It's not a bad map, if it's a textbook that's trying to keep things simple. But, there are a few details missing.

First, the land of New France, which included Canada and lands east of the Mississippi, would indeed go from France to England in 1763, with the end of the French and Indian War. And, with the end of the War for American Independence, all that land in theory did transfer to the new United States. But there would be real problems unresolved. One important one would be with the Native Nations in the northwest- they had not signed onto the peace treaty, and did not see why they had to cede their lands to the US. Their strenuous resistance resulted in the disastrous St. Clair expedition, in 1790, and expansion was halted until the US prevailed in the Battle of Fallen Timbers in 1794. The northern boundary of Michigan and Wisconsin was also unclear, and the British kept the forts in places like Detroit and Michilimackinac until the Jay Treaty in 1794 dealt with a lot of residual problems between the US and England, including trade and tariffs. But that northwest border really wasn't really worked out until after 1800. The Potawatomie, Ojibway, and Ottawa there were firmly aligned with the British, and plenty of other Native settlements further south on the Mississippi were as well, justifiably fearing US encroachment. It was something that would not be settled really until after the War of 1812.

Making the map date at 1787 does remove one complication, in that many of the 13 colonies previously had had large, even ludicrous claims to western territories. Under the Northwest Ordinance those were surrendered, and rules worked out by which the new territories were to be mapped and admitted as new states. But there were still some odd little quirks: Vermont did not have admittance as a new state until 1791, and so ran as a sovereign republic until then, even briefly negotiated with the British to be part of Canada- an idea it gave up when the British lost at Yorktown. As the map actually shows, it also had some territorial issues to be settled with New York. And then there was the almost-state of Franklin. Colonists and land-speculators from Virginia rushed into what's now east Tennessee when it seemed as though North Carolina was relinquishing authority over the region, staking out claims and making efforts to be recognized as a state. However, there were plenty of well-connected land speculators within North Carolina who had already filed claims there, and as result North Carolina blocked Franklin from joining the US. There was also the nation of the Cherokee, who disagreed violently with some of Franklin's boundaries. So, in 1787, Franklin was, like Vermont, forced to be a sovereign country. And a very poor one, using animal hides for currency. In desperation it had even made overtures to the Spanish to join the Spanish empire. In 1791 essentially North Carolina's own land speculators won, and with them charging new settlers the price of admission, the state of Tennessee was created.

Again, the textbook authors surely knew all this, but I can imagine the editors telling them, look, let's not get lost in the weeds, here: what if we just make that section two colors to let people know that it's complicated.

It is very inaccurate. This map omits all Native nations, hundreds of whom asserted control over their territories in 1787. I've written about the erasure of Native nations in US history textbook maps here.