Decimals & Place Value

Here’s a question that trips up more fifth graders than you’d expect: is 0.45 greater than 0.6? A surprising number of kids say yes, because 45 is bigger than 6. That misconception is what this entire program is built to dismantle — not by telling kids “that’s wrong,” but by giving them enough practice with place value that the correct answer becomes obvious.

The first week focuses on reading and writing decimals to the thousandths place. Place value charts, word form, expanded form — the kind of foundational work that seems basic but matters a lot when kids start comparing and computing with decimals later. We don’t rush past it.

The Tricky Parts

Comparing decimals gets its own full week because it deserves it. The problems start simple — 0.7 vs 0.70, that sort of thing — and ramp up to situations where the number of decimal places doesn’t match and kids have to think carefully about what each digit actually represents. There are real-world comparisons mixed in too, like race times and prices, because context helps the abstract click.

Place value relationships are where fifth-grade math gets genuinely interesting. Understanding that a digit in one place is ten times what it would be one place to the right (and one-tenth in the other direction) — that’s a big conceptual leap. The worksheets use the “how many times greater” framing that shows up on standardized tests, but we build toward it rather than just throwing it at kids cold.

Later weeks bring in mystery number puzzles and error analysis. Finding where another student went wrong with decimals forces a kind of thinking that straight computation never does. And the challenge problems use real scenarios — comparing cereal prices per kilogram, ranking swim times, figuring out whether “more decimal places” means “bigger number” (spoiler: it doesn’t).