Why the strategy — not the algorithm — comes first

Practice mode flashes a problem and reveals the strategy in one animated pass, the same rhythm as Fact Fluency Strategy Flash. Model mode steps through that identical sequence one teacher click at a time, so a class can pause on exactly the move it needs to see — every step carries its own narration line and a discussion question, never just a shape moving on a screen.

Dutch research on the empty number line (Klein, Beishuizen & Treffers, 1998) supports it as a genuine computation tool, not just a picture. Beishuizen (1993) found that jump strategies — moving along the line in friendly chunks — hold up better than splitting a number into tens and ones and operating on each place separately, especially as problems get harder; that's why Split by Place Value appears only under Addition here. For subtraction, splitting by place value reconstructs the same regrouping difficulty children hit with the standard algorithm, just done mentally instead of on paper. Selter (2001) found the jump-over-split advantage holds as numbers grow to three digits, which is exactly this tool's range. Compensation and Constant Difference are related but distinct moves — adjusting one number to a friendlier one, versus shifting both numbers by the same amount so their difference never changes — and Lawson (2016) documents Compensation as the strategy that typically develops first, with Constant Difference emerging later as students trust that a difference stays fixed under an equal shift. Watch for two specific slips: with Compensation, students often adjust one number but forget to compensate back on the other side; with Constant Difference, the usual error is shifting or changing only one of the two numbers instead of both. This tool covers CCSS 2.NBT.B.7 (adding and subtracting within 1000 using strategies based on place value) and 3.NBT.A.2 (fluently adding and subtracting within 1000).