and equals 18. Alcorn argues that the time it takes to solve a basic multiplication fact with an efficient strategy versus memorization is negligible. 

A Word About Teaching Efficient Strategies

We know that some students will come up with efficient strategies on their own, especially if they have strong number sense and conceptual understanding. However, some students will need more support and explicit instruction in order to wrap their brains around these strategies. 

Let’s come back to the example 6 x 7, which can be a tricky one for students. Some will automatically use what they already know (5 x 7) and add 7 more. If we need to be explicit with other students, just explaining the efficient strategy might not work. We may need to ask questions to scaffold their learning. Questions such as…

Do you know a helper fact that might help you solve 6 x 7?

Do you know the answer to 5 x 7? How can that help you solve 6 x 7?

6 x 7 means six groups of seven.  How can five groups of seven  help you?

These types of questions not only scaffold a student’s learning but they also require a student to do the thinking and hopefully help them understand why the efficient strategy works. 

Focus Practice on a Few Challenging Facts

Sometimes it seems overwhelming for teachers and students when they think about all the basic facts that need to be learned. But when you think of it, most of the basic facts are ones that students learn easily (1s, 2s, 5s, 10s). And when you consider the commutative property, it pretty much halves the number of facts that students need to learn.

Focusing on just a few difficult facts at a time can make everyone’s  job easier. Consider the following visual, which helps students and teachers recognize what they already know and which facts to focus on. 

Students can set weekly goals using a Multiplication Fact Weekly Plan (see an example below). This plan raises a student’s awareness of what they already know, what they need to focus on, and which strategies might help. They can also write down in the chart the efficient strategies they are learning to solve the more difficult facts.

Play Pirate Math!

The purpose of the game Pirate Math is for students to find missing factors and to build fluency with basic multiplication facts. Find the directions here.

Here’s how it works:

• Students play in groups of three. Two of the players are ‘pirates’, and the third is a ‘caller.’ Playing cards are put in a pile face down. Aces stand for one; face cards stand for a 10. 
• Each pirate draws a card from the top of the pile of cards. They can’t peek at their card! Each pirate holds their card over their eye (like a patch) so that the other pirate can see their number but can’t see their own number. 
• The caller calls out the product of the two factors. Each pirate determines the value of their own card or factor. 

Differentiate the Game: 

To meet the needs of the pirates and caller, adjust the playing cards so that players are practicing basic facts they already know, including just a few that they haven’t memorized yet. 

Play Rolling Rectangles

Rolling Rectangles  is a game that partners play. The purpose is to create rectangular arrays on a field of 100 squares. Students practice their basic multiplication facts while also learning how multiplication can be represented geometrically. Find the gameboard here and the directions here. 

Here’s how it works: 

• Players each have their own gameboard and take turns rolling two dice.
• After rolling the dice, a player draws a rectangle on their gameboard anywhere they wish. For example, if they roll a 5 and a 2, they can draw a 5-by-2 array or a 2-by-5 array.
• After drawing the array, the player writes the equation inside the rectangle and also at the bottom of their gameboard.
• Play continues until a player cannot place an array on their gameboard (no overlapping rectangles allowed). They count up how many squares they’ve covered out of 100. The other player continues until they can’t make a rectangle. 
• The player who covers the most squares on their gameboard is the winner.

Tips for Supporting Students’ Fluency with Basic Facts 

We know that when students have basic math facts at their fingertips it frees up their working memory so that they can attend to problem-solving, applying procedures to more difficult problems and other tasks. But what are the best ways to go about supporting students? We hope that this post has given you some ideas for getting started. The following list sums up some of our recommendations.

• Provide activities/games that simultaneously offer basic fact practice and support concept development.
• Focus on student mastery of a few challenging facts at a time, and space practice out. 
• Avoid having students practice all the number combinations randomly.
• Provide some time each day for basic fact practice. 
• Avoid using timed tests since this practice mostly benefits students who already know most of their math facts and can be stressful for those who haven’t yet learned them.  
• Explicitly teach efficient strategies for finding single digit sums and products.