Decimals on the line

• CCSS-M · 4.NF.C.6
  Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.C.6 literally asks children to locate 0.62 on a number line diagram, so this task includes that exact number. Placing 0.05 next to 0.5 also confronts the tenths-versus-hundredths size difference the standard depends on.

The 0.05 card is the one to watch. Many children will place it near 0.5. Let that happen and use the drops to expose it.

1. Start: 0 at 8.3%
2. Drop 1: 1 at 91.7%
3. Drop 2: 0.5 at 50.0%
4. Drop 3: 0.25 at 29.2%

When to dropAfter two cards, drop 1 to fix the whole, then 0.5 to anchor the middle, then 0.25 to help place 0.3 and to give a hundredths-scale reference near the lower end.

Drop unlocks after 2 cards placed.

• 0.3

  at 33.3%
  Three tenths along, between 0.25 and 0.5.
• 0.62

  at 60.0%
  Just past the middle. The standard's own example number.
• 0.9

  at 83.3%
  Nine tenths, near the end.
• 0.05

  at 12.5%
  Five hundredths, very close to 0. Tests the difference between a tenth and a hundredth.
• 0.45

  at 45.8%
  Just short of 0.5. Tests placing near, but not on, the half.

• How many tenths is 0.3? Where do three tenths land?
• 0.05 and 0.5. Are these close together or far apart? Why?
• Is 0.45 more or less than a half?

• Looks like
  0.05 placed near 0.5.
  Means
  Reading 0.05 as five of something and matching it to 0.5 without attending to place value.
  Respond with
  Ask how many hundredths are in 0.5, and how many in 0.05, then let the gap on the line speak.

Ask the class to write 0.62 as a fraction over 100, linking the position back to 62/100.

Decimals are numbers with a position, tenths are big steps and hundredths are small ones, and 0.05 is nowhere near 0.5.