When it comes to teaching kids multiplication, the immediate focus often lands on multiplication facts. While this is undeniably crucial, there’s an aspect that surpasses in significance – multiplicative reasoning. Let’s delve into the depth of this perspective through the following scenarios:

1. Calculate 5×6

2. Jesse’s Cookie Adventure: Jesse plans to bake cookies as Christmas gifts for 6 friends, putting 5 cookies in each gift bag. How many cookies does Jesse need to bake?

3. Jesse’s Cookie Consumption: After baking some cookies, Jesse ate 6 in the first week and 5 in the second week. How many cookies did Jesse ate in total?

While the first problem can be swiftly solved if one knows the multiplication facts, the real challenge lies in the second and third problems, especially for students just beginning to grapple with multiplication. How does a student distinguish between multiplication (as in the second problem) and addition (as in the third problem)?

The essence of teaching math isn’t solely about memorizing facts, as facts are readily available online. It’s about imparting problem-solving skills. In the second and third scenarios, students need to comprehend the problem, identify known and unknown elements, distinguish between provided units (5 cookies per bag, 6 bags; 6 cookies, and 5 cookies), and then determine the appropriate operation (multiplication for the second and addition for the third). The final step involves utilizing facts to expedite the calculation. Without a foundational understanding of the mathematical problems,  the multiplication facts become mere rote memorization.

Consider why multiplication is applied in the second scenario and addition in the third. The key lies in the nature of the given units. In the third problem, the given units (6 cookies and 5 cookies) are of the same level (both are cookies), allowing for addition. Conversely, in the second problem, the given units (5 cookies per bag and 6 bags) differ and cannot be added directly. The 5 cookies per bag are embedded in the unit of bags. To get the total number of cookies, students need to coordinate the cookies per bag and the total number of bags to get a total number of cookies, which is the core of multiplicative reasoning. Understanding these nuances empowers teachers and homeschool parents to guide their kids effectively through diverse mathematical situations.

However, fostering a genuine understanding of multiplication and problem-solving skills goes beyond mere numerical calculations. It involves contextualizing math concepts and problem-solving activities. Introduce real-life situations, design relevant math tasks, encourage students to articulate their thought processes, and guide them in comparing and contrasting scenarios (as illustrated by the second and third problems). By embracing this holistic approach, teachers and parents can ensure that their children not only master multiplication facts but also develop a deep comprehension of mathematical concepts and the ability to apply them in various contexts.

If you’re interested in learning more about how kids progress in math and discovering fun math activities to do at home, feel free to reach out to me at bingqian.wei@mathempowerfamily.com. Let’s explore math learning together!