Welcome to "Cost-Per Decimal Lab", a 6th Grade Decimaldivision mission at the Explorer (core) level, staged in our bakery scenario. The mission opens with a hands-on prompt: "Shift both decimals one place right: 85 ÷ 1.7 = 850 ÷ 17. Long-divide 850 ÷ 17 on the template." You'll work with the numbers 85, 1, 7 and arrive at a final answer of 85 across 3 guided steps.
Behind the bakery story, this lesson is really about decimaldivision aligned to CCSS 6.NS.B.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm. The key strategy this mission asks you to internalise: Answer: 50.
A general pattern to watch for in 6th Grade decimaldivision — illustrated with example numbers below, which may differ from this lesson's: Shifting only the divisor, not the dividend. BOTH decimals shift the same number of places. Otherwise the quotient changes. If you get stuck on "Cost-Per Decimal Lab", the adaptive Socratic hints below escalate from a gentle nudge to a worked-out strategy — the same way a one-on-one tutor would coach you through it.
Grade 6 · Decimaldivision
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Thinking Summary · 1
Mastered[object Object]
[Discovery] Shift both decimals one place right: 85 ÷ 1.7 = 850 ÷ 17. Long-divide 850 ÷ 17 on the template.
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Active StepCompute 850 ÷ 17 by filling each quotient digit.
Everything you need to know about the Socratic experience.
Shift both decimals one place right: 85 ÷ 1.7 = 850 ÷ 17. Long-divide 850 ÷ 17 on the template. Hint: Multiplying both numerator and denominator by 10 keeps the quotient unchanged.
Verify: 1.7 × 50 = ? If you get stuck, the adaptive hint is: Answer: 85.
Explorer missions hit the core abstraction at typical numeric ranges — this is where conceptual mastery is built. Within 6th Grade Decimaldivision, expect numbers in the corresponding range.
Misplacing the decimal in the quotient. Place the quotient's decimal point directly above where the dividend's decimal landed AFTER shifting.
Decimalops (Decimal division builds on decimal × from Grade 5.). Open /grade-6/decimalops to start that topic's missions.
C-P-A is the Singapore Math sequence proven to deepen number sense: first manipulate physical objects (Concrete), then draw pictures of them (Pictorial), and only then write equations (Abstract). Inquiry AI structures every mission as exactly these three steps — a manipulative, a picture/grid model, and finally the equation. Skipping straight to symbols is the #1 cause of math anxiety; the platform refuses to do it.
Socratic teaching answers a question with a better question. Instead of "the answer is 12", the system asks "if you had 3 groups of 4, how could you skip-count?" The goal is to externalize the learner's reasoning so they hear themselves think. Every Inquiry AI hint follows this pattern: nudge → reframe → analogy → only then a worked example, in that order.
