๐Ÿงญ

The Coordinate Rescue

A search-and-rescue team uses integers and the coordinate plane to order readings, measure distances, and reflect positions on a grid map.

Enrichment Reading + Math Integers & the Coordinate Plane 6.NS.6โ€“8 Challenge Level
Part 1 โ€” Ordering the Readings

The rescue team logged temperatures (ยฐC) from four sensors: โˆ’3, 5, โˆ’8, 0. To prioritize the coldest zone, they ordered the readings from least to greatest.

Least to greatest: โˆ’8, โˆ’3, 0, 5. The most negative value (โˆ’8) is the least โ€” the coldest.

Analyze โ€” Q1

Why is โˆ’8 the least value, even though 8 is a big number?

Solve It โ€” #1

Type the least value of โˆ’2, โˆ’9, 3.

Part 2 โ€” Farther from Zero (Absolute Value)

Two elevation alerts came in: โˆ’15 m and +12 m. "Which is farther from sea level?" The team compared absolute values.

|โˆ’15| = 15 and |12| = 12. Since 15 > 12, the reading โˆ’15 is farther from zero โ€” even though โˆ’15 is the smaller number.

Solve It โ€” #2

Find |โˆ’20|.

Analyze โ€” Q2

How can โˆ’15 be "less than" 12 but "farther from zero" than 12?

Part 3 โ€” Distance on the Grid

On the grid map, base camp was at (5, 2) and a stranded hiker at (5, 8). Because the points share the same x-coordinate, the distance is the difference of the y-coordinates.

(5, 2) (5, 8)

Distance = |8 โˆ’ 2| = 6 units.

Solve It โ€” #3

Find the distance between (โˆ’4, 1) and (โˆ’4, 7) (same x-coordinate).

Part 4 โ€” Reflecting Across an Axis

A drone at (4, โˆ’5) needed to mirror its path across the river โ€” the x-axis. Reflecting across the x-axis keeps x the same and changes the sign of y.

Reflect (4, โˆ’5) across the x-axis โ†’ (4, 5). (x stays; y flips sign.)

Solve It โ€” #4

Reflect (3, 6) across the x-axis. Type the new point like (3,-6).

Analyze โ€” Q3

When you reflect a point across the x-axis, what changes?

After You Read โ€” Analytical Writing

Make a Mathematical Argument

Prompt A โ€” Order vs. distance. Explain how a number can be "less than" another yet "farther from zero." Use โˆ’15 and 12 with their absolute values as evidence.
Prompt B โ€” Map the rescue. Explain how the team found the distance between two grid points that share a coordinate, and how reflecting across the x-axis changes a point. Use specific coordinates from the story.

Optional academic frame: "Because ______, the point/value is ______; the math shows ______."

Challenge Extension

Think Further

A point is at (โˆ’6, 3). Reflect it across the y-axis, then find the distance from the new point to (6, 9) (they will share an x-coordinate). Explain each step. (Try it, then check with your teacher.)

How You Are Scored

Rubric

Category4 โ€” Advanced3 โ€” Proficient2 โ€” Developing
Comprehension & inferenceAll analysis questions correct; explains order vs. distance & reflection2 of 3 correct1 correct
Multi-step mathAll 4 Solve-It answers correct (order, absolute value, grid distance, reflection)3 correct2 correct
Mathematical argumentClear claim; uses coordinates/values as evidenceClaim with some evidenceLittle evidence
๐Ÿ”‘ Teacher Answer Key (click to expand)
  1. Q1 โ€” โˆ’8 is farthest left on the number line, so it is smallest.
  2. Solve It #1 โ€” โˆ’9 (least of โˆ’2, โˆ’9, 3).
  3. Solve It #2 โ€” 20 (|โˆ’20|).
  4. Q2 โ€” Order uses number-line position; distance uses absolute value.
  5. Solve It #3 โ€” 6 units (|7 โˆ’ 1|).
  6. Solve It #4 โ€” (3, โˆ’6) (reflect across x-axis).
  7. Q3 โ€” The y-coordinate changes sign; x stays the same.
  8. Extension โ€” reflect (โˆ’6, 3) across y-axis โ†’ (6, 3); distance to (6, 9) = |9 โˆ’ 3| = 6 units.

Grading accepts (3,-6) with or without spaces.

Neft Teacher ยท Reading + Math (Enrichment) ยท Integers & the Coordinate Plane ยท