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Problem 54 · Jules and the Crooked Shadow ScreenPrint one blank worksheet now, download its PDF, or prepare a family or classroom packet.

Problem 54

Jules and the Crooked Shadow Screen

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Jules and the Crooked Shadow Screen

Complete to collectTumbled CalciteLevel 3 · 5 Glints

A Puzzle House repair

Jules finds a crooked shadow screen made from 8 identical square panels.

A lantern behind the screen casts silhouettes across its movable panels.

Every panel touches another panel along at least one full side.

The screen has area 8 square panels and perimeter 16 panel-edges.

Jules may move exactly one panel, without turning or overlapping any panels, to make one solid rectangle. Corner-touching does not connect panels.

A puzzled Jules inspects a lantern-lit shadow screen. The top row has translucent panels in positions 1, 3, and 4 with empty openings in positions 2 and 5; all five bottom positions hold panels. Bat and crooked-branch silhouettes fall across the eight panels.
Lantern light throws spooky silhouettes across the movable screen panels.

Make one careful move

  1. Circle the panel Jules should move, draw an arrow to its new position, and draw the finished rectangle on the reconstruction grid.

    Original shadow screen
    Area = 8 Perimeter = 16
    Your finished rectangle

    Shade exactly 8 squares.

    When all 8 panels make one solid rectangle, turn the page to measure what changed.

The move: Move exactly one of the 8 panels so all 8 form one solid rectangle.

Measure what changed

  1. What are the area and perimeter of the finished rectangle? How much did the perimeter change?

    New areasquare panels
    New perimeterpanel-edges
    Perimeter changed bypanel-edges

  2. Explain why moving one panel changed the perimeter but did not change the area. Use the panel’s number of full-side neighbors before and after the move in your explanation.

    Before moving The panel hadfull-side neighbor(s).
    After moving The panel hadfull-side neighbor(s).
    What that means It gainedshared side(s).

At a glance

About this problem

These tags show what the problem is about and the math you’ll use. Choose one to find similar problems.

Theme

Setting

Skills

Grade

Math area

Topics

Is this a good fit?

Before you choose this problem

A plain-language look at readiness, thinking, time, and the expected response.

Math readiness

Designed for Grade 3 · Grade 4

Uses Early Grade 4 math.

Thinking

Stretch challenge

A nontrivial plan using familiar mathematical ideas.

Time & response

About 6–17 minutes

Moderate amount of written work · Construction response.

How to support: Ask the learner to find the move before discussing shared sides or counting boundary edges.

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Pick the option that best matches this challenge. Recommendations use topic, math area, grade, story, and thinking challenge.

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Technical reference

Rating, skills & curriculum

Designed for Grade 3 · Grade 4 · Uses Early Grade 4 math · About 6–17 minutes

Grade 3 · Grade 4 · Measurement and units · Area and perimeter

MJ 4.1 · C3 · W2

Precise MJD coordinates, factor scores, skill weights, calibration evidence, and curriculum crosswalks. This reference is available to everyone and is intentionally last.

Content level

MJ 4.1

Grades 3–5

Grade 4 progression · point 1

Likely range
MJ 3.8–4.2
Confidence
92%

Challenge

C3 · Stretch

A nontrivial plan using familiar mathematical ideas.

  • Method selection2
  • Reasoning depth3
  • Novelty2
  • Constraint management2
  • Proof or justification3

Workload

W2 · Moderate

Several coordinated calculations, representations, or explanation steps.

Active time
6–17 minutes · typically 10
Response
Construction
Known-method steps
9
  • Mechanical execution1
  • Written output2
  • Representation production2
  • Bookkeeping1

Learning focus

Skills this problem practices

What a successful response demonstrates, with each skill’s share of the content rating.

  • Distinguish and compare area and perimeter

    The learner can distinguish and compare area and perimeter. This capability is distinct from mere exposure to or isolated use of area; perimeter.

    • Transfer mastery
    • 45% focus
    • MJ 4.1 milestone

  • Find perimeters and unknown side lengths of polygons

    The learner can find perimeters and unknown side lengths of polygons. This capability is distinct from mere exposure to or isolated use of length addition.

    • Transfer mastery
    • 35% focus
    • MJ 4.1 milestone

  • Understand area as the number of unit squares covering a region

    The learner can understand area as the number of unit squares covering a region. This capability is distinct from mere exposure to or isolated use of arrays; tiling.

    • Transfer mastery
    • 20% focus
    • MJ 3.6 milestone

External alignment

Curriculum and standards crosswalks

Approved evidence-backed locations that support discovery. They do not define the MathJewels rating.

Bridges in Mathematicsthird-edition · 9 locations
Modules6 locations · Representative: Module 4: Introducing Area
Number Corner workouts3 locations · Representative: February: Calendar Grid
Common Core State Standards for Mathematics2010 · 3 locations
Standards3 locations · Representative: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.