Does more digits mean bigger?

• CCSS-M · 4.NF.C.7
  Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

4.NF.C.7 asks children to compare decimals to hundredths by reasoning about size. This task sets a trap the standard is designed to defuse: numbers that look big because they have more digits. The line forces the true comparison.

This is a misconception task. The interesting placements are the wrong ones, so slow down and let them happen before correcting.

1. Start: 0 at 8.3%
2. Drop 1: 1 at 91.7%
3. Drop 2: 0.5 at 50.0%

When to dropAfter two cards, drop 1 to fix the whole. Hold 0.5 as the final drop, the referee. Reveal it once 0.45 and 0.54 are placed: if 0.45 has drifted above the mark, the class sees the error at once.

Drop unlocks after 2 cards placed.

• 0.4

  at 41.7%
  Four tenths, a little under a half.
• 0.45

  at 45.8%
  Just above 0.4 and just below 0.5. The gap between 0.4 and 0.45 is small.
• 0.05

  at 12.5%
  Five hundredths, close to 0. Deliberately near 0.4 and 0.45 in wording but far from them in size.
• 0.54

  at 53.3%
  Just past the half, a little above 0.5.
• 0.7

  at 66.7%
  Seven tenths, in the upper part.

• 0.45 has more digits than 0.5. Does that make it bigger?
• How far apart are 0.4 and 0.45, really?
• 0.05 and 0.54 both have a 5. Do they belong near each other?

• Looks like
  0.45 placed above 0.5.
  Means
  Longer decimal read as larger, the classic digits-mean-bigger error.
  Respond with
  Ask which is more, forty-five hundredths or fifty hundredths, then check against the 0.5 drop.
• Looks like
  0.05 placed near 0.45 or 0.54.
  Means
  Matching the digit 5 rather than reading the place value.
  Respond with
  Ask how many hundredths 0.05 is, and where five hundredths sits relative to a half.

Write the class's order as a chain with > and < symbols, and ask if the digit count ever decided the winner. It never does.

More digits after the point does not mean a bigger number. 0.45 is not bigger than 0.5, and 0.05 is tiny.