Fractions and decimals together

• CCSS-M · 5.NBT.A.3
  Read, write, and compare decimals to thousandths.
• 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.

This bridges 4.NF.C.6, decimal notation for fractions, with 5.NBT.A.3 comparison. Putting 1/4 and 0.3 on the same line means the class has to convert one to compare them, and the line confirms whether they were right.

Mixing forms is the point. Resist the urge to convert everything to decimals for them; let the comparison force the conversion.

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, then 0.5 to sort the cards into under a half and over a half, which straddles both forms at once.

Drop unlocks after 2 cards placed.

• 1/4

  at 29.2%
  A quarter along. The same point as 0.25, which is worth naming.
• 0.3

  at 33.3%
  Three tenths, just past 1/4.
• 3/5

  at 58.3%
  Three fifths, which is 0.6, just past the middle.
• 3/4

  at 70.8%
  Three quarters, the same point as 0.75.
• 0.9

  at 83.3%
  Nine tenths, near the end.

• 1/4 and 0.3. Which is bigger? How can the line settle it?
• What is 3/5 as a decimal? Does its position agree?
• Which of our cards land on the same spot as a simple decimal?

• Looks like
  0.3 placed above 1/4 by a large gap, or below it.
  Means
  Not converting to a common form before comparing.
  Respond with
  Ask what 1/4 is as tenths, or as a decimal, then compare like with like.
• Looks like
  3/5 placed at 3/4 or near it.
  Means
  Reading three fifths as close to three quarters because both start with three.
  Respond with
  Ask what 3/5 is out of ten, then place six tenths.

List each card in both forms, fraction and decimal, and mark the pairs that share a point.

Fractions and decimals share one line. 1/4 and 0.25 are the same place, and you can compare a fraction to a decimal by position.