Into the negatives

• CCSS-M · 6.NS.C.6.c
  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.C.6.c asks children to find and position integers on a number line, including negatives. Zero is the pivot, and this task starts from zero alone so the class has to reason outward in both directions before any scale is given.

Zero is the single start benchmark. That is enough to place negatives left and positives right by feel, which is the reasoning to draw out before the scale drops arrive.

1. Start: 0 at 50.0%
2. Drop 1: 10 at 91.7%
3. Drop 2: -10 at 8.3%
4. Drop 3: 5 at 70.8%
5. Drop 4: -5 at 29.2%

When to dropAfter two cards, drop 10 and -10 to set the range in both directions, and expect the class to spread the cards out. Then drop 5 and -5 as a landmark in each half; they make -6 and -7 easy to separate and 4 and 8 easy to place.

Drop unlocks after 2 cards placed.

• -7

  at 20.8%
  Between -10 and -5, in the lower negative stretch.
• -3

  at 37.5%
  Between -5 and 0, closer to zero.
• 4

  at 66.7%
  Between 0 and 5, on the positive side.
• 8

  at 83.3%
  Between 5 and 10, near the positive end.
• -6

  at 25.0%
  Just past -5 toward -10. Sits between -7 and -5.

• Is -7 more or less than -3? Which is further from zero?
• How is the position of -6 related to the position of 6?
• Which card is the smallest number? Where does the smallest one go?

• Looks like
  -7 placed to the right of -3.
  Means
  Treating the seven as larger and ignoring the minus sign, so -7 feels bigger than -3.
  Respond with
  Ask which is colder, minus seven degrees or minus three, and let the temperature analogy settle the order.

Ask which pairs of cards are the same distance from zero, and what that distance is called.

Negative numbers live to the left of zero, and the further left you go the smaller the number, so -7 is less than -3.