Discovering Effective Approaches to Teaching Multiplication

After learning addition and subtraction, students move on to the next fundamental operation: multiplication. However, each child has a unique learning style, which means they will progress at their own pace. Therefore, teachers must utilize diverse learning resources and strategies to effectively teach the fundamentals of multiplication. This guide will explore the best practices for teaching multiplication in an engaging and effective manner.

Mastering the Basics—Step 1 to Multiplication

Memorizing the steps to multiplication is not enough; students must understand the basics and comprehend why this mathematical operation functions the way it does. Therefore, the first step in multiplication involves giving students an understanding of subtraction, skip counting, and the commutative property. 

• Subtraction as a Building Block: A strong understanding of subtraction allows students to comprehend the inverse relationship with addition. Once they understand this, students can recognize the inverse relationship between multiplication and division. 

• Skip Counting Techniques: Skip counting is a technique used to count numbers by a constant increment other than 1. For instance, counting by twos (2, 4, 6, 8, etc.) or counting by tens (10, 20, 30, 40, etc.) are common examples of skip counting. This strategy proves highly effective for mastering multiplication because it enhances fluency and reinforces comprehension of number patterns. By practicing skip counting, students develop a deeper understanding of multiplication, making it easier to perform multiplication calculations accurately and efficiently.

• Embracing the Commutative Property: The commutative property is a fundamental principle in mathematics that states when numbers are added or multiplied numbers, an order change of the numbers does not alter the result. For instance, in addition, 2 + 3 is equal to 3 + 2, and in multiplication, 4 × 5 equals 5 × 4. To make this concept relatable to students, teachers can employ real-life examples and interactive exercises. For instance, teachers can have students visualize how when packing bags of groceries, the order in which items are placed in the bag does not change the total number of items. Additionally, interactive exercises such as games or group activities can reinforce understanding. For example, students can engage in a game where they rearrange numbers to create different addition or multiplication equations while discussing how the commutative property applies. This hands-on approach helps solidify the concept and its practical implications in students' minds.

Making Learning Multiplication Fun

Learning multiplication can be overwhelming, but incorporating fun into the learning process can keep students engaged and enthusiastic about learning. These creative methods can be used to effectively teach multiplication while ensuring educational value: 

• Ditching Rote Memorization for Interactive Games: Drilling students with rote memorization does not guarantee conceptual understanding. Instead, educators should use interactive games such as multiplication bingo or digital multiplication puzzles to engage students. This fosters a deeper understanding, leading to fluent memorization of the times tables. 

• Real-world Applications in English and Math: Instead of relying on memorization of times tables, real-world applications can be used to better students’ understanding of multiplication. Word problems alongside fact fluency allow students to get a sense of how multiplication applies to everyday scenarios. This makes the learning experience more relatable and seamlessly integrates reading comprehension into math lessons. 

• The Role of Fun Games in Reinforcement: Games serve as an entertaining tool for getting students interested and involved in math. They make learning more enjoyable and encourage students to strive for improvement. When students play games, they experience a sense of accomplishment, boosting their confidence. Most importantly, games take away the fear of failure, making the learning environment most positive and helpful to growth. 

Varied Approaches for Different Learners

Learning difficulties, anxiety, or a negative view of the subject can make learning math hard. To ensure the unique needs of all learners are met, teachers can differentiate instruction so students receive the support required for multiplication mastery. To maintain an inclusive approach, here are some methods to help students learn and retain multiplication concepts: 

• The Role of Manipulatives: Using math manipulatives reduces the need to rely on rote memorization. Manipulatives, such as counters or blocks, represent multiplication concepts concretely, helping students to develop a strong conceptual understanding of multiplication. 

• Flashcards for Visual Learners: Flashcards may help visual learners master multiplication facts more quickly and confidently. This is because, when students can see the numbers and equations, it makes it easier for them to understand and memorize the information. 

• Leveraging Free Printable Worksheets: Free printable worksheets are a quick and effective way for teachers to ensure understanding. Worksheets are also very diverse and can accommodate various learning styles. While visual learners may benefit from diagrams or illustrations, auditory learners may engage with the worksheet through verbal prompts. Worksheets can even cater to kinesthetic learners by including interactive activities. 

