The great news about the 9 times table is that by pointing out a few patterns within it, you can help your students learn them in short time.  What at first seems daunting turns out to be quite manageable.  

Strategy 1: Teach the 9 Times Table with Patterns

My fifth graders students have had a lot of math fact instruction and practice before coming to me, but when I see students still struggling with x9 multiplication facts, I sit down with them, and we start a pattern dive together.  

Step 1: Spot the Patterns in the Tens and Ones Place

I'll begin by writing down the following:

• 1 x 9 =  0 9
• 2 x 9 =  1 8
• 3 x 9 =  _ _ 
• 4 x 9 =  _ _
• 5 x 9 =  _ _
• 6 x 9 =  _ _
• 7 x 9 =  _ _
• 8 x 9 =  _ _
• 9 x 9 =  _ _
• 10 x 9= _ _

I'll then ask if they can tell me what 3 x 9 is.  Most can; otherwise, we solve it together.  After we write down '27' on the list above (see below), I ask them to tell me what they notice in the tens place.  

• 1 x 9 =  0 9
• 2 x 9 =  1 8
• 3 x 9 =  2 7
• 4 x 9 =  _ _
• 5 x 9 =  _ _
• 6 x 9 =  _ _
• 7 x 9 =  _ _
• 8 x 9 =  _ _
• 9 x 9 =  _ _
• 10 x 9= _ _

They immediately see that the digits in the tens place are counting up.  It doesn't take much prompting for them to also tell me that the digits in the ones place are counting down.  

At MathFactLab, we teach this first pattern using a table and divide it into two stages.  Students first just fill in a single digit of the product.  In the second stage, student fill in both.  

Step 2: The Sum of the Digits is Always 9

I then ask the student to used those two patterns to tell what 4 x 9 is.  It doesn't take much for the student to tell me it's 36 and that 5 x 9 is 45.  

They could use this pattern to complete the rest of the 9 times table, but before we do that I ask them about the sums of the digits in each of the products we have uncovered so far: "What's 1 + 8?"; "What's 2 + 7?"; "What's 3 + 6?"  The student is usually a little surprised to realize that the sum each time is nine.

The 'Sum is 9' strategy is introduced as a hint in the Stage 3 of MathFactLab's Nines Patterns strategy.  

Step 3: The Tens Digit is One Less than the Number of Nines

The next step in the process is slightly trickier, but will allow to solve their nines without the above table.  I next ask my students to spot the connection between the number of nines and the tens digit of the product.  3 nines starts with a 2.  4 nines starts with a 3.  5 nines starts with a 4.  6 nines must start with a __.   8 nines must start with a __. 

This step is also introduced in the third stage of MathFactLab's Nines Patterns strategy.  

Step 4: Apply the Above Strategies 

Sometimes I have to point it out to them, but most students pretty quickly see that the tens digit of the product is one less than the number of nines.  Putting the above table aside, I can then ask them what 7 nines is.  Student thinking usually goes along the following line:

1. It starts with a 6.
2. 6 plus 3 equals 9.
3. 7 nines must be 63.  

Let's be clear: This strategy is not a reasoning strategy.  Instead, it's a pattern-based method for getting the correct products.  It's efficient and effective, but students aren't truly 'calculating' or 'solving', they're using patterns to get the correct product.  It's a method of mentally solving without causing cognitive overload. 

The next method is more of a traditional method for solving the 9 times table, but it's more mentally taxing.  

Strategy 2: 9 Groups = 10 Groups - 1 Group

For this approach, students are encouraged to begin with 'my friend ten'.  To solve for 9 sixes, students begin by thinking (quite easily) of 10 sixes.  At this point, I'll typically say to my students, "You wanted 9 sixes.  I just gave you 10 sixes.  How many sevens are you going to give me back?  

Students then see that 9 x 6 = 10 x 6 - 6.  

In many ways, if you're introducing the x9 multiplication facts for the first time, this should be your starting point.  It's going to take a fair amount of practice for it to become second nature for students, and some students will continue to be confused about which factor to subtract.  Using the above example, these students may unsure whether to subtract the 6 or 9 from 60.  

Ideally, if this is the case, more practice with multiple models is the solution.  But if this method is causing more confusion for some students than it's worth, for them, I would suggest you encourage the pattern approach above: Strategy 1.  

Strategy 3: The Fingers Trick for x9 Multiplication Facts

If all else fails, there's always the fingers trick.  This is a quick way - for any student who needs it - to easily get the product of any x9 multiplication fact.  I don't recall ever having a student who struggled with this method.  

Before we begin, let's be clear, this is a trick of sorts.  It happens to work to help the student get the correct product, but it doesn't develop any math sense.

Step 1: Face the Palms towards You

Ask students to face both palms towards themselves. 

Step 2: Find the Finger to Bend

Ask your students to begin counting from the left thumb, stopping when they reach the number of nines they are solving for.  For example, if solving 7 x 9, the student counts the five fingers of the left hand beginning with the thumb and continues onto the right hand, beginning with the pinkie.  The seventh finger will be the ring finger on the right hand.  Students then bend that finger.  

Step 3: Read the Fingers

The fingers to the left of the bent finger represent the tens digit - in this case, 6.

Please keep in mind, this is an if-all-else-fails strategy.  It should only be the go-to method for students who have not been able to find success with either of the methods above.  

At MathFactLab, the finger method is available, but teachers need to turn it on for individual students.  This can be done under to the 'Actions' icon (three dots) on the selected student's line on the teacher dashboard.  

About MathFactLab

MathFactLab is a teacher-created solution to the need for a better way to help students develop fluency with the basic math facts.  While math fact websites abound, online strategy-based math fact instruction is rare.  

I began MathFactLab as a way to help my own fifth-grade students develop math fact fluency.  I found that taking a strategy-based approach turned out to do just what the research suggested it would: Help my students develop long-lasting fact fluency while building number sense.  

This blog was written by Mike Kenny, 5th grade math teacher and founder of MathFactLab.