Grade 6 · A mathematical adventure · Growing story curriculum

The Missing Map

Every place has a story. Every claim needs evidence.

Begin the story →
Illustrated map of Meridian: a harbor town with an old workshop, market square, stone bridge, hilltop observatory, lighthouse, beach, and offshore Gull Island.

Welcome to Meridian

Choose a place above. The adventure begins at the Old Workshop.

Chapter 1 · Area and evidence

1.1 The Room That Wasn’t There · 1.2 A Shape Can Change · 1.3 Half the Evidence · 1.4 The Cabinet’s Outline · 1.5 A Box of Records · Checkpoints

Chapter 1 · Episode 1

The Room That Wasn’t There

The workshop was supposed to be empty by Friday.

Mara thought this was a terrible idea. Most of the town’s good ideas had started there, and several of its terrible ideas had at least become interesting machines.

She pushed open the broad wooden doors. Behind her, Eli carried a notebook, Tess carried the inventory list, and Jun carried a sandwich.

“You were supposed to bring something useful,” Tess said.

“I’m planning ahead.”

Their assignment was simple: record what remained before the town decided what to keep.

Eli found a floor plan beneath a cracked drawing board. Tess unfolded the survey made last week. Both showed the front doors, the long workbench, and the windows facing the harbor.

But the rooms were different.

“Someone moved a wall,” Mara said.

“Maybe,” Eli replied.

Jun leaned over his shoulder. “Or someone drew it wrong.”

Tess cleared a space on the table. “Before we accuse a dead mapmaker of being bad at maps, could we check?”

On the older plan, a narrow room occupied the back corner. In the workshop, that corner was behind a solid wall.

Your task: compare the records. What can the measurements establish—and what still needs checking?

Examine the evidence →
Investigation 1.1 · Area and evidence

Two records. One workshop.

Both records show the same outer rectangle: 10 m by 8 m. The old plan identifies a back room measuring 4 m by 3 m. The current survey marks that corner as inaccessible.

Old workshop floor planTen by eight meter outer rectangle. A four by three meter back room lies in the upper right corner. The remaining L-shaped space is accessible.10 m8 m4 m3 mBack roomMain workspace

Old record: both rooms are identified. Dimensions are labeled; do not measure the drawing.

Build your argument

  1. Find the area inside the outer walls.
  2. Find the area of the back corner.
  3. Find the main workspace area in two ways.
  4. Does the area difference prove that a hidden room exists? Explain.

Use graph paper for diagrams and calculations. Label your page “1.1 — Area and Evidence.”

A starting hintFirst consider the whole rectangle. Then decide what to subtract. For a second method, split the L-shaped workspace into two rectangles.

This page does not save or submit responses. Keep your work on graph paper.

Make sense of the mathematics

Area measures how much two-dimensional space a region covers. Rectangle area = length × width. Multiplying meters by meters gives square meters, written m².

For a composite shape, add the areas of non-overlapping pieces or subtract a missing piece from a larger shape. Both methods must describe the same region.

Another example: a 9 m × 7 m rectangle with a 2 m × 3 m corner removed has area 63 − 6 = 57 m².

Practice beyond Meridian

1. A rectangular garden measures 12 m by 7 m. A 3 m by 2 m corner is reserved for a path. Find the planting area.

2. Draw two different rectangles with an area of 24 square units. Do their perimeters match?

3. A student says equal floor areas prove two rooms have the same shape. Give a counterexample.

Check after you have tried

1. 78 m². 2. For example, 4 × 6 and 3 × 8 have perimeters 20 and 22 units. 3. Those same rectangles have equal areas and different shapes.

The investigation continues

A difference is a clue. It is not yet an explanation.

“Twelve square meters,” Eli said. “That’s what the old plan puts in the corner.”

“So there’s a room?” Mara asked.

Tess shook her head. “There’s a record of a room. We still need to check the record.”

Continue to 1.2 — A Shape Can Change →
Your fellow investigators

Four ways to see a problem.

Mara

A builder who wants to save the workshop. Quick to try an idea; learning to test it.

Eli

A careful mapmaker. Loves exact records; learning to work with uncertainty.

Jun

A skeptical investigator with a sense of humor. Asks questions; learning to support his claims.

Tess

An organizer who makes room for everyone. Turns disagreements into questions the group can investigate.