I knew that the "algorithm" for addition with regrouping (or carrying as I was taught) would be a cinch to teach my daughter. However, I wanted her to really understand why it works and realized that incorporating manipulatives into the lesson would be the best way to explain it to her. With Valentine's Day coming up, I thought using conversation heart candies and marshmallow hearts would be fun way to do it.
To start, I explained that:
1 small heart = 1
1 medium heart = 10
1 large heart = 100
Next I asked her to show me how many small hearts equal a medium heart, and how many medium hearts equal a large heart.
Then we did a quick review of place value and worked out how to represent a given number with the hearts.
Next we did a couple addition problems without regrouping....
Finally, we worked on addition with regrouping. I explained to her that a sum greater than 9 in one's column (90 in in the ten's column) does not "fit". With the manipulatives, it was easy for her to visualize that a medium heart does not belong in the one's column and a large heart does not belong in the ten's column. I instructed her to move it to the top of the correct column and then add it up. At the same time we worked the sum out on paper and I showed her how to carry the one. After working a few problems she had her aha! moment and squealed "Mommy I get it!".
My daughter now calls this the "Heart Game". You gotta love it when your child is working math problems and thinks she is playing! Tonight I am going to throw a sum of three numbers at her to see what she does with it. And soon we will change the rules of the "Heart Game" to learn subtraction with regrouping!