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Problem 10 · Rotom’s Pokédex RectangleOnly the worksheet will be included when you print.
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Hundred-chart mystery

Rotom’s Pokédex Rectangle

Jewel value 10 jewels

Rotom displays the numbers 1–100 in its Pokédex chart, with 10 numbers in each row. Pikachu, Eevee, Squirtle, and Charmander each cover one corner of a rectangle whose sides follow the chart’s rows and columns. The rectangle has two different rows and two different columns. Eevee and Squirtle are at opposite corners, and their hidden numbers add to 69.

One possible orientation is shown. Rotom may choose any rectangle with four different corners.

Your challenge

What is the total of all four hidden numbers? Explain why your total is forced for every possible rectangle, not just the one pictured.

Show your answer

Use an equation and the chart’s structure. You do not need to find each hidden number.

Sketch, test, and explain

Teacher & family guide

Difficulty & skills

Grade 2 · Number and operations · Patterns and algebra · Place value · Sequences

MJ 2.7 · C4 · W2

MathJewels rates content readiness, problem-solving challenge, and workload separately. These estimates describe the easiest reasonable solution path and do not reveal the solution.

Content level

MJ 2.7

Grades K–2

Grade 2 progression · point 7

Likely range
MJ 2.5–2.9
Confidence
84%

Challenge

C4 · Insight

A hidden structural insight is needed to unlock the problem.

  • Method selection3
  • Reasoning depth3
  • Novelty2
  • Constraint management2
  • Proof or justification3

Workload

W2 · Moderate

Several coordinated calculations, representations, or explanation steps.

Active time
7–18 minutes · typically 12
Response
Proof
Known-method steps
6
  • Mechanical execution1
  • Written output2
  • Representation production1
  • Bookkeeping1

Learning focus

Skills this problem practices

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

  • Use hundred-chart structure

    Use the constant changes across rows and down columns of a ten-column hundred chart to determine and justify relationships among entries.

    • Independent mastery
    • 70% focus
    • MJ 2.5 milestone

  • Add and subtract quantities

    Combine and compare whole-number quantities in contextual problems and use addition or subtraction to find an unknown result.

    • Independent mastery
    • 30% focus
    • MJ 2.7 milestone

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