Effective Multiplication Strategies for Supporting Struggling Learners

Teaching multiplication can be a challenging endeavor, especially when working with students who struggle with math. However, by understanding the common obstacles these learners face and implementing targeted strategies, educators can help them develop a solid understanding of multiplication and build confidence in their mathematical abilities. This article explores various strategies for teaching multiplication to struggling learners, drawing upon research, practical classroom experiences, and expert recommendations.

Understanding the Challenges

Before delving into specific strategies, it's essential to understand why some students struggle with multiplication. Several factors can contribute to these difficulties, including:

Learning difficulties: Dyscalculia, sometimes referred to as "math dyslexia," can significantly impact a child's ability to understand number-related concepts and develop number sense.
Poor working memory: Multiplication involves remembering different numbers and their meanings, which can be challenging for students with poor working memory. They may struggle to keep track of the number of groups and the number of objects in each group.
Weak mental maths skills: A lack of fluency in counting in 2s, 5s, and 10s can hinder a student's ability to solve multiplication problems independently.
Anxiety and negative attitudes: A negative view of math can create a barrier to learning, making it difficult for students to engage with the subject matter.

Strategies for Building Multiplication Fluency

To effectively address these challenges, educators need to move away from rote memorization and embrace strategies that promote conceptual understanding and flexibility in thinking. Here are some effective strategies for building multiplication fluency:

1. Concrete Examples and Manipulatives

Start with Concrete Examples: Before moving to abstract multiplication, use physical objects to demonstrate multiplication concepts. To overcome the barrier of poor working memory, ensure children always have access to concrete resources. Encourage them to use resources to show the problem. Having a physical representation in front of them meant they could always refer back to how many groups there were. It also helped them internalise the problem as they physically made the groups. We encouraged the children to write down how many groups they had or gave them number cards so they could select the amount of groups and then how many objects were in each group. This took a lot of pressure off the children, letting them focus on solving the problem. Manipulatives are physical tools or objects students can physically move or manipulate to better grasp a concept. Using tiles or blocks-or sometimes even candy-teachers can visually show students how a number may increase. Students will line the manipulatives in equal groups to represent the problem and more clearly see the numbers or groups they are counting.

2. Skip Counting

Encourage children to skip count as a stepping stone to mastering multiplication tables. Skip counting is when students will use intervals-or skip counts-by adding a number each time to the previous number. For example, skip counting by 3 is 3, 6, 9, 12, and so on. Skip counting is helpful when it comes to multiplication facts and tables, which can help them memorize the facts. This is a problem that we weren’t able to immediately tackle and solve. Instead, we’ve started including counting in 2s, 5s, and 10s on a more regular basis throughout the day. We’ve also encouraged these children to count at home whenever possible.

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3. Arrays

Introduce Arrays: Use arrays to teach multiplication. Arrays are visual ways to show multiplication patterns using rows and columns. This arrangement of rows and columns will match a multiplication equation. These arrays can be used with pictures, numbers, or even physical items to display a clear visual of a numerical concept.

4. Commutative Property

Utilize the Commutative Property: Teach children that the order in multiplication doesn’t affect the result (e.g., 4 x 3 is the same as 3 x 4). The commutative property of multiplication simply means that the order in which numbers are multiplied does not change the end product. For example, 2 x 6 = 12 and 6 x 2 = 12. This is an important skill for students to learn because it will reduce the number of multiplication facts that have to be memorized, thus leaving more room in their long-term memory for additional skills.

5. Subitizing Cards

Subitizing cards show a collection of items (usually dots) that students learn to identify without having to count each individual object. Just like we can identify the amount shown on dice without having to count, subitizing cards arrange objects in a way that students can look at the cards and quickly know the value using grouping strategies. Consider using subitizing cards in similar ways that you would use traditional flashcards. Show students the cards, but instead of moving on to the next card after a correct answer is given, ask students how they got their answer. You can also use these cards for classic games like War or Go Fish. The more students work with these visuals, the more efficient strategies they will develop. You can also watch a short video of how he uses them with students! This is a fantastic page to share with parents if they are looking for something to do at home with their child to help them with their multiplication facts.

