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Alyssa can count to 30, recognize and write to 20, knows simple patterns, number order, ordinal numbers, and we're almost finished greater than-less than. She's becoming quite the little math whiz, but I'm not sure where to go next? Should I move on to addition, or would things like time to the hour or money be easier for her to learn first?
Yes, time and money might be introduced in K-1st, but they're usually not the focus until around age 8 (2nd-3rd). I'd move on to addition and subtraction facts up to 10 (making 4 facts per family... like 2+1=3 ... 1+2=3 ... 3-1=2 ... 3-2=1) and skip counting by 2's, 5's, and 10's. If you want to teach time, I'd do only :00 and :30, and if you want to teach money, I'd teach only recognition of coins, not values.
A number line or number grid is a great way to teach skip counting, counting with objects (money, buttons, counters, candy, blocks...), for twos you can jump, for 5's hands and feet, but the easiest is just writing it out and repeating it.
Skip counting is easy to learn if you just add it your routine. If you do a circle time or calendar time do it then. Two minutes a day and she'll have it down in no time. You could do more complicated patterns and start addition and subtraction (I'd use manipulatives.) If she doesn't know the value of coins, you could at least start with that and lay a foundation for later.
I taught this to my kids when they were 4 or 5, and they still sing it today if they forget:
A penny is one cent, a penny is one cent
A nickel is five, a nickel is five
A dime is ten pennies, a dime is ten pennies
A quarter twenty-five, a quarter twenty-five.