Cuisenaire Rods do the trick

I started using Miquon Math and Cuisenaire rods with Sparkle.

I decided to start with the Orange book (the first book). Sparkle could do the initial addition and subtraction calculations in the book due to her background in RightStart. (I haven't started the fractions/multiplication stuff yet.) However, I had the gut feeling that Sparkle had some comprehension gaps that I couldn't quite define. So, I set aside the book and started working with the rods on our own.

As I suspected, Sparkle had a horrible time "finding all the combinations" that make a number.

Sparkle has a fluency with adding numbers that masks a lack of understanding. For example, she can calculate 1+5, 2+3, 3+3, and 6+0 and come up with 6 for all of them. However, she would get confused when trying to determine whether 1+5 equals 3+3. When I asked her to find all the combinations of numbers that equal 6, the only one she could come up with was 3+3. She was close to tears when I asked for other combinations.

In desperation, I found an article about number bonds, part-whole circles, and fact family equations. The article also talked about moving from concrete manipulatives, to pictorial representations, to the more abstract mathematical notation. I discussed the concepts from the article with Sparkle. Then I tried using the C-rods and some blank paper to teach Sparkle.

We worked our way back up to the idea of finding all the combinations that equal six. Here's the basic steps that I had Sparkle go through:

First, select two of each rod, so she had two of every number from 1-10.

Next, pick out a six cm rod to be the "whole" for this exercise.

Next, set aside all the rods longer than 6cm, as a larger number cannot be part of the "whole."

Next, use *all* of the remaining rods to create two car trains equal to 6cm. Then, discard "duplicate" trains with identical rods. Each two-car train represents a number bond.

Finally, record each number bond on paper. Draw the the part-whole circle and rod diagram. Write the equations in the fact family.



Next week we'll do the same activity for the numbers 7-10. If she flies through them, I'll know that she finally understands the concept.