6.NOS.9 Lesson 7-6-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.6 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Distance on the Coordinate Plane · Distance · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do you find distance on the coordinate plane?
1If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me
  1. I will find the distance from (-3, 2) to (4, 2). Both have y = 2, so they sit on the same horizontal line.
  2. The points are on opposite sides of zero, so I add the absolute values.
  3. |-3| = 3 and |4| = 4.
  4. I add: 3 + 4 = 7. The distance between them is 7 units.
3Second Model — Try it together — then prove it
  1. Now let's find the distance from (2, 3) to (2, 8). What do these points share? The same x = 2, so it is a vertical line.
  2. These points are on the SAME side of zero (both positive), so do we add or subtract? We subtract.
  3. The distance is |8 - 3| = 5 units. When points sit on the same side of zero, subtract to find the distance.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Distance on the Coordinate Plane (Distancia en el plano de coordenadas) — The positive space between points, found from the absolute difference of coordinates on a horizontal or vertical line.
  • Distance (Distancia) — How far apart two points are. It is never negative.
  • Absolute value (Valor absoluto) — How far a number is from zero. It is never negative.
  • Horizontal distance (Distancia horizontal) — How far apart two points are going left or right.
  • Vertical distance (Distancia vertical) — How far apart two points are going up or down.
  • Coordinate plane (Plano cartesiano) — A grid with a line going across and a line going up to plot points.
5Watch out
  • 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 — and if so, did I add the absolute values instead of subtracting?'
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    The Park is at (-4, 5) and City Hall is at (3, 5). How many blocks apart are they?

    1. A1 block
    2. B7 blocks
    3. C12 blocks
    4. D5 blocks
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A vertical path starts at (3, −2) and is exactly 7 blocks long. Where could it end?

    1. A(3, 5) or (3, −9) — seven blocks up, or seven blocks down
    2. B(3, 5) only — distances always count upward
    3. C(10, −2) or (−4, −2)
    4. D(3, 9) or (3, −5)
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Two points are at (-3, -7) and (-3, 5). What is the distance between them?

    1. A12 units
    2. B2 units
    3. C7 units
    4. D8 units
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:How far apart are the points (-2, 5) and (-2, -3)?
    2. 2A classmate at our table answered:15 units

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 OPEN RESPONSE

    Every distance in this lesson used two points that shared a coordinate. Take (−3, 4) and (2, −1), which share NEITHER. Explain why subtracting coordinates does not give the distance between them, and say exactly what the two subtractions DO tell you.

    ✏️ Mathematical Justification & Response
  3. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:Find the distance between (-5, 2) and (3, 2).
    2. 2Student thinking:Both share y = 2, so subtract the x-values: 5 - 3 = 2.
    3. 3Student answer:The distance is 2 units.

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It