Fill the table by solving knowns first

3.MD.B.33.OA.D.8 · take · grade 3

Archetype: Solve a Table or Graph Step by Step from Clues · step in a 5-type progression

Sojin's class surveyed their favorite seasons and recorded the results in a table. If the number of students who like winter is $2$ more than the number who like summer, how many students like winter?

Favorite Season by Number of Students

Season	Spring	Summer	Fall	Winter	Total
Number of students	$4$		$7$		$27$

Show solution

Understand

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.

Givens

Spring = 4, Fall = 7.
Total students = 27.
Winter = Summer + 2.

Unknowns

The number of students who like winter (and summer).

Constraints

All four season counts must add to 27.
Counts are whole numbers of students.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

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.

Execute

#11 Work Backwards 3.MD.B.3

Subtract the known counts from the total: summer and winter must 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.

#11 Work Backwards 3.OA.D.8

Winter is summer plus 2. If we take those extra 2 away from the 16, the rest splits into two equal summer-sized parts: (16 - 2) / 2 = 7, so summer = 7.

(16 - 2) \div 2 = 14 \div 2 = 7

Removing the difference, then halving the remainder, is the standard way to split a sum into two unequal parts.

#6 Guess and Check 3.OA.D.8

Winter is 2 more than summer, so winter = 7 + 2 = 9.

7 + 2 = 9

Adding the known difference back gives the larger count.

Answer: 9 students

Review

Check the whole table: 4 + 7 (summer) + 7 (fall) + 9 (winter) = 27, matching the total, and winter 9 is exactly 2 more than summer 7.

Guess and Check: try summer 6/winter 8 -> 4+6+7+8=25 (too small); summer 7/winter 9 -> 27 (correct).

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Using the table total and filled cells to find the missing pair's sum.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Splitting 16 into two parts differing by 2 to get summer and winter.

💡 Total minus what you know, then split the rest using the '2 more' clue - all Grade 3!