Problem 48 · Pairing PacketsPrint one blank worksheet now, download its PDF, or prepare a family or classroom packet.

MathJewels.com

Name

Date

Pairing Packets

Complete to collectTumbled HematiteLevel 2 · 3 Glints

The problem

One mail cart must carry more than 12 but fewer than 19 packets. The cart may leave only when every packet can be put into a pair.

Questions

Record your complete list and explanation on separate paper.

Find every possible total that lets the cart leave.
For each answer, write how many pairs it makes. Explain why each other allowed total does not work.

What to include

List every valid total with its number of pairs. Give one brief explanation covering every remaining allowed total.

Skills

Determine whether a group up to 20 is even or odd

Helpful first

Math readiness

Designed for Grade 2

Uses Late Grade 2 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: Ask how the learner knows no total was skipped; organizing the complete list remains part of the work.

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 2.5–2.7
Confidence: 84%

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 4
Response: Short Explanation
Known-method steps: 10

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.

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
- 100% focus
- MJ 2.7 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

Count objects with one number word per object
The learner can count objects with one number word per object. This capability is distinct from mere exposure to or isolated use of stable order principle.
- Fluent readiness
- Required
- MJ K.4 milestone
Use the last count word as the total
The learner can use the last count word as the total. This capability is distinct from mere exposure to or isolated use of one-to-one counting.
- Fluent readiness
- Required
- MJ K.5 milestone
Count up to 20 arranged objects and up to 10 scattered objects
The learner can count up to 20 arranged objects and up to 10 scattered objects. This capability is distinct from mere exposure to or isolated use of one-to-one counting.
- Fluent readiness
- Required
- MJ K.7 milestone
Compare groups as greater, less, or equal
The learner can compare groups as greater, less, or equal. This capability is distinct from mere exposure to or isolated use of count or match objects.
- Fluent readiness
- Required
- MJ K.7 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 · 5 locations

Modules4 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: 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 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

Number Corner workouts1 location · Representative: September: Daily Rectangle

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

Common Core State Standards for Mathematics2010 · 2 locations

Standards1 location · Representative: 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.

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

Practice locations1 location · Representative: Construct viable arguments and critique the reasoning of others.

Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP3
The exact response requires an explanation that rules out an invalid odd pairing.
- Strong
- Consolidates
- Overlapping
- Independent
- High Confidence

Prepare print packet

Pairing Packets

The problem

Questions

What to include

About this problem

Skills

Helpful first

Grade

Math area

Topics

Before you choose this problem

Designed for Grade 2

Standard challenge

About 2–6 minutes

Keep exploring

Rating, skills & curriculum

MJ 2.7

C2 · Standard

W1 · Light

Skills this problem practices

Determine whether a group up to 20 is even or odd

Helpful prerequisites

Count objects with one number word per object

Use the last count word as the total

Count up to 20 arranged objects and up to 10 scattered objects

Compare groups as greater, less, or equal

Curriculum and standards crosswalks

Module 2: Number Facts with the Number Rack

Module 3: Introducing Addition & Subtraction Strategies

Module 4: Thinking in 2s

Module 4: Sequences & Growing Patterns

September: Daily Rectangle

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.

Construct viable arguments and critique the reasoning of others.

Pairing Packets

The problem

Questions

What to include

Skills

Helpful first

Grade

Math area

Topics

Designed for Grade 2

Standard challenge

About 2–6 minutes

Choose what to try next

Keep exploring

MJ 2.7

C2 · Standard

W1 · Light

Skills this problem practices

Determine whether a group up to 20 is even or odd

Helpful prerequisites

Count objects with one number word per object

Use the last count word as the total

Count up to 20 arranged objects and up to 10 scattered objects

Compare groups as greater, less, or equal

Curriculum and standards crosswalks

Module 2: Number Facts with the Number Rack

Module 3: Introducing Addition & Subtraction Strategies

Module 4: Thinking in 2s

Module 4: Sequences & Growing Patterns

September: Daily Rectangle

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.

Construct viable arguments and critique the reasoning of others.