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Unit 05 · Rational Numbers and CoordinatesLesson

Day 074Distances Across the Axes

LearnClassworkAnswer keyPDF packet ↗
Standards 6.NS.C.8
LEARNING TARGET

I can graph points and find horizontal or vertical distance.

01 · LEARN

Build the idea

Plot both points. If x-coordinates match, count the vertical units; if y-coordinates match, count horizontal units. On opposite sides of zero, add distances to zero. On the same side, subtract magnitudes.

WORKED EXAMPLE 1

Plot (-8, 5) and (-13, 5). Find their distance.

5 units

Only one coordinate changes. Same side of 0: subtract magnitudes to get 5.

WORKED EXAMPLE 2

Plot (-8, 4) and (7, 4). Find their distance. Explain why adding magnitudes works or does not work for these points.

15 units

Only one coordinate changes. Opposite sides of 0: 8 + 7 = 15.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Plot (4, -4) and (4, -8). Find their distance.

  2. Plot (-6, 4) and (-10, 4). Find their distance.

  3. Plot (6, -4) and (6, -10). Find their distance.

  4. Plot (-8, 6) and (3, 6). Find their distance.

  5. Plot (3, -2) and (3, 2). Find their distance.

  6. Plot (-3, 2) and (3, 2). Find their distance.

  7. Plot (6, -5) and (6, 6). Find their distance. Explain why adding magnitudes works or does not work for these points.

  8. Plot (-8, 5) and (2, 5). Find their distance. Explain why adding magnitudes works or does not work for these points.

  9. Plot (2, -8) and (2, 5). Find their distance. Explain why adding magnitudes works or does not work for these points.

  10. Plot (-3, 2) and (3, 2). Find their distance. Explain why adding magnitudes works or does not work for these points.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 4 units

    Only one coordinate changes. Same side of 0: subtract magnitudes to get 4.

  2. 4 units

    Only one coordinate changes. Same side of 0: subtract magnitudes to get 4.

  3. 6 units

    Only one coordinate changes. Same side of 0: subtract magnitudes to get 6.

  4. 11 units

    Only one coordinate changes. Opposite sides of 0: 8 + 3 = 11.

  5. 4 units

    Only one coordinate changes. Opposite sides of 0: 2 + 2 = 4.

  6. 6 units

    Only one coordinate changes. Opposite sides of 0: 3 + 3 = 6.

  7. 11 units

    Only one coordinate changes. Opposite sides of 0: 5 + 6 = 11.

  8. 10 units

    Only one coordinate changes. Opposite sides of 0: 8 + 2 = 10.

  9. 13 units

    Only one coordinate changes. Opposite sides of 0: 8 + 5 = 13.

  10. 6 units

    Only one coordinate changes. Opposite sides of 0: 3 + 3 = 6.

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