Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.9

Lesson 7.6Comparing Distances on the Plane

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the distance between two points on the coordinate plane using absolute value.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
DistanceSpanish: Distancia How far apart two points are. It is never negative. always a positive length
Absolute valueSpanish: Valor absoluto How far a number is from zero. It is never negative. |−7| = 7
Horizontal distanceSpanish: Distancia horizontal How far apart two points are going left or right. From (-2, 3) to (5, 3): count from -2 to 5 = 7 units across
Vertical distanceSpanish: Distancia vertical How far apart two points are going up or down. uses the y-coordinates
Coordinate planeSpanish: Plano cartesiano A grid with a line going across and a line going up to plot points. Two number lines crossing at (0, 0), creating four quadrants
IntegerSpanish: Número entero Whole numbers and their opposites, like -2, -1, 0, 1, 2. ..., -3, -2, -1, 0, 1, 2, 3, ...

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Jo walks from (−3, 10) to (−3, 2). Sam walks from (6, −8) to (−7, −8). Each unit is 1 block. Who walks farther?

  1. Jo: same x, both positive, so 10 − 2 = 8 blocks.
  2. Sam: same y, opposite signs, so 6 + 7 = 13 blocks.

Answer: Sam walks farther, by 13 − 8 = 5 blocks.

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The two points share the -coordinate, so I compare the -coordinates.
  • Their signs are , so I the absolute values.
  • One trip is units and the other is units, so is farther.
  • A distance is always positive because .

Word bank distanceabsolute valuecomparequadrantaxisaddsubtractsame signopposite signsfartherunitscoordinate

Watch out!A common mistake

A common mistake in Distance on the Coordinate Plane is subtracting the coordinates as if both points were on the same side of zero, instead of adding their absolute values when the points are on opposite sides. For example, to find the distance between (-6, 3) and (2, 3), a student might subtract 6 − 2 = 4, but since -6 and 2 are on opposite sides of zero, the absolute values must be added instead: |-6| + |2| = 6 + 2 = 8. The correct distance is 8 units, not 4. Before you submit, ask: 'Are these two points on opposite sides of zero

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.9

Lesson 7.6Comparing Distances on the Plane

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the distance between two points on the coordinate plane using absolute value.

  1. 1Complete each step, then write the final answer.

    Find the distance between (−1, 3) and (5, 3).

    Show your work

    Hint 0 is between −1 and 5. Add the distances from 0.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Find the distance between (2, 1) and (2, 9).

    Show your work

    Hint Both y-values are positive. Subtract them.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the distance between (−4, 2) and (−4, −5).

    Show your work

    Hint The y-values have different signs. Add the distances from 0.

    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.9

Lesson 7.6Comparing Distances on the Plane

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the distance between two points on the coordinate plane using absolute value.

  1. 1Complete each step, then write the final answer.

    Leo finds the distance from (2, −1) to (2, −7). He adds 1 + 7 = 8. Is he right? What is the distance?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find the distance between (−3.5, 1) and (2.25, 1).

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the distance between (−5, 3) and (4, 3).

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.9

Lesson 7.6Comparing Distances on the Plane

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the distance between two points on the coordinate plane using absolute value.

  1. 1Circle the letter of the best answer. Show how you know.

    A chest sits at (−3, 2) and a cave at (4, 2). How far apart are they?

    1. A1 unit
    2. B2 units
    3. C5 units
    4. D7 units
    Show your work
  2. 2Complete each step, then write the final answer.

    Kim says the distance from (5, −4) to (5, 9) is 9 − 4 = 5. She always subtracts the distances from 0. What is the correct distance?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the distance between (−9, −5) and (−2, −5).

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help