Welcome to "Fuel Tenths Lab", a 4th Grade Decimals mission at the Explorer (core) level, staged in our space exploration scenario. The mission opens with a hands-on prompt: "Shade 12 cells on the 10×10 hundredths grid to model 12/100 = 0.12." You'll work with the numbers 12, 10, 100 and arrive at a final answer of 100 across 3 guided steps.
Behind the space exploration story, this lesson is really about decimals aligned to CCSS 4.NF.C.6. Use decimal notation for fractions with denominators 10 or 100. The key strategy this mission asks you to internalise: Decimal = 0.12.
A general pattern to watch for in 4th Grade decimals — illustrated with example numbers below, which may differ from this lesson's: Reading 0.7 as "zero point seven" without grasping that it equals 7/10. Always say "seven tenths" alongside "zero point seven". Tie the symbol to the meaning. If you get stuck on "Fuel Tenths 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 4 · Decimals
Mission Progress
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Thinking Summary · 1
Mastered[object Object]
[Discovery] Shade 12 cells on the 10×10 hundredths grid to model 12/100 = 0.12.
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Active StepShade 12 of 100 cells.
Everything you need to know about the Socratic experience.
Shade 12 cells on the 10×10 hundredths grid to model 12/100 = 0.12. Hint: Each cell is 1/100. You need 12 shaded.
Which is bigger: 12/100 or 1/2? If you get stuck, the adaptive hint is: Convert both to the same denominator and compare numerators.
Explorer missions hit the core abstraction at typical numeric ranges — this is where conceptual mastery is built. Within 4th Grade Decimals, expect numbers in the corresponding range.
Treating 0.5 and 0.05 as the same value (ignoring the place). 0.5 = 5/10. 0.05 = 5/100. The position of the 5 changes its value tenfold.
Comparefractions (A decimal IS a fraction with a special denominator.). Open /grade-4/comparefractions to start that topic's missions.
Research on "productive struggle" shows that 20–60 seconds of focused effort BEFORE help dramatically improves long-term retention — the brain encodes the strategy more deeply. Inquiry AI's hint timing is calibrated to this window: short enough to prevent frustration, long enough to lock in the learning. Parents can adjust the threshold in settings if a learner needs faster scaffolding.
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.
