Problem
Find the total first, then divide
Tangerines were packed 12 to a bag into 3 bags. The same tangerines are then repacked equally into 6 bags. I need to find how many go in each of the new bags.
Operations
Your answer
Watch out Don't divide the original bag size by the new bag count directly — first find the total number of tangerines, then split that total.
How to solve
Strategy Identify Subproblems — This is a two-step calculation: first find the total number of tangerines (a multiplication subproblem), then split that total equally into 6 bags (a division subproblem). Breaking it into these two smaller problems makes the path clear, and watching the units (tangerines per bag times bags = tangerines) keeps the setup honest.
1STEP 1
Find the total number of tangerines
3 bags of 12 tangerines each multiply to 36 tangerines in all.
12 × 3 = 36
Equal groups of objects are counted by multiplying the group size by the number of groups.
3.OA.A.3Identify Subproblems2STEP 2
Split the total equally into 6 bags
The same 36 tangerines split equally into 6 bags gives 6 tangerines per bag.
36 ÷ 6 = 6
Sharing a total equally into a known number of groups is exactly what division finds.
3.OA.A.3Analyze The UnitsRepacking the same tangerines equally into 6 bags puts 6 tangerines in each new bag.
Why?
Repacking moves the tangerines into new bags but adds and loses none, so the total is still the same 36 as before.
Why?
That 36 comes from 3 bags of 12, because equal groups are counted by taking the size of one group as many times as there are groups.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Pouring one pile into several bags only splits it into parts, and parts with no gaps or overlaps always add back to the whole pile.
🧱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?
Filling 6 bags with the same number in each means that number, taken 6 times, must rebuild the 36, and dividing 36 by 6 is how you find it.
Why?
Six bags each holding the same amount is 6 equal groups, so the number in one bag counted 6 times gives back the whole 36.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Finding the number that times 6 makes 36 is undoing a multiplication, and division is exactly the operation that undoes multiplication.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Answer
6
Going from 3 bags to 6 bags doubles the number of bags, so each bag should hold half as many: half of 12 is 6, which matches. Also 6 tangerines per bag times 6 bags equals 36, the same total we started with.
Takeaway
Find the whole pile first, then share it out: that's all this Grade 3 problem needs!
- Find the total number of tangerines
- Split the total equally into 6 bags
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested