Here is a piece of mathematical thinking entirely invented by Antonia. It is sort of a mixture of sets and addition. She is still a bit confused about the difference between writing down two numbers next to each other and two numbers with a plus sign stuck between them. Hence we eventually got from "4 5; that makes forty-five" to "4+5=9". Antonia explains as follows:
The blue line is where the ones are that have tiny dots and we're trying to find out which is which. The red line goes around the ones that have green crosses. There are five of those. Then there's four inside the blue line.