# Tips for Teaching Multiplication (Confusion-Free)

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Memorizing multiplication facts helps elementary students learn more complex mathematical skills later on. But flashcards and multiplication drills may not be the best way to reach all elementary students, especially those who learn better with conceptual and reasoning strategies rather than rote memorization. Learn how to teach multiplication in a more incremental and intuitive way with these tips and fun activities designed for parents and teachers.

If you want to know how to teach multiplication, you need to start with addition. After all, multiplication is simply repeated addition — 8 + 8 is the same as 8 x 2, and 8 + 8 + 8 + 8 is the same as 8 x 4. Tips for teaching repeated addition include:

• Ensure that students know all their single-digit doubles (1 + 1, 5 + 5, etc.).
• Start with multiples of three (1 + 1 + 1, 5 + 5 + 5) and see if students can figure out the answer.
• Use word problems or draw pictures of word problems that use repeated addition (For example: Draw three boxes with five apples each, and have students use repeated addition instead of counting to figure out how many apples there are).
• Once students are comfortable with the concept of repeated addition, introduce multiplication problems in place of repeated addition (5 x 3 instead of 5 + 5 + 5).
Introduce Arrays

Arrays, which are ordered arrangements of items, are an effective tool for learning multiplication. Some ideas for teaching repeated addition with arrays include:

• Be sure that students know the difference between rows (horizontal) and columns (vertical).
• Draw a row of dots to represent the 1 times table, then add more rows to show the 2s, 3s, 4s, etc.
• Show students how to count the rows and columns of arrays to find the equation they are solving (for example, five rows and two columns would be 5 x 2), and demonstrate how to count the array items to check their work.
• Hand out small toys or blocks for students to create their own arrays that show various multiplication problems.
• Find examples of arrays in your everyday life, such as cookies on a cookie sheet or windows on a building. Have students constantly solve these arrays as quickly as possible.

## Focus on Zeroes and Ones

In multiplication, the zero property (anything multiplied by 0 is 0) and the identity property (multiplying a number by 1 doesn't change its identity) are good basic skills to master. Helping students understand these properties can be easy and fun with these tips:

• Think of crazy items that would never appear in the room, such as mutant bats or 10-foot pythons. How many mutant bats are in the ten cups in the cupboard? (10 x 0 = 0). How many 10-foot pythons are sleeping in the four beds in the house? (4 x 0 = 0)
• Identify a group of items around the room, and ask the student how many items there are (for example, there are six bananas in a bowl). Because there is only one group, the number will always remain the same.

## Use Multiplication Charts

For visual learners, multiplication charts can really bring the concept of multiplication together. These number grids allow students to find the multiplicand on the top row and the multiplier on the first column, and to draw a line between them to find the answer. Create or find a multiplication chart that lists every number 1-144, and use them in the following ways:

• Hang up a large, laminated multiplication chart for students to use dry-erase markers and find the answer.
• Print up several smaller copies and quiz students on different multiplication problems (they can use the same sheet with different colored markers or pencils).
• Crop the chart as needed to focus on beginning multiplication tables (for example, only up to the 5 x 5 section, or the top few rows to focus on the 12 times tables).
• Once students have mastered a times table or equation, have them cover it or color it a dark color so they can focus on the tricker ones.

## Reinforce the Commutative Property

The commutative property defines equations as reversible — that is, 3 x 4 has the same result as 4 x 3. This can be confusing for students who have only memorized multiplication facts, so you can reinforce it in the following ways:

• Use small toys or crayons to demonstrate that four groups of 3 is the same as three groups of 4 (or any other equation you'd like to work on).
• Draw an array of a multiplication problem, then turn the paper 90 degrees to show that reversing the numbers of rows and columns results in the same product.
• Have students decide which is better: five servings of two desserts, or two servings of five desserts? Use more examples until they can answer "they're the same" almost immediately.

