# Multiplication (Times tables)

**Note: A huge part of learning times tables is practice.  Scroll down for a blank times table chartworksheets (40 and 100 problem sets), times table sprints (for competitive practice), and times table tesselations (for artistic practice).**

Multiplication is the process of adding groups, multiple times.  It's a streamlined and faster way to add, if you need to add the same number repeatedly.

$4+4+4+4+4=5 \times 4$

Learning multiplication often involves a lot of adding.  When a student who is just learning to multiply tries to do the problem $5\times4$, the student will often draw (or use fingers) to count up 5 groups of 4 (or 4 groups of 5 -- there is a commutative property of multiplication, so it does not matter what order you multiply numbers).

In the very early stages of learning to multiply, it's helpful to draw groups and count or add them.  This process helps students to understand what multiplication is.  But, once they understand the concept, students want to work towards doing multiplication more quickly and fluidly (after all, it's meant to be a more efficient way of doing a lot of addition).

The best tool that students can acquire to speed their math work is memorization of the times tables.  Most students find that, once they memorize the times tables (at least 1 - 10, though 1 - 12 is even better!), all of their math goes faster.

But, there are some intermediary steps that can help memorizing times tables go faster.

First, start by skip counting.

Adding up is time consuming, but skip counting makes that process go faster.  Start with easy numbers to skip count: 2, 10, 5.

Have the student count by 2s, 5s, and 10s.

Then, when the student has mastered skip counting, ask the student a basic question: What is $2\times3$? Have the student count by 2 three times: 2, 4, 6 = 6!

Once the student sees the benefit in skip counting, he or she might want to learn to skip count other numbers, like 3s, 4s, and 6s.  Other students will jump right to times tables.  Either way, a student who is fluid in skip counting will find times tables easy.  And, a student who knows his or her times tables should be able to skip count.

Second, do the easy times tables first:

• 0s
• 1s
• 2s
• 10s
• 5s
• 11s

The best part about starting with these easy multipliers, is that they include a lot of harder multipliers.  Sixes are hard.  But a student who has mastered the easy times tables already knows $6\times0$, $6\times1$, $6\times2$, $6\times5$, $6\times10$, and $6\times11$.  That student already knows half of the 6 times tables.

Third, learn the fun times tables:

Find some times tables that you like (or that your student likes).  We like to teach:

• Doubles ($4\times4$, $9\times9$)
• Their favorite number
• 9s (many students already have a trick for 9s, so they like this one-- see alternate method below for one way to teach 9s)

Fourth, remember to remind them of the commutative property.

Once they learn $7\times8$, they know $8\times7$. Essentially, every time they learn a full set of times tables, they cut down the problems that remain in each subsequent set!

Finally, drill.

There is really only one effective way to learn times tables, that's to do them over and over again.  We find that writing out the answers on worksheets is often more effective than quizzing orally, but do what works for the student (often a combination of both).

Drill in sets.  It's very overwhelming, when you're first learning times tables, to find a mixed set of problems, 1-12.  Have students master a set of times tables at a time.  Have them do all of the easy ones.  Then when you give them a set of 3s, they will find that they know a lot of them already.  Not only does that give them confidence, but it gives them benchmarks to count up from when they encounter problems they don't know.

For example:

If you teach a student 1s, 2s, 5s, 10s, and 11s, first, the next obvious set is 3s.

Give the student a worksheet of 3 times tables.  Let the student fill in the problems he or she knows.

Then, think about what's left: $3\times3$ is a double.  The student probably already knows that that's 9.

$3\times4$ is just 3 more than 9: 12.

$3\times6$ is just 3 more than $3\times5=15$ so: 18

You can see the pattern.  Soon, the student will know all of the threes (including $3\times4$, which means that the student already knows one more problem when he or she starts the 4s). By the time you get to 12s, the only "new" problem that students have to learn is $12\times12$.

Overall, learning times tables can be arduous -- but it's worth it in time and aggravation saved over 10 (or more!) more years of math!  Push students to learn them and learn them well.

Alternate Method:

There's a common trick used to teach 9s.  We don't emphasize it, because we try not to push students to rely on their hands.  But it can come in handy.

Here's how it works:

• Put both of your hands out in front of you, palms up, fingers extended.  You have fingers 1-10 in front of you (starting with your left thumb, ending with your right thumb).
• Take a 9s times table: $9\times8$
• Take the multiplier that is not a 9: 8 (REMEMBER: THIS TRICK ONLY WORKS FOR 9s.)
• Fold your 8th finger over (the middle finger on your right hand).
• The number of fingers standing to the left of that folder finger is your 10s digit: 7
• The number of fingers standing to the right of that folded finger is your 1s digit: 2
• You have the answer to $9\times8$: 72