I was in a lesson recently where a teacher used inverse to find square roots. They had calculated 3² as 9 so they used that fact to do the square root, but when a student got stuck with a question I noticed that they had previously looked at area of squares and rectangles so I reminded the student of finding the area of the square to help him find the square number/area and that the root was like the length of the side of a square if you know the area. This isn’t new and i have used this idea before, but the worksheet i made below was a response to the questions the students were given in that class. They weren’t just given 3² or find the √9. They were given 2 x 3² or √49 + √81.

I started to think of the area model again and how it would help students to solve those types of problems. Instead of 2 x 3² = 6², They could see that it was 2 squares of length 3 and not a square of length 6. Also, the shapes wold show that 8² – 6² wasn’t equal to 2².

Here is a copy of the ppt

I have had a thought on how i could extend this to surds