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Problem 3 · Steve’s Big DigOnly the worksheet will be included when you print.
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Date

Steve’s Big Dig

Total reward 3 jewels

In Minecraft, Steve digs a cube-shaped hole. The hole is 5 blocks long, 5 blocks wide, and 5 blocks deep.

Your challenges

  1. How many blocks does Steve remove?

    Reward 1 jewel

  2. On average, 1 out of every 10 blocks contains coal. How many coal blocks should Steve expect to find in the hole?

    Reward 2 jewels

Show your answer

Show an equation for each part. If an expected amount is not a whole number, explain what it means.

Show your work

Teacher & family guide

Difficulty & skills

Grade 3 · Geometry · Number and operations · Data and probability · Three-dimensional shapes · Volume · Fractions and decimals · Expected value

MJ 5.3 · C2 · 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 5.3

Grades 3–5

Grade 5 progression · point 3

Likely range
MJ 5.0–5.6
Confidence
76%

Challenge

C2 · Standard

The solver chooses and coordinates familiar methods.

  • Method selection1
  • Reasoning depth2
  • Novelty1
  • Constraint management1
  • Proof or justification2

Workload

W2 · Moderate

Several coordinated calculations, representations, or explanation steps.

Active time
5–14 minutes · typically 9
Response
Short Explanation
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.

  • Find volume by multiplication

    Determine the number of unit cubes in a rectangular prism by multiplying its three whole-number dimensions or equivalent layer counts.

    • Independent mastery
    • 35% focus
    • MJ 5.3 milestone

  • Find one tenth of a quantity

    Find one tenth of a whole-number quantity, including cases whose result is represented by a decimal or mixed number.

    • Independent mastery
    • 30% focus
    • MJ 5.0 milestone

  • Interpret a non-whole expected value

    Explain a fractional expected count as a long-run average while recognizing that any single observed count must be a whole number.

    • Developing mastery
    • 35% focus
    • MJ 5.2 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

  • Multiply equal groups

    Represent and solve whole-number situations made from equal groups, including choosing and evaluating a multiplication equation.

    • Fluent readiness
    • Required
    • MJ 3.7 milestone

  • Find volume by multiplication

    Determine the number of unit cubes in a rectangular prism by multiplying its three whole-number dimensions or equivalent layer counts.

    • Independent readiness
    • Required
    • MJ 5.3 milestone

  • Find one tenth of a quantity

    Find one tenth of a whole-number quantity, including cases whose result is represented by a decimal or mixed number.

    • Independent readiness
    • Required
    • MJ 5.0 milestone

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