Problem 49 · The Oran Berry Passing CirclePrint one blank worksheet now, download its PDF, or prepare a family or classroom packet.

Name

Date

The Oran Berry Passing Circle

Complete to collectMaster-Cut GarnetLevel 5 · 8 Glints

In Pokémon, Pikachu, Eevee, and Bulbasaur each start with a positive whole number of Oran Berries. They make three passes in order, and every pass works.

On each pass, the giver matches the receiver’s current pile: Pikachu passes to Eevee, then Eevee passes to Bulbasaur, then Bulbasaur passes to Pikachu.

After the third pass, all three Pokémon have the same number of berries.

1

Pikachu → EeveeMatch Eevee's pile

2

Eevee → BulbasaurMatch Bulbasaur's pile

3

Bulbasaur → PikachuMatch Pikachu's pile

Track the three piles

State	Pikachu	Eevee	Bulbasaur
Start
After pass 1
After pass 2
After pass 3

Questions

Use the state table. Write the proof on separate paper.

What is the smallest possible total number of berries they could have at the start?
For that smallest total, how many berries did Pikachu, Eevee, and Bulbasaur each start with? Show all three passes to check your answer.
Prove that no smaller starting total can work.

Theme

Pokémon

Skills

Helpful first

Grade

Grade 2

Math area

Topics

Math readiness

Designed for Grade 2

Uses Late Grade 2 math.

Thinking

Olympiad challenge

A sustained original strategy with several significant insights and proof.

Time & response

About 12–28 minutes

Heavy amount of written work · Proof response.

How to support: Use the state table to reduce bookkeeping; do not suggest reversing the passes.

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 2.7

Grades K–2

Grade 2 progression · point 7

Likely range: MJ 2.5–3.0
Confidence: 88%

Challenge

C5 · Olympiad

A sustained original strategy with several significant insights and proof.

Method selection3
Reasoning depth3
Novelty3
Constraint management3
Proof or justification3

Workload

W3 · Heavy

Sustained mathematical work and a substantial written response.

Active time: 12–28 minutes · typically 18
Response: Proof
Known-method steps: 12

Mechanical execution2
Written output3
Representation production3
Bookkeeping3

Learning focus

Skills this problem practices

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

Double and halve whole-number quantities
The learner can double and halve whole-number quantities. The capability is credited only when the task makes that demand necessary for success.
- Independent mastery
- 45% focus
- MJ 2.6 milestone
Determine whether a group up to 20 is even or odd
The learner can determine whether a group up to 20 is even or odd. This capability is distinct from mere exposure to or isolated use of pairing and skip counting.
- Independent mastery
- 25% focus
- MJ 2.7 milestone
Solve one- and two-step addition/subtraction stories within 100
The learner can solve one- and two-step addition/subtraction stories within 100. This capability is distinct from mere exposure to or isolated use of Grade 1 story structures.
- Independent mastery
- 30% focus
- MJ 2.3 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

Double and halve whole-number quantities
The learner can double and halve whole-number quantities. The capability is credited only when the task makes that demand necessary for success.
- Developing readiness
- Required
- MJ 2.3 milestone
Determine whether a group up to 20 is even or odd
The learner can determine whether a group up to 20 is even or odd. This capability is distinct from mere exposure to or isolated use of pairing and skip counting.
- Independent readiness
- Required
- MJ 2.7 milestone
Solve one- and two-step addition/subtraction stories within 100
The learner can solve one- and two-step addition/subtraction stories within 100. This capability is distinct from mere exposure to or isolated use of Grade 1 story structures.
- Independent readiness
- Required
- MJ 2.3 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 · 19 locations

Modules11 locations · Representative: Module 2: Number Facts with the Number Rack

