Multiplication: The Queen of Facts
“I’m just not very good at math. It’s not my thing,” sixth grade Amelia explained earnestly, looking up at me from her desk.
I looked at her thoughtfully. She had carefully followed my explanation finding the least common multiple in order to expand fractions. She understood how to rename fractions with a common denominator. She was a capable student, enthusiastic and attentive. But when it came time for her to solve problems on her own, she got stuck. There must be something going on for her under the surface that I was not seeing.
“Let’s look at this together,” I suggested. “You have two fractions here, one with a denominator of 8 and the other with 6. Can you find a bigger number that they can both go into evenly? Think of your number families and skip counting.”
I was hopeful that she would quickly land on 24.
I waited, and she began to guess, “12? No, no. 16? No, 18? Oh, I’m just bad at math!”
It quickly became clear to me that this otherwise capable student was hindered in her ability to solve fraction problems for one big reason: she did not know her multiplication facts! She could not easily and effortlessly see that 8 and 6 were both factors of 24.
She understood working with fractions conceptually. She could quickly demonstrate understanding with hands-on experiences. But when she needed to translate her understanding to the algorithms and abstract numbers, she came to a stand-still.
Indeed, Amelia was not “bad at math” at all! She simply did not know her times tables from memory and this interrupted her ability to solve multi-step problems.
Why Are Multiplication Facts So Important?
The math facts of all four operations are important for students to know from memory: addition, subtraction, multiplication, and division. But, I’ve discovered over the years that the multiplication facts are the most essential set of facts for students to master in order to solve upper grades math problems — the queen of all the facts!
Some of us remember these multiplication facts as the good, old-fashioned “times tables”! Students who don’t know these facts, who can’t easily retrieve them from memory, are significantly limited in their ability to solve multi-step problems when they get to 4th grade and above.
Multiplication facts are essential for so many standard multi-step problems, including:
2-digit and 3-digit multiplication with whole numbers and decimals
Long division
Simplifying fractions
Additing and subtracting fractions and mixed numbers with different denominators
Multiplying and dividing fractions and mixed numbers
Converting fractions to decimals
Ratio and proportion
Percentages
Over and over again, students have to rely on their multiplication facts. If they are in the middle of a more complex problem, their thinking processes are abruptly interrupted when they have to stop and rely on finger counting as a calculation strategy to solve a component of the problem. When this happens, they easily lose their place in the problem and miss certain steps. And even more concerning, they often begin to believe that they are not good at math!
They just don’t have the math tools in their mental toolbox necessary for the calculation.
What About the Other Three Operations?
This focus on multiplication facts is not to say that the division, addition and subtraction facts are not important!
They certainly are!
But, division facts can be easily derived from working backward with the multiplication facts. Students rarely struggle with these, if they know their “times tables.”
Addition and subtraction facts, the number bonds of all single digits up to 20 are also very important for efficient problem solving in math. A good deal of time and effort is spent in grades one through three really mastering these facts.
We want students to know them from memory effortlessly, as well as the multiplication facts.
However, if students don’t know these facts from memory, they can function successfully in the upper grades more easily than they can if they don’t hold their multiplication facts from memory.
The Road to Multiplication Fact Success
After many years supporting and observing children struggling to memorize their multiplication facts, I’ve learned several strategies that support fact mastery.
Don’t mix operations when children are in the learning and memorizing phase. Work on only multiplication on a worksheet until students demonstrate general mastery of those facts. Only at after that, experiment with mixing in math facts in addition, subtraction, and division. You will likely see students slow down considerably on their recall once they are jumping from one operation to another in their mental processing. While moving flexibly from one operation to another is eventually important, it can be a hinderance to developing automatic recall in the memorizing phase.
Work systematically with students over each grade to build multiplication fact fluency, and once they have demonstrated memorization, keep on practicing facts daily.
Each developmental phase benefits from a different type of practice:
1st grade — introduction to counting by groups with hands-on activities, skip-counting in 2s, 5s, 10s and 11s families
2nd grade — hands-on activities and movement to support conceptual understanding, skip-counting of all number families up through 12, writing number families (skip counting) from memory
3rd grade — continuation of skip-counting, support memorization with hands-on activities, games, and movement, begin to isolate individual facts within number families and recognize answers from memory, especially in the 2s, 5s, and 10s families
4th grade — work toward mastery of all individual facts from memory by sight, support with games and movement
5th - 8th grades — solidify and refine visual recognition and memorization of all facts with daily practice, working toward quick and efficient retrieval
I like to create my own multiplication practice worksheets because I can focus on the trickier problems that I know the students need to repeat and learn. I don’t find it necessary to put too much time and attention on the facts involving 0, 1, 2, and 10. Once the students know the underlying concepts and patterns behind solving these facts, they don’t really need too much practice. They benefit much more in practicing the harder facts — the ones in the 6, 7, 8, and 9 families. When I create my own worksheets, I can include more of these harder facts that I know they need to practice.
Check out a sample of my multiplication fact worksheets here: Multiplication Fact Worksheet Samples
You can download these samples, photocopy them, and try them out. I’ve designed one with 45 problems for 4th-5th grade students, and one with 80 problems for 5th-8th grade students. Both of these are designed to give repeated practice on the facts that are consistently hardest for many students to memorize. You’ll find a division fact worksheet sample there as well. I’m currently working on math practice sheets for multiplication families for 2nd and 3rd grade, so stay tuned!
Even after students demonstrate that they know these facts, I find it still important to give them these daily practice worksheets, which support them in visually recognizing the facts and retrieving the answers from memory. In all of my upper grades math skills classes, I start out the period with a five minute math fact warm-up that requires students to generate these facts accurately and from memory.
I want my students to know the facts inside-out so that they can use them as tools in solving more complex problems. The lower grades are the best time to focus on the number sense concepts underlying the facts. By the upper grades, the facts now support higher order thinking and problem solving. With consistent practice and repetition, most students can improve their ability to retrieve multiplication facts from memory!
