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FRUIT MARKET

GRAND TRADE

Magic fruits. Sharp deals.
Out-math every scam on the Five Isles!

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WHO'S TRADING TODAY?

🏝️ THE FIVE ISLES

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🐯 TRADER

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ISLE 1

Sprout Isle

fractions on the number line

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ISLE 2

Market Bay

ratios + unit rates

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ISLE 3

Ledger Lagoon

proportions

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ISLE 4

Boost Bazaar

percents + percent change

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ISLE 5: BOSS

Scam Cove

accept fair deals, refuse scams

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Tap any isle to sail there, even locked ones. Traders check every port.

ISLE 1 Lesson 1/6

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Welcome!

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MARKET INSTINCT!

4 in a row! You clearly know this isle.
Want to jump straight to the last deal?

I1 Q1/9

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STREAK:

Question

🦊 SCAM COVE 🦊 ACCEPT FAIR DEALS. REFUSE SCAMS. SAY WHY.

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YOU

❤️❤️❤️

VS

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SCAM ARTIST

SCAM ARTIST HP

6/6

Question

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ISLE CLEARED!

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GRAND TRADER
OF THE FIVE ISLES!

You out-priced every stall
and out-mathed the Scam Artist!

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COINS

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STARS

🏆 ISEE FRACTIONS + RATIOS + PERCENTS: READY!

🔮 REVIEW MODE Q1/5

🧺 THE PRACTICE STALL

Endless trading drills 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 coin.

🪙 Practice coins today: 0/15

📜 TRADER'S CODE: MATH WORDS

📚 THE RESEARCH

FOR PARENTS & TEACHERS: Every mechanic in Fruit Market is tied to published evidence, and the evidence is sorted honestly. TIER 1 lists causal evidence: randomized controlled trials and strong quasi-experiments that justify the game's instructional choices. TIER 2 lists descriptive research: large surveys and assessments that document the misconceptions the game targets (no causal claim needed to know an error is common). TIER 3 lists longitudinal, correlational work that motivates why this topic is worth the effort. Where a source is correlational or descriptive, it is labeled as such.

TIER 1: CAUSAL EVIDENCE (randomized and quasi-experimental trials)

🎮 Isle 1's fruit-juice number line: every fraction lives at a POINT from 0 to 1

Randomized controlled trials: a fraction intervention centered on magnitude and the number line outperformed control instruction with at-risk fourth graders (Fuchs et al.), and number-line training beat area-model (pie-piece) training on transfer in younger children (Hamdan & Gunderson; second and third graders, one short session). Newer trials extend this to the target grades: an RCT with 205 fifth graders with math difficulties found large gains across fraction outcomes including number-line estimation (Jayanthi et al.), and an RCT with struggling sixth graders found a number-line-centered intervention improved estimation, comparison, and concepts at posttest and delayed posttest (Barbieri et al.). That is why this game's fractions live on a line, not just in pies.

Fuchs et al. (2013): RCT, fraction-magnitude intervention, grade 4. Hamdan & Gunderson (2017): RCT, number line vs. area model, grades 2-3. Jayanthi et al. (2021): RCT, grade 5. Barbieri et al. (2020): RCT, grade 6.

🎮 The same quantity shown four ways: number line, trade-ledger table, percent bar, and symbols

Large classroom-randomized trial (66 classrooms, 1,600+ fourth and fifth graders): the Rational Number Project curriculum, built on translating among multiple representations, outperformed commercial curricula on 4 of 6 subscales: concepts, ordering, transfer, and estimation. The percent bar and double number line ride under this multiple-representations evidence.

Cramer, Post & delMas (2002): classroom-randomized comparison, RNP vs. commercial curricula.

🎮 Isle 3's ladder: trade-ledger table, then unit rate, then "the butterfly, revealed," compared side by side

Randomized classroom experiment: students who compared solution 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. A follow-up experiment found comparison helps most once students already know one strategy, which is why Isle 3 teaches the buildup table first, then puts it, the unit-rate strategy, and cross-multiplication next to each other on the same problem, and delays the butterfly until players can see it is just scaling.

Rittle-Johnson & Star (2007): randomized experiment on comparing solution methods. Rittle-Johnson, Star & Durkin (2009): prior knowledge moderates the benefit.

🎮 The Scam Artist boss: every deal hides a taught misconception, and refusing requires picking WHY

Randomized in-vivo classroom experiments: studying INCORRECT worked examples, and explaining what is wrong and why, improved students' conceptual understanding beyond correct examples alone (no differences were found on procedural measures). The boss is an error-analysis engine wearing a fox costume.

Booth, Lange, Koedinger & Newton (2013): randomized experiments with correct and incorrect examples.

🎮 Jokes that ENCODE the math: each lesson gag restates the concept, and wrong-option zingers restate the error

The design basis is Ziv's two semester-long randomized experiments with college students (same instructor, same syllabus, only the content-related humor varied): humor groups scored significantly higher on the same final exams. Separately, randomized experiments with young children found well-PACED humorous inserts, unrelated to the lesson content, increased attention and information acquisition from educational TV; that supports attention and pacing effects, not content-linked humor itself. Honest caveat: experimental evidence on classroom humor in K-8 is thin, and one recent college experiment found integrated humor REDUCED learning. That is exactly why this game's humor follows strict content-linked guardrails: load-bearing jokes are about the math itself, a joke option is never the correct answer, at most one per question, and never a defensible answer.

