Problem 21 · Neow’s CounterexamplePrint one blank worksheet now, download its PDF, or prepare a family or classroom packet.

Name

Date

Neow’s Counterexample

Complete to collectTumbled CarnelianLevel 2 · 3 Glints

The problem

In the game Slay the Spire, the Ironclad spends Energy to play cards. He starts this turn with 3 Energy. After each card, subtract its cost. He can keep playing while he can pay the next cost. Ignore other card effects.

Neow claims, “Every hand of three different cards from the table lets the Ironclad play at least two cards.” A counterexample is one allowed hand that makes his word “every” false.

One working turn: start with 3 Energy, play Strike for 1, then play Cleave for 1. The Ironclad has played two cards and has 1 Energy left.

One working turn: start with 3 Energy, play Strike for 1, then play Cleave for 1. The Ironclad has played two cards and has 1 Energy left.

Available cards

Card	Energy cost
Strike	1
Cleave	1
Bash	2
Heavy Blade	2
Uppercut	2
Bludgeon	3

Questions

Circle in the table; use separate paper for sums and explanations.

Find a counterexample: circle three different cards in the table. Explain why, no matter which card the Ironclad plays first, he cannot afford a second card.
The picture shows one hand where Neow’s claim works. Why does your one counterexample still prove that his word “every” is false?

Theme

Slay the Spire

Skills

Solve one- and two-step addition/subtraction stories within 100

Helpful first

Compose and decompose within 5

Grade

Grade 3

Math area

Operations and computation

Topics

Addition and subtraction

Math readiness

Designed for Grade 3

Uses Middle Grade 2 math.

Thinking

Standard challenge

The solver chooses and coordinates familiar methods.

Time & response

About 2–7 minutes

Light amount of written work · Short Explanation response.

How to support: Keep the distinction between one working hand and a claim about every hand in view; several counterexamples may 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 2.3

Grades K–2

Grade 2 progression · point 3

Likely range: MJ 2.3–3.4
Confidence: 84%

Challenge

C2 · Standard

The solver chooses and coordinates familiar methods.

Method selection1
Reasoning depth2
Novelty2
Constraint management1
Proof or justification2

Workload

W1 · Light

A short response with only a few steps.

Active time: 2–7 minutes · typically 4
Response: Short Explanation
Known-method steps: 5

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.

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
- 100% focus
- MJ 2.3 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

Compose and decompose within 5
The learner can compose and decompose within 5. The capability is credited only when the task makes that demand necessary for success.
- Fluent readiness
- Required
- MJ 1.0 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 · 12 locations

Modules7 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

Number Corner workouts5 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

Common Core State Standards for Mathematics2010 · 1 location

Standards1 location · 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