## Test the Associative Property

Once students are getting used to one-digit multiplication, challenge them with the associative property. The associative property states that multiplying numbers in any order results in the same product. Try multiplying three, four and even five one-digit numbers with these tips:

• Write out a multiplication equation with three numbers (such as 4 x 2 x 5) and allow the student to draw parentheses wherever they want (4 x (2 x 5) or (4 x 2) x 5). Remind them that PEMDAS requires them to solve the parentheses first. Once they solve both, they'll see they are the same.
• Roll dice three times and write the numbers they land on. Have them multiply all three in different orders and see if the answers are the same.
• Use blocks to create two identical arrays. Emphasize that students can solve the array and then multiply by 2 for the total number, or they can multiply the rows by 2 and the columns by 2 beforehand.

## Teach Tricks and Shortcuts

Memorizing multiplication tables is a lot of work. There's nothing wrong with a trick or two to make them a little easier! Popular multiplication tricks and shortcuts include:

• Add a 0 to any number when multiplying by 10. (The same goes for two zeroes when multiplying by 100, three zeroes when multiplying by 1,000, etc.)
• If you forget a 4 times equation, just double the double. For example, if you forget 4 x 6, double 6 (12) then double it again (24). You can even double it again to master the 8 times tables!
• If you forget a 5 times equation, multiply it by 10 instead, then cut it in half. For example, if you forget 5 x 7, make it 10 x 7 (70) then cut it in half (35).
• If you forget any times equations, think of the closest one you do know, and then add or subtract the multiplicand. For example, if you forget 3 x 8 but you know 3 x 7 is 21, just add 3 one more time (24).
• For the 11 times tables, simply repeat the multiplier (2 x 11 = 22, 9 x 11 = 99).
• All products of 9 times tables have digits that add up to 9, so you can easily check your work. For example, 9 x 7 = 63, and 6 + 3 = 9.
• To figure out the 9 times tables, hold up all ten fingers. From the left, count the number of fingers for the multiplier (for example, in 9 x 2, count two fingers) and put down the last finger. The number of fingers on the left of the lowered finger is the tens place of the answer; the number of fingers on the right is the ones place (so 9 x 2 is 18, because there is one finger on the side of the lowered finger, and eight on the other side.

## Introduce the Classics

Once students conceptually understand multiplication facts and are ready to learn how to memorize the multiplication table, they're ready for the classics. These activities are best when helping students solve multiplication problems more quickly, rather than learning them for the first time. Classic multiplication ideas include:

• Put up a large multiplication table poster in a highly visible area of the home or classroom. Make it brightly colored so that students' eyes are often drawn to it. (If students are struggling with one table in particular, only include that table in the poster).
• Perform timed math drills to see how quickly students can recall multiplication facts. Note which tables take longer than three seconds and focus on those going forward.
• Create multiplication facts flashcards for students to reference and drill.

## Incorporate Fun Multiplication Activities

Many students learn best by doing projects or activities. Use these engaging activities to reinforce multiplication skills:

• Multiplication Rock, Paper Scissors - Play Rock, Paper, Scissors with a student, but instead of forming a rock, paper or scissors, each person puts out a certain number of fingers (for example, one person puts out two fingers and the other puts out four). The first person to solve the multiplication problem wins the round!
• Multiplication War - Split a deck of cards in half and hand one half to each player. Each person puts down the top card without looking at it first. Both players work on quickly multiplying the two numbers (or 10 for jacks, 11 for queens and 12 for kings). The first one to solve it collects both cards.
• Lego Multiplication Game - Legos are instant array activities! Reach into a box of Legos and pull out a random one. Have the student multiply the studs on each Lego (they may be 2 x 4 studs or 1 x 6). For extra practice, have them multiply the studs on each Lego by additional Legos.
• Waldorf Multiplication Flowers - Artistic students will enjoy a visual representation of different multiplication tables. Have them draw a circle with the multiplicand inside, then a layer of petals with numbers 1-12 (the multipliers). Then, they draw a layer of petals outside the first one with the products of the main multiplicand and the multiplier in each inner petal. Display the flowers for extra review and reinforcement.

## Multiplying Knowledge and Engagement

Math can be way more fun — and effective — when you know how to teach multiplication in a conceptual way before focusing on memorization. Once students can multiply numbers 1-12, infinity is the limit! Keep the math engagement going with these tips for teaching math to English learners. You can also learn all about long division with the steps to long division problems (with answers).