6. Number Strings

Number strings (sometimes called problem strings or number talk strings) are a series of problems that are intentionally designed to lead students towards a specific strategy or way of thinking. Most of the time the number strings routine is done as a whole class just as you would carry out a number talk. Instead of discussing a single problem, students would go through a string of problems and discuss how these problems relate and how one or two of the problems could help you solve the other problem. Take a look at the following string of problems:

2 x 8

5 x 8

7 x 8

Think about how a student might use the first two problems (which use students’ knowledge of foundational facts) to help them solve the last multiplication problem? When students understand multiplication as equal groups, they know that 7 x 8 is seven groups of eight. 7 groups of 8 is the same as 2 groups of 8 and 5 groups of 8… 7 x 8 = (2 x 8) + (5 x 8). If students know the first two problems, then they can figure out the last problem. This string of problems was created to show students the “decomposing a factor” strategy. If you know the strategy you would like students to explore, number strings are fairly easy to create! If you are looking to use number strings that are already created for you, Sherry Parrish’s Number Talks books are excellent resources!

7. Highlighting Patterns and Tricks

Show children how to recognize patterns in multiplication tables, such as the results for multiplying by 5 or 10. Multiplication-as with all of math-ultimately breaks down into rules that follow patterns. Once students understand the rules and begin to notice the patterns, they can then move on to the next skill with more confidence and more opportunity for success. Putting these rules and patterns onto anchor charts for the classroom can give students those visual cues to help them remember what they have learned as they practice problems.

8. Area Model

The area model demonstrates that when multiplying two numbers, you can find partial products and add them together to find the overall product. The open area model is my favorite alternative multiplication strategy and where I would start. The steps are already built in. They know that each box needs to be filled in. I always start with an anchor chart showing a basic problem, like 24 × 31. (Quick confession: I keep this anchor chart up ALL year. Quick teacher tip: Download my area model template with built-in steps. This is where I often hear the first “Ohhhh!” from students. Here’s where the magic happens. Teacher Tip: Watch for common errors like forgetting to add all the partial products or misaligning place values.

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9. Partial Product Multiplication

Partial product multiplication is the open area model without the boxes. Essentially, students are completing the exact same steps in the same order, but without the array format. Remember how we broke apart those numbers in the area model? The partial products method uses that same concept, but in a vertical format that many of our students find easier to manage. (Between you and me, this is my favorite strategy for students who say “But Mr. Teacher Tip: I’ve created a partial products organizer that helps students track their steps. Teacher Tip: I often create an anchor chart showing the area model and partial products side by side.

10. Distributive Property

Using the distributive property is a multiplication strategy that will later reinforce another important math skill.

11. Ratio Table

You can use a ratio table to split a factor into chunks (in this case 24 was broken down into 4 and 20) to find partial products that are then added together to find the final product.

12. Friendly Numbers

In order to use friendly numbers, multiply by more (or less) groups than necessary. In this example, I traded 18 for 20. After finding the product of 31 and 20, I found the product of 31 and 2 (since 20 - 18 = 2). In this case, I shot under by trading 31 for 30. Most students are comfortable with at least the foundational facts (0s, 1s, 2s, 5s, and 10s), so it’s okay to temporarily modify problems to include more friendly numbers. Multiplying 532 x 15 is much more accessible than multiplying 986 x 47 to students who are still building their fluency with multiplication facts. In this situation, modifying the problem to include friendly numbers gives students the opportunity to work with grade-level concepts even though they are still working on mastering those single-digit multiplication facts. As students progress in their fluency with derived facts (3s, 4s, 6s, 7s, 8s, and 9s), they will be able to apply those to the more advanced math concepts that they’ve already been exposed to. Consider how this subtle modification impacts students’ confidence as a learner. Rather than being a 5th grade student working on single-digit multiplication while the rest of the class works on multi-digit multiplication, this student is now able to participate and learn the strategies and models everyone else is learning. Modifying the problems or giving students numbers choices allows for differentiation and is a much better option than keeping students from grade-level work entirely because they aren’t fluent with their multiplication facts YET.

Supporting Students in Upper Grades

We cannot use students’ lack of fluency with multiplication facts as an excuse not to expose them to grade-level content. I understand how frustrating it can be to work on multi-digit multiplication or division or many other concepts in upper elementary when students are still struggling with their basic math facts. We can’t assume that a student who doesn’t “know” all of their multiplication facts also does not have the ability to think deeply about more advanced math concepts. Their lack of “fact mastery” does not mean they are stuck at a 3rd grade math level (whatever that means) and typically is a reflection of ineffective teaching methods and not students’ ability to think and reason. I think it’s reasonable to make modifications and put supports in place so that students can access grade-level content, as long as we are committed to building their fluency with multiplication facts in other ways.