• Adapting Strategies for Specific Grade Levels: Recognizing that students learn and develop differently at each grade level is important for creating effective strategies to meet their unique needs. Each strategy can be adapted to fit the needs of students in third grade, elementary school, or even high school. By adapting the way they teach based on the cognitive and emotional development of their students, teachers can ensure all students are equipped to succeed. 

Targeted Strategies for Specific Grade Levels

Some multiplication strategies are useful throughout all of elementary school and well into high school. However, some will need to be adjusted to compensate for the cognitive growth students experience as they get older. Here are some targeted strategies:

• Building on Elementary School Foundations: As students transition from third grade to the remainder of elementary school, it becomes imperative to build upon the foundational understanding of multiplication established in earlier years. This is the time to start introducing more advanced multiplication concepts, such as times tables and basic word problems. Using hands-on materials, integrating visual aids, and incorporating fun games are engaging ways to progress students toward mastery. Voyager Sopris Learning’s Vmath^® math intervention program offers this and more for struggling students in grades 2–8. 

• High School Mastery: Because high school math focuses on college and career prep, students may require a more sophisticated approach to multiplication. Teachers can present complex problems, such as those focused on larger numbers and fractions, to challenge their skills and promote a deeper understanding. Real-world applications and word problems can also help prepare students for the challenges they may encounter in future advanced math courses. 

• Differentiated Instruction: Differentiated instruction should be used to accommodate varying skill levels within each grade. Educators should assess students’ proficiency levels through various methods and techniques and then tailor their approach accordingly. 

Beyond the Basics—Multiplication and Division

It is common for students to face challenges with both multiplication and division since they are related concepts. Because of this, educators can use their students’ mastery of multiplication as a foundation for teaching division. To make this learning engaging, teachers should use strategic and creative approaches including: 

• Exploring Multiplication and Division Relationships: Division is the inverse of multiplication. To help students understand this inherent connection, teachers may introduce the concept of fact families or arrays. This will show them how multiplication represents combining equal groups, whereas division represents separating into equal groups. 

• Advanced Problem-Solving With Multiplication and Division: Advanced problem-solving involves both multiplication and division. Through real-world scenarios and complex word problems, teachers can encourage critical thinking and strategic approaches to problem-solving. This reinforces the practicality of both division and multiplication. 

• Mastery of Multiplication Tables: Strategies like mnemonic devices, songs, or charts can help students memorize multiplication tables, enhancing their ability to solve division problems effectively.  

Embracing Technology in Math Learning

Technology can be utilized in different ways, depending on the grade level and needs of students, to create meaningful learning experiences. Examples include:

• Interactive Multiplication Games and Apps: Incorporating interactive multiplication games and apps into the curriculum can benefit students in more ways than one. Not only are games fun for all ages, but students can engage in challenges, earn rewards, and enjoyably reinforce multiplication concepts. 

• Online Platforms for Practice and Assessment: Finding online platforms designed for both practice and assessment of multiplication skills can not only make learning fun but can differentiate learning to support individual students' needs for pace and understanding. 

• Virtual Manipulatives: Virtual or online manipulatives such as digital counters, arrays, and number charts can simulate hands-on experiences for students. They are an easy way to help students visualize multiplication concepts and can also be used in and outside of the classroom. Voyager Sopris Learning’s VmathLive^® incorporates interactive and visual representations of math to keep students engaged and bridge their understanding. 

• Multimedia Resources for Concept Reinforcement: Multimedia resources, such as videos and interactive simulations, can reinforce multiplication concepts by catering to visual and auditory learners. 

• Digital Flashcards and Quizzes: Digital flashcards and quizzes serve as quick resources that can be used individually or in whole-group lessons to provide a personalized and interactive approach to memorization. Teachers may allow students to work through them at their own pace for practice, or turn it into a game for students to practice efficiency. 

Additional Resources Available

The jump from learning addition and subtraction to multiplication and division can be daunting for students. By using a variety of strategies to teach multiplication effectively, teachers can foster a positive and effective learning environment for them as they make this transition. For more insight and tools to implement these strategies effectively, explore Voyager Sopris Learning’s math solutions.