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Problem 2

The Necklace Code

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The Necklace Code

Complete to collectPolished MoonstoneLevel 2 · 3 Glints

A jeweler makes a necklace by repeating the same four-jewel pattern: ruby, sapphire, sapphire, emerald.

The first jewel is a ruby. The jeweler stops after placing 19 jewels.

The repeating jewel pattern becomes a necklace.

Your challenge

  1. What kind of jewel is in position 19?
  2. How many rubies, sapphires, and emeralds are in the necklace?

Show your answer

On separate paper, name jewel 19, count each jewel type, and show how the four-jewel repeat gives your answer.

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.

Skills

Helpful first

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

Uses Late Grade 3 math.

Thinking

Standard challenge

The solver chooses and coordinates familiar methods.

Time & response

About 2–6 minutes

Light amount of written work · Short Explanation response.

How to support: Help the learner separate complete groups from the unfinished group without naming the remainder result.

How did it feel?

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 · Uses Late Grade 3 math · About 2–6 minutes

Grade 3 · Discrete mathematics and logic · Cycles and invariants

MJ 3.8 · C2 · W1

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 3.8

Grades 3–5

Grade 3 progression · point 8

Likely range
MJ 3.7–3.9
Confidence
90%

Challenge

C2 · Standard

The solver chooses and coordinates familiar methods.

  • Method selection1
  • Reasoning depth2
  • Novelty1
  • Constraint management1
  • Proof or justification1

Workload

W1 · Light

A short response with only a few steps.

Active time
2–6 minutes · typically 3.5
Response
Short Explanation
Known-method steps
4
  • Mechanical execution1
  • Written output1
  • Representation production1
  • Bookkeeping1

Learning focus

Skills this problem practices

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

  • Identify a position in a repeating cycle

    The learner can identify a position in a repeating cycle. The capability is credited only when the task makes that demand necessary for success.

    • Independent mastery
    • 45% focus
    • MJ 3.5 milestone

  • Count categories in a repeating pattern

    The learner can count categories in a repeating pattern. The capability is credited only when the task makes that demand necessary for success.

    • Independent mastery
    • 55% focus
    • MJ 3.8 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

  • Identify a position in a repeating cycle

    The learner can identify a position in a repeating cycle. The capability is credited only when the task makes that demand necessary for success.

    • Independent readiness
    • Required
    • MJ 3.5 milestone

External alignment

Curriculum and standards crosswalks

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

Common Core State Standards for Mathematics2010 · 1 location
Standards1 location · Representative: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.