My 8 year old can add and subtract 2 and 3 digit numbers in his head more quickly than his 15 year old sister, who didn’t learn your strategies in grade school. I am also delighted at how quickly and naturally he has grasped multiplication, division and fractions this year — it is truly amazing. As your presentation of the concepts is so logical and understandable, he sometimes anticipates the next lesson. My own mathematical skills have improved as I have employed your strategies also!