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Neft Teacher · Grade 6 HyperDoc

Unit 9 — The Coordinate Plane

CCSS 6.NS.C.6 & 6.G.A.3

Follow the 5 steps: Engage, Explore, Explain, Apply, and Reflect. Type your name in the box below before you start so your work is saved with your name.

Learning Target

📋Standard: CCSS 6.NS.C.6 & 6.G.A.3
⏱Estimated time: 50 – 60 minutes
📦Materials: This page, pencil (optional graph paper)
🎯Unit: Number Sense & Geometry — Unit 9
Teacher Notes — Pacing, Grouping & Differentiation

Pacing Guide

  • Engage (5 min) — Hook discussion; no writing required yet.
  • Explore (10–15 min) — Students open game/hub in new tabs; circulate and ask "Which quadrant is your character in?"
  • Explain (10 min) — Class reads together; cold-call vocab and SVG diagram.
  • Apply (15–20 min) — Self-check items first (independent), then NTKit graded set; pair-share before submit.
  • Reflect (5–8 min) — Students type responses; collect PDF or DOC at end of class.

Grouping Suggestions

  • Apply Self-Check: individual, then turn-and-talk after each item.
  • NTKit graded form: individual; partners may discuss after submit.
  • Reflect: individual only.

Differentiation — Support

  • Provide a printed four-quadrant grid and counters to physically plot points.
  • Allow calculator for fraction / negative arithmetic if needed.
  • Pre-teach quadrant sign rules with a mnemonic: "+ + I, − + II, − − III, + − IV".
  • Reduce Apply to Q1–Q4 and offer Q5–Q6 as extension.

Differentiation — Challenge

  • Ask students to create a polygon with at least 5 vertices across 3 quadrants, list its vertices, and compute the perimeter.
  • Pose: "If A(a, b) reflects over the y-axis to A', what are A's coordinates? Justify algebraically."

ESOL / Language Supports

  • Display a labeled coordinate plane anchor chart with translations for key terms (origin, axis, quadrant, reflect).
  • Sentence frames: "The point ___ is in Quadrant ___ because the x-value is ___ and the y-value is ___."
  • Pair newcomers with a bilingual partner during Explore.
  • Allow labeled diagrams as evidence in Reflect instead of prose.

Your Name

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Step 1 · Engage

Chart the Star Map

You are a space navigator in Coordinate Quest. To reach each star, you must give its exact spot on a grid using two numbers: (x, y).

Think: How can you tell a friend exactly where a dot is on a grid, using only numbers?

Step 2 · Explore

Play and explore

Open these in a new tab. Explore first, then come back to finish.

Step 3 · Explain

How the coordinate plane works

The coordinate plane has two number lines that cross at (0, 0), called the origin.

x-axis
The line that goes left and right. The x number is first.
y-axis
The line that goes up and down. The y number is second.
ordered pair (x, y)
Two numbers that name one point. Go right/left first, then up/down.
quadrant
One of the 4 corners of the plane. Named I (top-right), II (top-left), III (bottom-left), IV (bottom-right).
reflect
To flip a point over an axis — like a mirror. Reflecting over the x-axis flips the y sign; over the y-axis flips the x sign.
I II III IV x y A (3, 2)

Worked example

To plot point A (3, 2): start at the origin (0, 0). Move 3 right (x = 3). Then move 2 up (y = 2). Mark the point. Because x and y are both positive, A is in Quadrant I.

To reflect A over the x-axis: keep x the same, flip y to negative. A(3, 2) → A'(3, −2). That new point is in Quadrant IV.

Distance example: Points (1, 4) and (6, 4) share the same y-value. Distance = |6 − 1| = 5 units.

Step 4 · Apply

Show what you know

Quick Self-Check — try these first!

Choose an answer, then press Check to see instant feedback.

SC 1. The point (−4, 7) is in which quadrant?

SC 2. Reflect the point (−3, 5) over the y-axis. What is the new point?

SC 3. Points P(2, −3) and Q(2, 4) are on the same vertical line. How many units apart are they?

Graded Practice — submit with NTKit

Answer every question. Type ordered pairs like (3, 2). Then press Check My Answers.

1. What is the name of the point (0, 0) where the two axes cross?

2. Start at the origin. Move 4 to the right and 1 up. Write the ordered pair.

3. The point (2, 3) has both numbers positive. Which quadrant is it in?

4. Reflect the point (5, 2) over the x-axis. What is the new point?

5. A rectangle has corners at (1, 1), (1, 4), and (6, 1). What is the 4th corner?

6. Point (1, 1) and point (6, 1) are on the same horizontal line. How many units apart are they?

Teacher Answer Key

Self-Check answers:

  1. SC 1: Quadrant II — x is negative (−4), y is positive (7). Rule: (−, +) → QII.
  2. SC 2: (3, 5) — reflecting over the y-axis flips the x sign: (−3, 5) → (3, 5).
  3. SC 3: 7 units — |4 − (−3)| = |4 + 3| = 7. Same x-coordinate means vertical distance.

Graded practice answers:

  1. Q1: origin
  2. Q2: (4, 1)
  3. Q3: Quadrant I (both x and y positive)
  4. Q4: (5, −2) — reflection over x-axis keeps x, negates y
  5. Q5: (6, 4) — the fourth corner that completes the rectangle
  6. Q6: 5 units — |6 − 1| = 5

Rubric

How your work is scored

Level Score Description
Mastery 5 – 6 / 6 All or nearly all graded questions correct. Self-check completed. Reflect responses explain reasoning with coordinate vocabulary (quadrant, ordered pair, reflect, axis).
Proficient 4 / 6 Most graded questions correct. Minor errors in reflection or distance. Reflect responses address both prompts with at least one vocab term.
Developing 2 – 3 / 6 Several questions incorrect; may confuse quadrant signs or x/y order. Reflect responses are short or missing vocab. Needs targeted reteach on signs and plotting steps.
Beginning 0 – 1 / 6 Most questions blank or incorrect. Reflect not attempted. Student needs one-on-one re-teaching of ordered pairs and the four-quadrant plane before attempting independently.

Step 5 · Reflect

Think and write

Use complete sentences. Try to use at least one math word from the Explain section (quadrant, origin, ordered pair, reflect, axis).

Deliverable: Type your responses below, then save your finished HyperDoc as a PDF or DOC using the Save buttons at the top. Submit the saved file to your teacher's Google Drive folder or turn it in as directed.