Finding our way through math

I'm following the provincial math curriculum with Nature Girl and feeling my way through what works best for her. It appears to get past her strict adherence to external rules - regardless of whether they actually help her learn something or not - the best route is to find a real life way for her to use the information first, let her figure out her own way around managing the information, and then give her the workbook stuff on it after she's done the investigation herself.

We are working with data management and probability right now. The workbook exercises are all about venn diagrams, and different ways of visually representing data. She is getting excited about doing these things herself BEFORE they show up in the "book" and as a result we can discuss why they work - tally sheets with ticks, or visual representations of objects, or a venn diagram, whatever the case may be.

I think she's successfully making math meaningful.

This would be really difficult in a classroom setting. As soon as she "invents" a tally system I can go with it and find an example it works really well with and I can pull out the worksheets that relate to it while it is still fresh in her mind. I can then tweak my examples so that she needs to figure out a more substantial way of managing the data - for example - using division. I can monitor things very closely to make sure she never reaches her frustration threshold while still pulling her through the various examples the curriculum wants us to explore.