Module 2: Number Facts with the Number Rack
grade-2-unit-1-module-2
The official publisher correlation lists this curriculum location for 2.OA.C.3, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 6, standard 2.OA.C.3: Unit 1, Module 2, Sessions 1
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 3: Introducing Addition & Subtraction Strategies
grade-2-unit-1-module-3
The official publisher correlation lists this curriculum location for 2.OA.C.3, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 6, standard 2.OA.C.3: Unit 1, Module 3, Sessions 2
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 4: Adding & Subtracting to 20
grade-2-unit-1-module-4
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Unit 1, Module 4, Sessions 4
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 4: Thinking in 2s
grade-2-unit-2-module-4
The official publisher correlation lists this curriculum location for 2.OA.C.3, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 6, standard 2.OA.C.3: Unit 2, Module 4, Sessions 3
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 2: Adding & Subtracting on the Number Line
grade-2-unit-3-module-2
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Unit 3, Module 2, Sessions 1, 2
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 3: Posing & Solving Contextual Problems
grade-2-unit-3-module-3
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Unit 3, Module 3, Sessions 1, 3, 4, 5, 7
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 4: Data & the Color Tiles Project
grade-2-unit-3-module-4
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Unit 3, Module 4, Sessions 1
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 3: Jessie & the Giant
grade-2-unit-4-module-3
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Unit 4, Module 3, Sessions 2, 5, 6
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 4: Thinking in 3s
grade-2-unit-4-module-4
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Unit 4, Module 4, Sessions 1, 2
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 4: Sequences & Growing Patterns
grade-2-unit-5-module-4
The official publisher correlation lists this curriculum location for 2.OA.C.3, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 6, standard 2.OA.C.3: Unit 5, Module 4, Sessions 1, 2, 3, 4
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 4: Exploring Equal Parts & Groups
grade-2-unit-7-module-4
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Unit 7, Module 4, Sessions 1
- Partial
- Develops
- Overlapping
- Medium Confidence

Number Corner workouts8 locations · Representative: November: Computational Fluency

November: Computational Fluency
grade-1-number-corner-november-computational-fluency
The official Grade 1 Number Corner scope and sequence explicitly names this workout 'Doubles & Halves to 10.' The curriculum location directly develops the skill over a narrower number range.
- Grade 1 Scope & Sequence - Number Corner Third Edition · Page 1, November, Computational Fluency: Doubles & Halves to 10
- Strong
- Develops
- Broader
- Introduced
- High Confidence
December: Computational Fluency
grade-1-number-corner-december-computational-fluency
The official Grade 1 Number Corner scope and sequence explicitly names this workout 'Doubles & Halves Within 20.' The curriculum location directly develops the skill over a narrower number range.
- Grade 1 Scope & Sequence - Number Corner Third Edition · Page 1, December, Computational Fluency: Doubles & Halves Within 20
- Strong
- Develops
- Broader
- Introduced
- High Confidence
September: Calendar Grid
grade-2-number-corner-september-calendar-grid
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Number Corner September, Calendar Grid
- Partial
- Develops
- Overlapping
- Medium Confidence
September: Daily Rectangle
grade-2-number-corner-september-daily-rectangle
The official publisher correlation lists this curriculum location for 2.OA.C.3, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 6, standard 2.OA.C.3: Number Corner September, Daily Rectangle
- Partial
- Develops
- Overlapping
- Medium Confidence
March: Number Line
grade-2-number-corner-march-number-line
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Number Corner March, Number Line
- Partial
- Develops
- Overlapping
- Medium Confidence
April: Number Line
grade-2-number-corner-april-number-line
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Number Corner April, Number Line
- Partial
- Develops
- Overlapping
- Medium Confidence
May: Calendar Grid
grade-2-number-corner-may-calendar-grid
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Number Corner May, Calendar Grid
- Partial
- Develops
- Overlapping
- Medium Confidence
May: Calendar Collector
grade-2-number-corner-may-calendar-collector
The official publisher correlation lists this curriculum location for 2.OA.A.1, which resolves from the MathJewels capability's recorded CCSS locator. The mapping is partial because a curriculum location can develop more than this single capability.
- Bridges & Number Corner Third Edition: Grade 2 Correlations to the Common Core State Standards · Page 5, standard 2.OA.A.1: Number Corner May, Calendar Collector
- Partial
- Develops
- Overlapping
- Medium Confidence

Common Core State Standards for Mathematics2010 · 2 locations

Standards2 locations · Representative: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
CCSS.MATH.CONTENT.2.OA.A.1
Solve one- and two-step addition/subtraction stories within 100 was reviewed against CCSS.Math.Content.2.OA.A.1. The ontology's CCSS locator 2.OA.A.1 resolves to this standard; the atomic skill is narrower relative to the published expectation.
- Strong
- Assesses
- Narrower
- Independent
- Medium Confidence
Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
CCSS.MATH.CONTENT.2.OA.C.3
Determine whether a group up to 20 is even or odd was reviewed against CCSS.Math.Content.2.OA.C.3. The ontology's CCSS locator 2.OA.C.3 resolves to this standard; the atomic skill is narrower relative to the published expectation.
- Strong
- Assesses
- Narrower
- Independent
- Medium Confidence