Welcome to "Cost-Per Decimal Probe", a 6th Grade Decimaldivision mission at the Explorer (core) level, staged in our space exploration scenario. The mission opens with a hands-on prompt: "Shift both decimals one place right: 31.5 ÷ 0.9 = 315 ÷ 9. Long-divide 315 ÷ 9 on the template." You'll work with the numbers 31, 5, 0 and arrive at a final answer of 31.5 across 3 guided steps.
Behind the space exploration 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: 35.
A general pattern to watch for in 6th Grade decimaldivision — illustrated with example numbers below, which may differ from this lesson's: Misplacing the decimal in the quotient. Place the quotient's decimal point directly above where the dividend's decimal landed AFTER shifting. If you get stuck on "Cost-Per Decimal Probe", 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
Mission Progress
0/3
Thinking Summary · 1
Mastered[object Object]
[Discovery] Shift both decimals one place right: 31.5 ÷ 0.9 = 315 ÷ 9. Long-divide 315 ÷ 9 on the template.
1
Active StepCompute 315 ÷ 9 by filling each quotient digit.
Everything you need to know about the Socratic experience.
Shift both decimals one place right: 31.5 ÷ 0.9 = 315 ÷ 9. Long-divide 315 ÷ 9 on the template. Hint: Multiplying both numerator and denominator by 10 keeps the quotient unchanged.
Verify: 0.9 × 35 = ? If you get stuck, the adaptive hint is: Answer: 31.5.
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.
Believing dividing by a decimal less than 1 makes the result smaller. Dividing by less than 1 makes the result LARGER. 6 ÷ 0.5 = 12, not 3.
Multidigitdivision (Same long-division algorithm, just with shifted decimals.). Open /grade-6/multidigitdivision to start that topic's missions.
Inquiry-based learning starts with a question, not a formula — students explore, hypothesize, and verify before being told the rule. In Inquiry AI, every mission opens with a "Discovery" step (manipulate the model), then "Abstraction" (write the equation), then "Reflect" (apply to a new case). The procedure is never given upfront; learners derive it from their own observations.
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.
