Skills & Strategies #2 - Four Non-Traditional Ways a Multiplication Table Can Support Mathematical Thinking

Some upper elementary, middle, and high school students do not know their basic multiplication facts.  These students not only struggle with using multiplication to find products, but they also have difficulty with other types of math problems and mathematical thinking that require an understanding of the quantitative relationships between specific factors and products, and between specific dividends and quotients.  A multiplication table has become an essential tool for my students who lack mastery in multiplication facts.  Once students become familiar and comfortable with using a multiplication table (stay tuned for more on to strategies to achieve this), it becomes an ally and a tool that can support their mathematical thinking in ways that cannot be achieved with a calculator.  Here are four examples of non-multiplication problems for which a multiplication table can help a student who struggles with his multiplication facts.

1. Finding the Lowest Common Multiple / Lowest Common Denominator

​Students with math fact difficulties cannot easily bring to mind the multiples of 6 and multiples of 8 and then hold them in their brain while comparing them in order to identify the lowest common multiple (24).

​Using a multiplication table, students can identify the multiples of 6 in one column and the multiples of 8 in another column, and then look for common multiples.  Students can use two parallel columns, or one horizontal column and one vertical column, as shown below.  It sometimes helps to use a straight edge to help students track the columns for easier visual scanning.

---

2. Finding the Greatest Common Factor (e.g., Reducing Fractions)

​Students with math fact difficulties cannot easily bring to mind the factors of 9 and the factors of 24 and then hold them in their brain while comparing them in order to identify common factors and then determine which one is the greatest (in this case, 3 is the only one).
 
Using a multiplication table, students can look for numbers (i.e., factors) that have both 9 and 24 as their multiples.

---

3. ​Long Division

Students with math fact difficulties cannot easily bring to mind the multiples of 3, determine which of those multiples is closet to but still less than 17 (i.e., 15), and then determine what the quotient is when you divide that multiple by 3 (or in my students’ heads, how many 3’s does it take to get to 15).
 
Using a multiplication table, students can easily identify the multiples of 3 and quickly see that 15  is the greatest multiple that is smaller than 17, which means that 3 can go into 17 5 times.

---

4. ​Factoring (e.g., Factoring Polynomials)

​Students with math fact difficulties cannot easily bring to mind the factors of 18 and hold them in their mind while determining which factor pairs add to 11.
 
Using a multiplication table, students can easily identify the different factor pairs that multiply to 18, then add each of these factor pairs together to determine which ones add to 11.

---

---