Addition and Subtraction: Facts to 20 and Strategies to 100
Grade 2 computational fluency has two layers: automatic recall of facts to 20 (built on Grade 1 strategies) and flexible multi-digit strategies to 100. The key insight connecting them is place value: 48 + 37 can be solved by adding the tens (40 + 30 = 70), adding the ones (8 + 7 = 15), and combining (70 + 15 = 85). This decompose-and-recompose strategy works because tens and ones operate independently. Students who understand this can compute any two-digit sum mentally.
From facts to strategies
Grade 1 built the foundation: counting on, making 10, doubles. Grade 2 extends these to two-digit numbers. Making 10 becomes bridging through 10 or 100: 48 + 7 = 48 + 2 + 5 = 50 + 5 = 55. Decomposing becomes adding tens then ones separately. Each strategy is a specific application of place value understanding.
Friendly numbers and compensation
Friendly numbers are multiples of 10 that are close to the addends. 48 + 37: 48 is close to 50 (add 2). 50 + 37 = 87. But we added 2 extra, so subtract 2: 87 - 2 = 85. This compensating strategy turns awkward numbers into easy ones. Students who use it are applying algebraic reasoning (adjusting one quantity and compensating) without knowing it.
Adding up to subtract
73 - 46 can be solved by asking: what do I add to 46 to reach 73? Count up from 46 to 50 (4), then 50 to 73 (23): total 27. This strategy converts subtraction into addition, which most students find easier. The open number line makes the jumps visible and the strategy transparent. It also connects to the inverse relationship between addition and subtraction.