This is a continuation of the April 10th entry, "Balanced Math Blog".
You may hold the turnaround card either way, as long as the writing is right side up. For the sake of simplicity, we'll start with holding the card this way:
******
****** This array represents 2(rows)x6(in each row)=12. Or, 2x6=12. Show the student this card, held this way, with the information on the tab folded down (so that the student cannot see what is written on it).
Have the student say out loud the heading at the top of the card, including the numbers that belong in the blanks. The student should say, "2 rows times 6 in each row equals 12." Now ask the student, "Can you say the mutiplication fact that this array shows?" The student should respond with "2x6=12". Flip up the tab for the student to see. This will confirm their answer. Call attention to the arrangement of the dots on the card and have the student observe and comment on it before turning the card.
Now turn the card so that the array has 6 rows with 2 in each row. Ask the student what is different about the arrangement of dots. Proceed as you did before, when the card was held to represent 2 rows with 6 in each row.
After the student has interacted with both views, ask, "Does the order of the factors in a multiplication fact effect the product? Do you see why we can say that when you know 1 turnaround fact, you actually know 2 facts?"
Once the student understands the concept of multiplication, they are ready for memorizing the facts. There are many other activities to try for multiplication understanding, and I will continue to enter them in future posts. However, if the student doesn't need any more concept development in multiplication, then I would suggest "balancing out the math"by moving on to a memorization system such as the CCM of www.margosmathandmore.com.