There are two schools of thought concerning early math. One is to teach memorization early and allow understanding to dawn later. The other is to teach understanding first and allow memorization to occur naturally through use. We tend to fall in the second camp, although I will say that it likely depends on the child. Most of our Math Activities create an environment where the child has a chance to explore and make connections naturally.
Use Hundred Boards, coins, and counters to allow children to explore numbers.
Counting From 1 to 100
Place pennies on numbers from 1 to 100. As simple as it seems, this activity seriously entertains my kids for a good 15-20 minutes or more. You can start this activity as soon as the child understands not to eat the coins! It’s not important they do it in order at first, but at some point you may wish to model it that way. As my children have done this activity (from ages 3 to 6) their knowledge of number sequencing has grown. Not only do they learn to count to 100, but they notice the transitions from 9-10, 19-20, etc. They practice ending a row, then moving down and left to start a new row. They start to understand that “12” is not the same as “21,” and have a concept of the 20s, the 30s, etc.
Trading Pennies for Dimes
Fill the board with pennies. Have the child count out 10 pennies from a row, and trade it in for a dime. Place the dime on the 10, 20, etc. This activity is a great pre-concept for regrouping (carrying and borrowing).
Use transparent plastic counters instead of pennies. Place counters on 1 to 20. Remove every other counter. Count out loud the numbers that are covered. Practice evens, odds, count by 3s, 4s, 5s, etc.
Example: Using the transparent counters, place 3 counters on 1-3. Ask the child to add 2 more counters. On what number do they end?
Bring this activity out occasionally without instructions. Let them explore and discover. My kids like to put pennies on all the numbers that have a 5, have a 2, etc. They also like to make patterns.
After spending a few months playing with the board, start to translate the concepts to paper. We will perform the activity on the board (like Simple Addition) and then write it on paper as we go. If the work on paper is confusing, go back to just the manipulatives, and try again in a month.
Trading Pennies for Dimes is an activity you will want to pull back out when you start regrouping with addition (I’ll post an example of this activity at a later time).