Memorizing the basic multiplication facts is a crucial step in the journey young kids take to mathematics competency. Many students, however, struggle with this important milestone. It is one of the first tasks in primary school where a student must memorize a large number of facts to be successful, and for many students this is an intimidating and frustrating experience.
Fortunately, there are many ways parents and teachers can help children master their multiplication skills. Here are a few ideas if you have a student struggling with learning their multiplication facts.
Always Have a Multiplication Chart Available
A multiplication chart can save the day when a child simply can’t recall a math fact, and it immediately takes away the fear of not being able to succeed. A multiplication chart also shows the relationship between numbers on the multiplication table and can reinforce strategies like skip counting to find related answers in families of multiplication facts.
There Are Only Half as Many Multiplication Facts
If you look at that multiplication chart, it’s clear that almost half of the problems are duplicates, which means there are about half as many multiplication facts to memorize compared to what you’re probably thinking. For example, the facts 6 x 7 and 7 x 6 are both the same fact with the same answer. A fun way to emphasize this is to let students use colored pencils to shade each pair of matching facts, which can turn memorizing the multiplication table into a unique art project.
Focus on the Easy Multiplication Facts for Early Success
Certain families of facts on the multiplication chart are easier than others. Working around the perimeter of the chart, we can see all the facts that include either times one or times 10 have obvious answers… On a chart with the 1 to 100 facts, that takes away 36 problems right away!
Most students with a command of addition will also be able to easily double numbers, which makes all of the times two facts easy to remember. This puts another 15 problems in the success column and means half of the 10×10 multiplication table is already half memorized!
Use Skip Counting to Find Related Multiplication Facts
Skip counting relies on a student’s mastery of addition to find related multiplication facts, and teaching this strategy is another great confidence builder. If a student can recall a basic fact, for example 2 x 5 = 10, they can use skip counting by fives to easily get the answer to 3 x 5 and then 4 x 5 and so on. The multiplication chart can come in handy using skip counting for situations where skip counting with unfamiliar increments like 7 or 8, or when a student may get confused when the tens digit needs to increase, but skip counting is often best used for multiplication products in familiar intervals like 2s, 3s and 5s.
Learn How to Multiply by Nine
The times nine multiplication facts are full of interesting patterns that make memorizing them easy. One trick many people learn is that the sum of the digits of each product will equal nine. For example, 3 x 9 and 9 x 3 both equal 27. The sum of the tens digit (2) and the ones digit (7) in the product is 2 + 7 = 9. This is true for all facts in the times nine family up to 9 x 9 = 81 (which checks out to 8 + 1 = 9). Here’s a quick table that makes this pattern super clear…
|Problems||Answer||10s + 1s = 9|
|2 x 9 and 9 x 2||18||1 + 8 = 9|
|3 x 9 and 9 x 3||27||2 + 7 = 9|
|4 x 9 and 9 x 4||36||3 + 6 = 9|
|5 x 9 and 9 x 5||45||4 + 5 = 9|
|6 x 9 and 9 x 6||54||5 + 4 = 9|
|7 x 9 and 9 x 7||63||6 + 3 = 9|
|8 x 9 and 9 x 8||72||7 + 2 = 9|
|9 x 9||81||8 + 1 = 9|
You can find other patterns in this table, and one that is useful is that the tens digit in the answer is always one less than the other number in the problem (the part of the problem that’s not nine). For example, with 3 x 9 = 27, you find the tens digit in the answer by solving 3 – 1 = 2. If you combine this trick with knowing the sum of the answer digits is always nine, you can easily find any of the nine family facts in two steps.
Another pattern is to see that the answers to nine family facts have a certain symmetry, and there are four pairs with swapped digits: 18/81, 27/72, 36/63 and 45/54. Recognizing this pattern, you can see there are only four sets of related numbers that make up the answers to the times nine multiplication facts. This can be another useful way to recall answers to these problems!
Memorize the Remaining Tricky Facts (There are Only A Few)
Once a child has some experience navigating the multiplication chart, other patterns emerge and there winds up being only a few tricky facts that really need memorization. Here is a list of multiplication problems kids (and adults!) often struggle with:
|6 x 6||36|
|6 x 7 and 7 x 6||42|
|6 x 8 and 8 x 6||48|
|7 x 7||49|
|7 x 8 and 8 x 7||56|
|8 x 8||64|
Use Multiplication Worksheets to Create Competition
Once kids have a grasp of the basic math facts, timed multiplication worksheets are a great way to build efficient recall and confidence. Finding a good collection of worksheets that focus on specific sets of math facts will let you tailor practice to just the problems a student is struggling with or allow them to focus on more difficult problems without over practicing easier problems on the multiplication chart. If you are working with multiple students (or a whole class) creating a bit of competition can motivate students to practice their multiplication facts, but even solo students may enjoy trying to beat the clock!
When students are ready for more complex multiplication problems, including multi-digit multiplication, check out this visual long multiplication calculator for tips on how to solve bigger multiplication problems!
Regardless of what strategies you use to teach multiplication, this skill remains a foundation of success for many disciplines. I hope the ideas on this page help you and your students make progress on their multiplication facts and prepare them for even longer strides on their journey in the world of mathematics.