A 0–12 multiplication chart can make fact fluency feel like a huge task. There are 169 problems staring back at you, and it’s easy to assume students need equal practice with all of them. But they don’t. Once you look past reversals and notice the patterns built into multiplication, the number of facts students truly need to learn drops quickly.
Students often know far more than we give them credit for, which is why it makes sense to focus on the hardest multiplication facts instead of giving every fact the same attention.
See the Chart as a Hinge
If you picture the multiplication chart, the square facts running from corner to corner act like a hinge. Every fact on one side has a matching reversal on the other side, meaning many problems are really the same relationship shown in a different order. When students understand that 6 × 7 and 7 × 6 belong together, the chart immediately gets cut in half. Instead of hundreds of separate facts, students are working within mirrored pairs that support one another.
Now It's Time to Remove the Easy Ones
After half of the chart is removed due to the commutative property, the list of multiplication facts gets even smaller. Facts involving 0, 1, 5, 10, and 11 follow patterns students recognize quickly, which means you can teach these patterns and move on quickly once there is understanding. We are not saying you shouldn't spend time on them or skip them altogether, but instead, teach and move on.
Students Can Relate Addition Fact Fluency to Multiplication
Next up are the 2s fact family. Because the 2's family connects closely to addition, most students will realize they are already fluent in their 2's. Doubling is familiar, and that familiarity carries into multiplication. Because your students have a strong foundation in addition, their understanding of multiplication grows also.
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Now, We're Getting Close
Once you have removed the “easy facts,” what remains is not a long list but a smaller group of combinations that tend to be the hardest multiplication facts for students. You already know this because every year you watch your students pause in the same places. These are the facts that sit just outside obvious patterns, where students cannot rely on simple doubling or visual shortcuts and instead need repeated exposure and time.
The 28 Hardest Multiplication Facts
Teachers who narrow the multiplication chart quickly notice that the number of difficult facts is much smaller than they thought. Instead of 169 separate problems, the focus often settles on a group of 28 multiplication facts. Many of these combinations involve factors such as 6, 7, 8, and 9, including facts like 6 × 7, 7 × 8, 8 × 9, 6 × 8, and 7 × 9. These are not the only facts students practice, but they are the ones that consistently require the most time. Seeing 28 facts instead of 169 helps fact fluency feel attainable rather than never-ending.
When you see the chart shrink like this, fact fluency starts to feel like an entirely different experience. It’s not about getting through every fact in the same way. It’s about noticing where students struggle and giving those facts the time they need. The work becomes clearer, the practice becomes more focused, and students begin to experience the repetition that leads to real recall. The chart hasn’t changed, but the way we approach it has.
If this way of thinking about multiplication facts feels helpful, targeted practice can make the next step easier. Instead of revisiting every fact, students can spend time with the combinations that need it most. Our Targeted Multiplication Fact Practice Brochures were created for exactly this purpose, giving students meaningful repetition with the facts that tend to slow them down.
FAQ:
Many students struggle most with facts involving 6, 7, 8, and 9 because these combinations do not rely on obvious patterns. Students often need more time and repeated exposure before recall becomes automatic. Rather than struggling across the entire chart, the hardest multiplication facts are within a small cluster of facts.
Students benefit from knowing all multiplication facts, but they do not need equal time with each one. Some families fall into place quickly because of patterns and prior knowledge. Fact fluency improves when teachers focus practice on the combinations that require more repetition instead of reteaching everything.
Start with facts that students already understand through patterns and connections, then shift attention to the hardest multiplication facts. This allows students to feel confident in their efforts. Many teachers notice that facts built around 6, 7, 8, and 9 require the most intentional practice. Focusing on these facts helps students build confidence and progress more efficiently.
