Addition & Subtraction Within 20

Here’s what nobody tells you about early math: the jump from adding within 5 to adding within 20 is enormous. A kid who can instantly tell you that 2 + 3 = 5 might completely freeze at 8 + 7. That’s not a lack of ability — they just need a bridge strategy, and that’s what this whole program is built around.

We start exactly where you’d expect. The first couple of weeks are counting review and addition/subtraction within 5. If your child already has that nailed, those weeks will feel easy, and that’s fine. Confidence matters more than challenge at the beginning. By Week 3, we’re working within 10 and introducing ten-frames — those two-by-five grids that make quantities visible in a way that counting on fingers never quite does. Something about physically seeing that 6 is “five and one more” rewires how kids think about numbers.

The Making-10 Strategy

This is the big one. When a child learns to break 8 + 5 into 8 + 2 + 3 — pulling that 2 over to make a clean 10, then just adding 3 more — they’ve unlocked a strategy that carries them through years of mental math. We don’t rush to get here. The program spends several weeks on number bonds and decomposition within 10 first, because making-10 only clicks if a child already knows their pairs to 10 cold.

Doubles facts show up around the same time (6 + 6, 7 + 7). Kids tend to memorize these almost accidentally — there’s something satisfying about doubles that makes them sticky. Once they know doubles, “doubles plus one” facts like 6 + 7 become quick mental shortcuts instead of counting marathons.

Word Problems and Mixed Practice

The last few weeks shift toward application. The worksheets present addition and subtraction mixed together, which is genuinely harder than it sounds — kids have to figure out which operation to use before they can solve anything. There are word problems set on a farm (because farm animals are inherently more interesting than abstract numbers), and a handful of error analysis problems where kids have to find and explain someone else’s mistake.

That last skill — spotting errors — is quietly one of the most valuable things in the program. A child who can look at “9 + 4 = 12” and explain why it’s wrong understands addition at a deeper level than a child who just gets the right answers through counting.