Honestly, for history, I had the youngest two children (at that kindergarten age) follow along with what my middle two children were doing at the time (9 and 11 then). And since this was before I had to report/”keep track” or write objectives for the youngest two, I can’t quite remember – lol! Sorry! But my suggestions would be, if your friend knew what she wanted to cover for history, say early American, she can read biographies, or historical fiction. SCM has some great suggestions that your friend could probably find at her library…she could even read one or two of the grade4-6 suggestions if she felt the content was appropriate for her child. I did read one Eggleston’s American history texts to these younger two, and had them alternate narrating. I have seen that just reading some good books, and simply narrating has been great! At that age, they enjoyed the Little House on the Prairie books, in particular Farmer Boy (we are rereading currently, about 3 years later, because they liked so much). Sometimes I gave them a plain piece of paper and asked them to draw something from the story….again if this is done 1 picture/ book or once a month, your friend will have “documentation” for her history portion of her portfolio. She could even have her child copy one word/name onto this picture.
For math, I had my youngers start with a public domain book, First Year in Number by Hoyt and Peet. We did most of the exercises orally, and had them practice writing number formation and identification. Also, I could print out extra pages – the ones in the beginning lend themselves well to coloring. This text is still one of my favorite beginning math books. I have used dried beans for manipulatives…but of course, there are a myriad of items that lend themselves to this that are around the house.
I find the suggestion, that so many others have made, of keeping things simple, especially in the beginning years, wise counsel. With my first two I did not, and thought I had to have a book/workbook for each subject…but one’s everyday talks about food choices, safe habits can easily be counted as “health”, for example, when logged down for the day.