Support Tools

For students who are really struggling with fact fluency, it is okay to temporarily give them a multiplication chart to use as they work on more advanced math concepts. Think about multiplication charts like you would think about crutches to someone who just had knee surgery. Even though they are doing the exercises and stretches needed to heal their knee, it still takes time and during that time they need crutches to support them so that they can do the things they need to do in life (getting to the shower, going to appointments, etc.). The crutches are not meant to be used forever. They are a temporary support. Multiplication charts are no different. They are only meant to be used temporarily so that they are not held back from working with other important math concepts. Giving students no supports to access grade-level work while they are still working to build their fluency with multiplication would be like sending the patient home from the hospital to heal without crutches. We want students to have some way to work with more advanced math concepts, even though they aren’t where we’d like them to be with multiplication yet. Consider giving students partially filled multiplication charts so that they are only using them for facts that they personally struggle with.

Strategies for Teaching Division to Struggling Students

Students struggle with multiplication and division alike. After all, they are related concepts, and because of this, teachers can use students’ prior learning of multiplication to help them activate that knowledge for division. In addition to this, some of the strategies for teaching division to students who may be struggling to understand division are similar to those of multiplication. Division also has math facts and times tables that can be memorized. And for those who struggle with memorization, there are strategies to help with that, too. Dividing physical items into groups that visually represent a division equation can help make numbers more engaging and approachable for students.

Manipulatives

As stated above, manipulatives are physical tools or objects students can physically move or manipulate to better grasp a concept. This time, instead of having a bunch of small items that can be sectioned into equal groups, students will start with the whole group of manipulatives and are asked to divide them among a given number.

Division Facts

Division facts are number sentences as they relate to times tables. There are an infinite number of division facts, but the ones most often taught are 0 to 12. These are usually taught using charts or tables and are necessary before students move on to learning long division.

Partial Quotients

Using partial quotients is helpful when it comes to solving larger division problems. A partial quotient is when students focus on a part, or a chunk, or the number. This can help a student view the larger number as more approachable and less abstract. If students are having a hard time with the numbers alone, they can use a box model or an area model to help even further.

Area Models

Area models, also referred to as box models, use a rectangular diagram that breaks down larger numbers into smaller numbers and then use boxes to make the calculation simpler. By using the rows and columns to devise smaller calculations, they can then use the numbers outside of the box to find the correct answer.

Engaging Activities and Resources

To make learning multiplication more enjoyable and effective, incorporate fun worksheets and games, integrate technology, and apply real-world examples. Here are some specific ideas:

Fun Worksheets and Games: Incorporate colorful and interactive worksheets and games to make learning multiplication exciting.
Integrate Technology: Use educational apps and online games to provide interactive and enjoyable ways for children to practice multiplication.
Apply Real-World Examples: Connect multiplication to real-life situations to make the concept more relatable and meaningful.
Encourage Group Learning: Allow children to work in pairs or groups to solve multiplication problems.
Gamify: Any time you can incorporate games into your activities, it can transform your lesson. Students love to play games, so combining learning with gaming can be highly beneficial. This is also a great opportunity to make learning math collaborative by incorporating some teamwork and competition. Games can range from board games that involve math, to a classic deck of cards, to online game-style activities.
Go Online: Incorporating technology into the classroom is common today as technology continues to be so prominent in the world around us. Finding some online programs that help teach students multiplication and division can not only make learning fun, but it can also help differentiate learning and allow students to move at their own pace and understanding.
Incentives: Using some consumable manipulatives is always a popular strategy with students. Try giving students candy or snack manipulatives they can eat after they successfully practice their equations. If food items aren’t allowed or encouraged in your room, you can always offer incentives like stickers or other small prizes.
Activate the Arts: Math is often associated with the left side of the brain, so incorporating some art into a math lesson can help activate the right side of the brain. This then encourages students to use their whole brain when learning. Whether you choose to sing songs when skip counting or draw flower petals when multiplying, incorporating art into a math lesson can help make learning more fun and meaningful.
Use What You Have: Having fun with lesson planning doesn’t have to mean going out and getting a bunch of new materials or supplies. Sometimes having fun in class means getting more creative with what you already have.

The Importance of Systematic Review and Corrective Feedback

Overall, we found it challenging to teach multiplication to our struggling mathematicians. But there was a silver lining. By working to increase learners’ exposure to the concepts along with the use of concrete resources, our struggling learners began to understand the ideas being taught. When it comes to students with a poor performance in mathematics, specifically in recalling multiplication facts, studies have found it highly meaningful to incorporate “systematic review and corrective feedback.” Therefore, the strategies listed above are all great places to start, but a routine system of review and correction is also crucial in solidifying the concepts. Drill and Practice: Regular practice is crucial. Use quizzes and flashcards to reinforce multiplication facts.

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