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Toolkit + CCSS Solution
Understand
Restated: One can holds 12 ounces of soda. A gallon is 128 ounces. Find the smallest number of whole cans whose soda adds up to at least 128 ounces.
Givens: Each can holds 12 ounces.; A gallon is 128 ounces.
Unknowns: The minimum number of cans needed to make at least 128 ounces.
Understand
Restated: One can holds 12 ounces of soda. A gallon is 128 ounces. Find the smallest number of whole cans whose soda adds up to at least 128 ounces.
Givens: Each can holds 12 ounces.; A gallon is 128 ounces.
Plan
Primary tool: #8 Analyze the Units
Secondary: #6 Guess and Check, #14 Extreme Principle
The problem links two units: ounces per can and total ounces needed. Track how ounces build up as cans are added, test whole numbers of cans against the 128-ounce target, and take the smallest count that reaches it.
Execute — Answer: E
#8 Analyze the Units 4.OA.A.3Step 1
Set the target
Each can adds 12 ounces, so n cans hold 12 times n ounces.
To make a gallon, that total must be at least 128 ounces.
$$12 \times n \geq 128$$
💡 More cans means more ounces, so we just need enough cans to reach 128.
#6 Guess and Check 4.NBT.B.5Step 2
Test 10 cans
Try 10 cans.
They hold 12 times 10, which is 120 ounces.
That is less than 128, so 10 cans are not enough for a gallon.
$$12 \times 10 = 120 < 128$$
💡 Ten is a round guess, but check the real ounces before trusting it.
#6 Guess and Check 4.NBT.B.5Step 3
Test 11 cans
Add one more can.
Now 12 times 11 is 132 ounces, which is at least 128.
So 11 cans make enough soda for a gallon.
$$12 \times 11 = 132 \geq 128$$
💡 One more can adds 12 ounces, pushing the total just past 128.
#14 Extreme Principle 4.OA.A.3Step 4
Pick the smallest that works
Ten cans fall short and eleven cans are enough, so the fewest cans that reach a gallon is 11.
The answer is (E).
$$\min\{\, n : 12n \geq 128 \,\} = 11$$
💡 The smallest whole number of cans that reaches the goal is the one right after it was still short.
[1]
#8 4.OA.A.3Each can adds 12 ounces, so n cans hold 12 times n ounces. To make a gallon, tha
[2]
#6 4.NBT.B.5Try 10 cans. They hold 12 times 10, which is 120 ounces. That is less than 128,
[3]
#6 4.NBT.B.5Add one more can. Now 12 times 11 is 132 ounces, which is at least 128. So 11 ca
[4]
#14 4.OA.A.3Ten cans fall short and eleven cans are enough, so the fewest cans that reach a
Review
Reasonableness: A gallon of 128 ounces is a little more than ten 12-ounce cans, which give 120 ounces, so the count should be just above 10, and 11 fits. Eleven cans give 132 ounces, only 4 ounces of spare soda, matching a 'just barely enough' answer. The smaller choices 7, 8, 9, and 10 all give fewer than 128 ounces, so none of them can make a gallon.
Alternative: Divide 128 by 12 to get about 10.7 cans. Since you cannot buy part of a can, round up to the next whole number, 11.
CCSS standards used (min grade 4)
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers (Setting up the at-least-128-ounce goal and interpreting that the leftover forces rounding up to a whole number of cans.)
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number (Computing 12 times 10 and 12 times 11 to see which count of cans reaches 128 ounces.)
⭐ When you can only buy whole items, work out how many you need and round UP so you have enough.
⭐ When you can only buy whole items, work out how many you need and round UP so you have enough.