In the midst of thinking about presenting the IS Curve to undergraduates, I came across this helpful blog post by Mark Thoma from 10/2011 that discusses David Romer's approach in Advanced Macro 4th ed. Spending today falls (rises) because the representative consumer (via the Euler condition) substitutes toward (away from) future spending when the interest rate rises (falls).
Maybe I'll present that intuition at some point, but I think undergraduates probably better comprehend the interest rate as the price of borrowing; when borrowing's price rises, borrowing and spending on investment and other durable goods falls.