Problem
Measure a target with unmarked jugs
Unmarked 4, 6 and 7 fl oz jugs must leave exactly 9 fl oz in the tank. Each move pours or dips one full jug. The tank may never go below empty. Find a method genuinely different from the one given.
Reasoning · Grade 3-2 Measuring Capacity
Your answer
Watch out The given method uses each jug once, but a jug may be poured twice.
How to solve
Strategy Guess and Check — We try small combinations of adding and removing jug-fulls and check whether the running total lands on 9. Because jugs may be reused, listing a few promising plus/minus combinations and checking each total quickly finds a valid equation that is not the one already shown.
1STEP 1
Aim a little above 9, then trim back
Two 4s and one 7 make 15 fl oz.
4 + 4 + 7 = 15
Overshooting by an amount that equals one of the jugs means one clean removal will land us on the target.
3.NBT.A.2Guess And CheckOvershooting the target by exactly one jug's worth means a single clean removal will land on it.
Why?
Counting how many whole jugfuls fit above the target and what is left over is what tells you which overshoot can be cancelled.
🧱Division with remainderAny number splits into a whole count of equal groups plus a leftover, and the leftover is always smaller than the group size.
Why?
Taking a jugful out reverses putting one in, so an overshoot that is exactly one jug disappears in one move.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Remove the extra with the 6-jug
The excess is exactly one jug, so dipping 6 out leaves 9.
15 - 6 = 9
Taking away one 6-jug exactly cancels the overshoot, leaving the target.
3.NBT.A.2Guess And Check3STEP 3
Check it is a different method
The tank reads 4, 8, 15, 9 — never below empty.
4 + 4 + 7 - 6 = 9
Reusing one jug gives a brand-new combination, so the plan really is different from the example.
3.OA.D.8Make A Systematic ListAnswer
4 + 4 + 7 − 6 = 9
Add and subtract in order: 4 + 4 = 8, 8 + 7 = 15, 15 - 6 = 9. The result is exactly 9 fl oz, and at no point does the tank go negative (4, 8, 15, 9), so the method works and is different from 7 - 4 + 6.
Takeaway
Pour in a bit past 9, then dip back out exactly one jug-full to land right on the target a brand-new way!
- Aim a little above 9, then trim back
- Remove the extra with the 6-jug
- Check it is a different method