6.NOS.9 Lesson 7-6-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.6 · Part II

On-Level Application · Standard Rigor

Distance on the Coordinate Plane · Distance

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 7.6 · Part II
1Distance on the Coordinate Plane
2The Structural Procedure
  1. Same quadrant / Same sign: Subtract absolute values of differing coordinates
  2. Different quadrants / Opposite signs: Add absolute values of differing coordinates
  3. Distance represents length, so it is always positive
3Mathematical 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.
4Watch 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?'
  1. 1 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
  2. 2 MULTIPLE CHOICE

    What is the distance between (2, 3) and (2, 8)?

    1. A11 units
    2. B5 units
    3. C6 units
    4. D5.5 units
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    What is the distance between (-4, 1) and (3, 1)?

    1. A1 unit
    2. B12 units
    3. C7 units
    4. D-7 units
    ✏️ Workspace & Solution Steps
📐 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
6.NOS.9 Lesson 7-6-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.6 · Part II

Extension & Non-Routine Application

Distance on the Coordinate Plane · Distance

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 7.6 · Part II
1Distance on the Coordinate Plane
2The Structural Procedure
  1. Same quadrant / Same sign: Subtract absolute values of differing coordinates
  2. Different quadrants / Opposite signs: Add absolute values of differing coordinates
  3. Distance represents length, so it is always positive
3Mathematical 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.
4Watch 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

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

    1. A7 units
    2. B1 unit
    3. C5 units
    4. D2 units
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A rectangle has corners (1, 2), (1, 5), (5, 5), and (5, 2). What is its perimeter?

    1. A7 units
    2. B12 units
    3. C14 units
    4. D10 units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    A rectangle has vertices at (-4, -2), (3, -2), (3, 5), and (-4, 5). Find the length, width, perimeter, and area of the rectangle. Show your work using absolute value.

    ✏️ Mathematical Justification & Response
📐 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