Problem 47 · The Museum DisplayPrint one blank worksheet now, download its PDF, or prepare a family or classroom packet.

MathJewels.com

Name

Date

The Museum Display

Complete to collectGarnet CrystalLevel 3 · 5 Glints

The museum has 6 display cases. Each case begins with 4 rubies. The curator may choose some of the cases to receive 3 sapphires each. Just before opening, the curator removes 5 jewels to polish them. She wants to share the remaining jewels equally among 5 display trays.

Test every choice

Cases with sapphires	Jewels left after polishing	Shares equally into 5 trays?
0
1
2
3
4
5
6

Your challenges

Which choices for the number of sapphire cases let the curator share the remaining jewels equally among 5 trays? Find every choice from 0 through 6. For each choice that works, tell how many jewels go on each tray.

Show your answer

Complete the case table here. Use scratch paper for equations, checks, and your explanation that no other choice works.

Skills

Helpful first

Grade

Grade 3

Math area

Operations and computation

Topics

Math readiness

Designed for Grade 3

Uses Middle Grade 3 math.

Thinking

Stretch challenge

A nontrivial plan using familiar mathematical ideas.

Time & response

About 5–12 minutes

Moderate amount of written work · Short Explanation response.

How to support: Invite the learner to test a small set of case choices and ask how they know the list is complete.

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 3.4

Grades 3–5

Grade 3 progression · point 4

Likely range: MJ 3.3–3.5
Confidence: 90%

Challenge

C3 · Stretch

A nontrivial plan using familiar mathematical ideas.

Method selection2
Reasoning depth2
Novelty1
Constraint management2
Proof or justification2

Workload

W2 · Moderate

Several coordinated calculations, representations, or explanation steps.

Active time: 5–12 minutes · typically 8
Response: Short Explanation
Known-method steps: 10

Mechanical execution2
Written output2
Representation production1
Bookkeeping2

Learning focus

Skills this problem practices

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

Interpret a product as equal groups or a rectangular array
The learner can interpret a product as equal groups or a rectangular array. This capability is distinct from mere exposure to or isolated use of Grade 2 arrays.
- Independent mastery
- 36% focus
- MJ 3.2 milestone
Interpret whole-number quotients as sharing or grouping
The learner can interpret whole-number quotients as sharing or grouping. This capability is distinct from mere exposure to or isolated use of equal groups.
- Independent mastery
- 36% focus
- MJ 3.4 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
- 29% focus
- MJ 2.3 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

Interpret a product as equal groups or a rectangular array
The learner can interpret a product as equal groups or a rectangular array. This capability is distinct from mere exposure to or isolated use of Grade 2 arrays.
- Independent readiness
- Required
- MJ 3.2 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.
- Fluent readiness
- Required
- MJ 2.5 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 · 23 locations

Modules14 locations · Representative: Module 4: Adding & Subtracting to 20

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 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: 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
Module 1: Multiplication in Context
grade-3-unit-2-module-1
The official publisher correlation lists this curriculum location for 3.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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.1: Unit 2, Module 1, Sessions 1, 2, 3, 5
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 2: Multiplying with Arrays & Number Lines
grade-3-unit-2-module-2
The official publisher correlation lists this curriculum location for 3.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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.1: Unit 2, Module 2, Sessions 1, 3, 4, 5
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 3: Exploring Multiplication Strategies
grade-3-unit-2-module-3
The official publisher correlation lists this curriculum location for 3.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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.1: Unit 2, Module 3, Sessions 2, 3, 4
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 4: Problem Situations with Graphs & Multiple Operations
grade-3-unit-2-module-4
The official publisher correlation lists this curriculum location for 3.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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.1: Unit 2, Module 4, Sessions 3
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 1: Linking Multiplication & Division
grade-3-unit-5-module-1
The official publisher correlation lists this curriculum location for 3.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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.1: Unit 5, Module 1, Sessions 1, 2, 6
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 2: Multiplication & Division Families
grade-3-unit-5-module-2
The official publisher correlation lists this curriculum location for 3.OA.A.2, 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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.2: Unit 5, Module 2, Sessions 1, 2
- Partial
- Develops
- Overlapping
- Medium Confidence
Module 3: Division Practice
grade-3-unit-5-module-3
The official publisher correlation lists this curriculum location for 3.OA.A.2, 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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.2: Unit 5, Module 3, Sessions 1, 2
- Partial
- Develops
- Overlapping
- Medium Confidence

Number Corner workouts9 locations · Representative: September: Calendar Grid

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
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
September: Calendar Grid
grade-3-number-corner-september-calendar-grid
The official publisher correlation lists this curriculum location for 3.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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.1: Number Corner September, Calendar Grid
- Partial
- Develops
- Overlapping
- Medium Confidence
October: Computational Fluency
grade-3-number-corner-october-computational-fluency
The official publisher correlation lists this curriculum location for 3.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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.1: Number Corner October, Computational Fluency
- Partial
- Develops
- Overlapping
- Medium Confidence
November: Computational Fluency
grade-3-number-corner-november-computational-fluency
The official publisher correlation lists this curriculum location for 3.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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.1: Number Corner November, Computational Fluency
- Partial
- Develops
- Overlapping
- Medium Confidence
May: Solving Problems
grade-3-number-corner-may-solving-problems
The official publisher correlation lists this curriculum location for 3.OA.A.2, 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 3 Correlations to the Common Core State Standards · Page 4, standard 3.OA.A.2: Number Corner May, Solving Problems
- Partial
- Develops
- Overlapping
- Medium Confidence

Common Core State Standards for Mathematics2010 · 3 locations

Standards3 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
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
CCSS.MATH.CONTENT.3.OA.A.1
Interpret a product as equal groups or a rectangular array was reviewed against CCSS.Math.Content.3.OA.A.1. The ontology's CCSS locator 3.OA.A.1 resolves to this standard; the atomic skill is narrower relative to the published expectation.
- Strong
- Assesses
- Narrower
- Independent
- Medium Confidence
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
CCSS.MATH.CONTENT.3.OA.A.2
Interpret whole-number quotients as sharing or grouping was reviewed against CCSS.Math.Content.3.OA.A.2. The ontology's CCSS locator 3.OA.A.2 resolves to this standard; the atomic skill is narrower relative to the published expectation.
- Strong
- Assesses
- Narrower
- Independent
- Medium Confidence