Problem
Fill the table by solving knowns first
A class table shows 4 like spring, 7 like fall, the total is 27, and the summer and winter counts are blank. Winter is 2 more than summer. We find how many like winter.
Measurement & dataOperations
Your answer
students
Watch out After finding summer (7), don't stop there — winter is summer plus 2, not 7 itself.
How to solve
Strategy Work Backwards — Start from the known total, subtract the known seasons to find what summer and winter must share, then use the 'winter is 2 more' clue to split it. A quick guess-and-check confirms the split.
1STEP 1
Find summer + winter together
Subtract the known counts from the total: summer and winter together account for 27 - 4 - 7 = 16 students.
27 - 4 - 7 = 16
Using the table total minus the filled-in cells to find the missing pair's sum is basic table/graph reasoning.
3.MD.B.3Work Backwards2STEP 2
Use the 'winter is 2 more' clue
Winter is summer plus 2 — remove that extra 2 from 16, then split evenly: (16 - 2) ÷ 2 = 7.
(16 - 2) ÷ 2 = 14 ÷ 2 = 7
Removing the difference, then halving the remainder, is the standard way to split a sum into two unequal parts.
3.OA.D.8Work BackwardsSummer must be 7: since winter is 2 more than summer, taking that extra 2 out of their shared 16 leaves 14, and halving 14 gives the summer count.
Why?
The 16 that summer and winter share is really two summer-sized parts with an extra 2 sitting on top.
Why?
The 16 is just the summer count and the winter count added together, because a whole is its parts combined.
🧱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?
Winter is the same amount as summer plus 2, so it can stand in for 'summer and 2' inside that total.
🧱Transitivity of equalityIf the first equals the second and the second equals the third, the first equals the third.
Why?
Pulling the extra 2 back out of 16 leaves 14, which is exactly the two equal summer parts with nothing extra.
Why?
Subtraction removes an amount that was added, so taking away 2 cancels the 'plus 2' that made winter bigger.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
The leftover 14 is two equal summer parts, so sharing it into 2 equal groups gives one summer, which is 7.
Why?
Two equal summer parts is exactly '2 groups of summer,' which is what a count of equal groups means.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Splitting 14 into 2 equal groups is the reverse of building it from 2 equal groups, so it hands back one group.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
3STEP 3
Find winter
Winter is 2 more than summer, so winter = 7 + 2 = 9.
7 + 2 = 9
Adding the known difference back gives the larger count.
3.OA.D.8Guess And CheckAnswer
9 students
Check the whole table: 4 (spring) + 7 (summer) + 7 (fall) + 9 (winter) = 27, matching the total, and winter 9 is exactly 2 more than summer 7.
Takeaway
Total minus what you know, then split the rest using the '2 more' clue - all Grade 3!
- Find summer + winter together
- Use the 'winter is 2 more' clue
- Find winter
Where next?
Another one like thissuggested
Same look, different logicsuggested
Step back and solidifysuggested