Ziv (1988): two randomized semester experiments, college students, content-related humor. Zillmann et al. (1980): randomized experiments, pacing of humorous inserts in children's educational TV. Bolkan, Griffin & Goodboy (2018): college experiments where integrated humor lowered test performance.

🎮 "Estimate FIRST" items, and delaying cross-multiplication until reasoning is built

The IES/WWC fractions practice guide is an evidence synthesis that grades each of its recommendations minimal, moderate, or strong; where trial evidence is thin, recommendations also rest partly on panel expert judgment. Its recommendations behind this game: make the number line central (Rec 2, moderate evidence), use estimation before computation (Rec 3, moderate evidence), and build proportional reasoning with buildup and unit-rate strategies before formal procedures (Rec 4, a minimal-evidence recommendation reflecting expert consensus and emerging research).

Siegler et al. (2010), NCEE 2010-4039: WWC evidence synthesis with per-recommendation evidence levels.

TIER 2: WHAT WE TARGET (descriptive research documenting the misconceptions)

🎮 The Additive Trap ("3 more fruits is 3 more coins") in Isle 3 and the boss fight

Large-scale survey of 11-16 year olds documenting the additive-instead-of-multiplicative proportion error as the classic failure mode. Descriptive: it tells us WHAT goes wrong; the game shows the wrong and right answers side by side so the error is visible.

Hart (1981): Children's Understanding of Mathematics 11-16 (survey).

🎮 "Numerator and denominator are a TEAM, not two separate numbers" (Isle 1)

Descriptive and theoretical account of whole-number bias: children importing whole-number rules into fractions. The game names the bias out loud and has players catch it in the wild.

Ni & Zhou (2005): origins and implications of whole number bias (review).

🎮 The "12/13 + 7/8 is about 19" trap item (Isle 1, and again at Scam Cove)

National assessment data: on the second NAEP mathematics assessment, over half (55%) of 13-year-olds estimated 12/13 + 7/8 as 19 or 21 by adding tops or bottoms; only 24% said about 2. The game reproduces the item as a spot-the-scam challenge. Descriptive: it documents the error rate, not a treatment.

Carpenter, Corbitt, Kepner, Lindquist & Reys (1980): results of the second NAEP mathematics assessment; see also Post (1981) for the item statistics.

🎮 Isle 2 teaches UNIT RATE ("the value of ONE fruit") before any formal proportion rule; bar and tape models throughout

Research synthesis: the unit-rate strategy is students' most natural entry into proportional reasoning, and premature cross-multiplication crowds it out (descriptive synthesis of student strategy data). The percent bar and ledger inherit the tape-model lineage documented in Singapore's model method (descriptive).

Cramer, Post & Currier (1993): synthesis on ratio and proportion. Ng & Lee (2009): the model method (descriptive).

TIER 3: WHY IT MATTERS (longitudinal, correlational motivation)

🎮 Why a whole game about fractions, ratios, and percents at this age

Longitudinal cohorts in the US and UK: fraction knowledge at age 10 uniquely predicts algebra achievement at 16, controlling for IQ, whole-number skill, and family background. Correlational, labeled as such: it motivates the target, while the Tier 1 trials justify the methods.

Siegler et al. (2012): early predictors of high school mathematics achievement (longitudinal, correlational).

FULL REFERENCES

Barbieri, C. A., Rodrigues, J., Dyson, N., & Jordan, N. C. (2020). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology, 112(3), 628-648.

Bolkan, S., Griffin, D. J., & Goodboy, A. K. (2018). Humor in the classroom: The effects of integrated humor on student learning. Communication Education, 67(2), 144-164.

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.

Carpenter, T. P., Corbitt, M. K., Kepner, H. S., Jr., Lindquist, M. M., & Reys, R. E. (1980). Results of the second NAEP mathematics assessment: Secondary school. Mathematics Teacher, 73(5), 329-338.

Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. Owens (Ed.), Research Ideas for the Classroom: Middle Grades Mathematics (pp. 159-178). New York: Macmillan.

Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the Rational Number Project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144.

Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., Jordan, N. C., Siegler, R., Gersten, R., & Changas, P. (2013). Improving at-risk learners' understanding of fractions. Journal of Educational Psychology, 105(3), 683-700.

Hamdan, N., & Gunderson, E. A. (2017). The number line is a critical spatial-numerical representation: Evidence from a fraction intervention. Developmental Psychology, 53(3), 587-596.

Hart, K. M. (Ed.) (1981). Children's Understanding of Mathematics: 11-16. London: John Murray.

Jayanthi, M., Gersten, R., Schumacher, R. F., Dimino, J., Smolkowski, K., & Spallone, S. (2021). Improving struggling fifth-grade students' understanding of fractions: A randomized controlled trial of an intervention that stresses both concepts and procedures. Exceptional Children, 88(1), 81-100.

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.

Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.

Post, T. (1981). Fractions: Results and implications from National Assessment. Arithmetic Teacher, 28(9), 26-31.

Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561-574.

Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836-852.

Siegler, R. S., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing Effective Fractions Instruction for Kindergarten Through 8th Grade (NCEE 2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education.

Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691-697.

Zillmann, D., Williams, B. R., Bryant, J., Boynton, K. R., & Wolf, M. A. (1980). Acquisition of information from educational television programs as a function of differently paced humorous inserts. Journal of Educational Psychology, 72(2), 170-180.

Ziv, A. (1988). Teaching and learning with humor: Experiment and replication. Journal of Experimental Education, 57(1), 5-15.

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

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