🕹️
⬅ ARCADE
🏴‍☠️

EQUATION PIRATES

GRAND NUMBER LINE ALGEBRA

The treasure x is trapped in equations.
ISOLATE x. Set it free!

HOW TO PLAY: choose each step to undo the operations on both sides until x is all alone.

🗺️💰⚖️

WHO'S SAILING TODAY?

🗺️ THE GRAND NUMBER LINE
💰 0 ⭐ 0
🏴‍☠️ PIRATE
ISLAND 1
Harbor Cove
one-step: + and −
☆☆☆
🍊
ISLAND 2
Barrel Bay
one-step: × and ÷
☆☆☆
🍯
ISLAND 3
Gull Isle
two-step equations
☆☆☆
🍽️
ISLAND 4
The Sea Galley
x on both sides + ( )
☆☆☆
🦈
ISLAND 5: BOSS
Blackfin Reef
Test-style twists + boss fight
☆☆☆

Tap any island to jump there, even locked ones. Pirates sail where they please.

ISLAND 1 Lesson 1/4

Ahoy!

🌊

FAIR WINDS, CAPTAIN!

4 in a row! You clearly know this island.
Want to sail straight to the last treasure?

I1 Q1/6
❤️❤️❤️
💰 0
STREAK:

Question

⚔️ BLACKFIN REEF ⚔️ DEFEAT BLACKFIN WITH ALGEBRA!
🏴‍☠️
YOU
❤️❤️❤️
VS
🦈
BLACKFIN
BLACKFIN HP
6/6

Question

🌅
🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊 🌊
🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊🌊

ISLAND CLEARED!

⭐⭐⭐
💰 +5

🎁 You earned coins! Spend them in the Avatar Lab on the main menu.

👑

PIRATE KING
OF ALGEBRA!

You conquered all 5 islands
and sank Blackfin Reef!

0
GOLD
0
STARS
🏆 EQUATIONS: BIG TEST READY!
🔮 REVIEW MODE Q1/5
🏋️ THE TRAINING DECK

Endless practice with fresh numbers every time. No hearts here. A wrong answer just teaches you and goes on your review list. Every correct answer earns +1 gold.

💰 Practice gold today: 0/15
📜 PIRATE CODE: MATH WORDS
NUMBERCADE

Design Evidence: Equation Pirates

Why this game teaches the way it does

FOR PARENTS & TEACHERS: Every mechanic in Equation Pirates implements a specific evidence-based recommendation from the IES What Works Clearinghouse (WWC) practice guides and peer-reviewed mathematics-education research. One honest note: the guide panels grade each recommendation's evidence MINIMAL, MODERATE, or STRONG (minimal-evidence recommendations rest partly on panel expert opinion), and every card below prints the level it leans on. The practice guides are free at ies.ed.gov/ncee/wwc.

🎮 Mystery chest → tape map → x (Island 1 lessons)
Concrete → Representational → Abstract (CRA) progression: physical quantities, then bar diagrams, then symbols.

Fuchs et al. (2021), WWC intervention guide, Rec 3: concrete & semi-concrete representations (Strong). Witzel, Mercer & Miller (2003): CRA for algebra (matched quasi-experiment). Bruner (1966): enactive→iconic→symbolic (theory). Ng & Lee (2009): Singapore tape models (descriptive).

🎮 Operation stepper: pick the move, watch BOTH sides transform
Explicit, step-by-step instruction with immediate corrective feedback; wrong picks are explained, not just marked wrong (and "legal-but-unhelpful" moves are distinguished from illegal ones).

Gersten et al. (2009), Rec 3: explicit and systematic instruction (Strong). Witzel et al. (2003): explicit instruction model for algebra (matched quasi-experiment).

🎮 "Explain the step" challenges (why did the solver do that?)
WWC Algebra Guide, Recommendation 1: use solved problems and prompt students to explain the reasoning behind each step. Honest label: the panel rated this recommendation MINIMAL evidence (it rests partly on expert consensus, supported by experiments such as Booth et al. 2013).

Star et al. (2015), Rec 1 (Minimal). Booth, Lange, Koedinger & Newton (2013): worked examples with self-explanation.

🎮 "Wrong Map detective" error-analysis challenges
Incorrect worked examples targeting documented misconceptions (one-sided operations, dividing only one term, wrong order, sign slips): randomized classroom experiments found that studying and explaining incorrect worked examples alongside correct ones improved students' CONCEPTUAL understanding beyond correct examples alone (no differences were found on procedural measures).

Booth et al. (2013): differentiating correct vs. incorrect examples. Star et al. (2015), Rec 1: incorrect solved problems (Minimal).

🎮 "Read the map first" structure checks & think-alouds
WWC Algebra Guide, Recommendation 2: teach students to notice and use the structure of algebraic representations before manipulating them. Honest label: the panel rated this recommendation MINIMAL evidence (expert consensus and emerging research); the reflective prompts alongside it implement a STRONG-rated recommendation.

Star et al. (2015), Rec 2 (Minimal). Woodward et al. (2012), Rec 2: reflective prompts during problem solving (Strong).

🎮 Deckhand vs. Navigator side-by-side strategies
WWC Algebra Guide, Recommendation 3: compare alternative solution strategies side by side and discuss when each is efficient (rated MODERATE evidence). In a randomized classroom experiment, students who compared strategies side by side gained more procedural knowledge and flexibility, with comparable conceptual gains, than students who studied the same strategies one at a time.

Star et al. (2015), Rec 3 (Moderate). Rittle-Johnson & Star (2007): comparing solution methods.

🎮 Story ↔ tape map ↔ equation translation challenges
Translate among verbal, visual, and symbolic representations of the same relationship.

Woodward et al. (2012), Rec 3: visual representations in problem solving (Strong). Ng & Lee (2009): model method as a bridge to algebra (descriptive).

🎮 Pirate Code glossary (Frayer cards) + "Captain's way" questions
Explicit instruction in formal mathematical vocabulary (definition, example, non-example, and precise phrasing) alongside kid-friendly language.

Fuchs et al. (2021), Rec 2: explicit vocabulary and mathematical language instruction (Strong).

FULL REFERENCES

Booth, J. L., Lange, K. E., Koedinger, K. R., & Newton, K. J. (2013). Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24–34.

Bruner, J. S. (1966). Toward a Theory of Instruction. Cambridge, MA: Belknap Press of Harvard University Press.

Fuchs, L. S., Newman-Gonchar, R., Schumacher, R., Dougherty, B., Bucka, N., Karp, K. S., Woodward, J., Clarke, B., Jordan, N. C., Gersten, R., Jayanthi, M., Keating, B., & Morgan, S. (2021). Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Ng, S. F., & Lee, K. (2009). The model method: Singapore children's tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282–313.

Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? Journal of Educational Psychology, 99(3), 561–574.

Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (NCEE 2015-4010). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.

Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18(2), 121–131.

Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving Mathematical Problem Solving in Grades 4 Through 8 (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

All WWC practice guides: ies.ed.gov/ncee/wwc/PracticeGuides

📝

GRAB YOUR
SCRATCH PAPER!

A navigator writes it down.

🎯 SHARPSHOT!

PIP THE SHARPSHOT'S DEMOLITION RANGE

GOLD: 0 SHOTS: ●●●●●

Take your time. Pull back, aim, release to knock it ALL down!

🎯 ROUND OVER!

🩹
OUT OF HEARTS!
Review your missed questions to patch up.