Problem
Constant increase yields a correspondence equation
A bathtub starts with 5 L of water. A showerhead adds 12 L every minute. We want to know how many minutes it takes until the tub holds 113 L.
Operations
Your answer
How to solve
Strategy Look for a Pattern — Because the water rises by the same 12 L each minute, the amount in the tub follows a steady pattern that links minutes to liters. We find that correspondence rule, then peel off the 5 L head start (work backwards) and split the rest into 12-L minutes, checking with units that liters divided by liters-per-minute gives minutes.
1STEP 1
Build the pattern (minutes to liters)
The tub holds 5 L at 0 minutes, 17 at 1 and 29 at 2, so the rule is 5 + 12 x minutes.
0 min→ 5, 1→ 17, 2→ 29, 3→ 41
Adding the same number again and again makes a steady staircase of values, which a 4th grader can extend by repeated addition.
4.OA.C.5Look For A Pattern2STEP 2
Remove the 5 L head start
The 5 L was already there, so the showerhead has to supply 113 - 5 = 108 L.
113 - 5 = 108
Starting from the final amount and undoing the head start tells us exactly how much new water the shower is responsible for.
5.OA.A.2Work BackwardsThe showerhead itself only has to supply 108 L.
Why?
The water in the tub at the end is the 5 L that was already sitting there plus the water the showerhead pours in, and nothing else.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Taking the 5 L head start off the 113 L target undoes the fact that it was already counted in that target.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
3STEP 3
Split the new water into 12-L minutes
Splitting 108 into 12-litre minutes gives 108 divided by 12 = 9 minutes.
108 ÷ 12 = 9
Sharing the added water into equal one-minute chunks turns the rule around to find the time, and the units confirm the answer is in minutes.
5.OA.B.3Analyze The UnitsAnswer
9 minutes
Plug 9 back into the rule: 5 + 12 times 9 = 5 + 108 = 113 L, which matches the target exactly, and the answer is a sensible whole number of minutes.
Takeaway
When something grows by the same amount each time, find the steady rule, take off the head start, and split the rest into equal steps.
- Build the pattern (minutes to liters)
- Remove the 5 L head start
- Split the new water into 12-L minutes
Where next?
Level upsuggested
Another one like thissuggested
Same look, different logicsuggested
Step back and solidifysuggested