Same distance from zero

• CCSS-M · 6.NS.C.7.c
  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

6.NS.C.7.c defines absolute value as distance from 0 on the number line. This task pairs numbers with their opposites so the class sees that the distance is the same even though the numbers differ.

Starting from zero alone is a gift here: the symmetry is the first thing the class can reason about. They can place 5 and -5 equidistant from zero before any scale exists, just by matching distances.

1. Start: 0 at 50.0%
2. Drop 1: 8 at 90.0%
3. Drop 2: -8 at 10.0%
4. Drop 3: 4 at 70.0%
5. Drop 4: -4 at 30.0%

When to dropAfter two cards, drop 8 and -8 to set the scale in both directions, then 4 and -4 as landmarks. Use the drops to confirm the pairs really are equidistant: -5 sits just past -4, and 5 sits just past 4, the same amount.

Drop unlocks after 2 cards placed.

• -5

  at 25.0%
  Five to the left of zero. Its distance from zero is 5.
• 5

  at 75.0%
  Five to the right of zero. Same distance as -5, opposite side.
• -3

  at 35.0%
  Three to the left of zero.
• 3

  at 65.0%
  Three to the right of zero. Mirrors -3.
• -6

  at 20.0%
  Six to the left. The furthest card from zero on the negative side.

• How far is -5 from zero? How far is 5?
• 5 and -5 are different numbers. What is the same about them?
• Which card is furthest from zero? What is its distance called?

• Looks like
  5 and -5 placed at different distances from zero.
  Means
  Not yet seeing that opposite numbers are equidistant from zero.
  Respond with
  Fold the line at zero in your mind, or with a gesture, and ask whether 5 and -5 would land on top of each other.

Ask the class to read off the absolute value of each card, and confirm that the pairs share a value.

Absolute value is distance from zero. 5 and -5 sit the same distance from the middle, on opposite sides.