← 3-2 · Fill the table by solving knowns first · Solve a Table or Graph Step by Step from Clues

Fill the table by solving knowns first · 10 practice problems

3.MD.B.33.OA.D.8

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 12 students

Hajun's class surveyed their favorite seasons and recorded the results in a table. If the number of students who like winter is $8$ 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	$4$		$4$		$24$

Show solution

Understand

A class table shows 4 like spring, 4 like fall, the total is 24, and the summer and winter counts are blank. Winter is 8 more than summer. We find how many like winter.

Givens

Spring = 4, Fall = 4.
Total students = 24.
Winter = Summer + 8.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 24 - 4 - 4 = 16 students.

24 - 4 - 4 = 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 8. If we take those extra 8 away from the 16, the rest splits into two equal summer-sized parts: (16 - 8) / 2 = 4, so summer = 4.

(16 - 8) \div 2 = 8 \div 2 = 4

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 8 more than summer, so winter = 4 + 8 = 12.

4 + 8 = 12

Adding the known difference back gives the larger count.

Answer: 12 students

Review

Check the whole table: 4 + 4 (summer) + 4 (fall) + 12 (winter) = 24, matching the total, and winter 12 is exactly 8 more than summer 4.

Guess and Check: try summer 3/winter 11 -> 4+3+4+11=22 (too small); summer 4/winter 12 -> 24 (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 8 to get summer and winter.

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

Variant 2 answer: 11 students

Taeyang's class surveyed their favorite seasons and recorded the results in a table. If the number of students who like winter is $6$ 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	$5$		$5$		$26$

Show solution

Understand

A class table shows 5 like spring, 5 like fall, the total is 26, and the summer and winter counts are blank. Winter is 6 more than summer. We find how many like winter.

Givens

Spring = 5, Fall = 5.
Total students = 26.
Winter = Summer + 6.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 26 - 5 - 5 = 16 students.

26 - 5 - 5 = 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 6. If we take those extra 6 away from the 16, the rest splits into two equal summer-sized parts: (16 - 6) / 2 = 5, so summer = 5.

(16 - 6) \div 2 = 10 \div 2 = 5

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 6 more than summer, so winter = 5 + 6 = 11.

5 + 6 = 11

Adding the known difference back gives the larger count.

Answer: 11 students

Review

Check the whole table: 5 + 5 (summer) + 5 (fall) + 11 (winter) = 26, matching the total, and winter 11 is exactly 6 more than summer 5.

Guess and Check: try summer 4/winter 10 -> 5+4+5+10=24 (too small); summer 5/winter 11 -> 26 (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 6 to get summer and winter.

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

Variant 3 answer: 7 students

Doyun'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	$2$		$9$		$23$

Show solution

Understand

A class table shows 2 like spring, 9 like fall, the total is 23, and the summer and winter counts are blank. Winter is 2 more than summer. We find how many like winter.

Givens

Spring = 2, Fall = 9.
Total students = 23.
Winter = Summer + 2.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 23 - 2 - 9 = 12 students.

23 - 2 - 9 = 12

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 12, the rest splits into two equal summer-sized parts: (12 - 2) / 2 = 5, so summer = 5.

(12 - 2) \div 2 = 10 \div 2 = 5

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 = 5 + 2 = 7.

5 + 2 = 7

Adding the known difference back gives the larger count.

Answer: 7 students

Review

Check the whole table: 2 + 5 (summer) + 9 (fall) + 7 (winter) = 23, matching the total, and winter 7 is exactly 2 more than summer 5.

Guess and Check: try summer 4/winter 6 -> 2+4+9+6=21 (too small); summer 5/winter 7 -> 23 (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 12 into two parts differing by 2 to get summer and winter.

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

Variant 4 answer: 10 students

Seoyeon's class surveyed their favorite seasons and recorded the results in a table. If the number of students who like winter is $4$ 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	$7$		$5$		$28$

Show solution

Understand

A class table shows 7 like spring, 5 like fall, the total is 28, and the summer and winter counts are blank. Winter is 4 more than summer. We find how many like winter.

Givens

Spring = 7, Fall = 5.
Total students = 28.
Winter = Summer + 4.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 28 - 7 - 5 = 16 students.

28 - 7 - 5 = 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 4. If we take those extra 4 away from the 16, the rest splits into two equal summer-sized parts: (16 - 4) / 2 = 6, so summer = 6.

(16 - 4) \div 2 = 12 \div 2 = 6

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 4 more than summer, so winter = 6 + 4 = 10.

6 + 4 = 10

Adding the known difference back gives the larger count.

Answer: 10 students

Review

Check the whole table: 7 + 6 (summer) + 5 (fall) + 10 (winter) = 28, matching the total, and winter 10 is exactly 4 more than summer 6.

Guess and Check: try summer 5/winter 9 -> 7+5+5+9=26 (too small); summer 6/winter 10 -> 28 (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 4 to get summer and winter.

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

Variant 5 answer: 12 students

Yuna's class surveyed their favorite seasons and recorded the results in a table. If the number of students who like winter is $6$ 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	$6$		$6$		$30$

Show solution

Understand

A class table shows 6 like spring, 6 like fall, the total is 30, and the summer and winter counts are blank. Winter is 6 more than summer. We find how many like winter.

Givens

Spring = 6, Fall = 6.
Total students = 30.
Winter = Summer + 6.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 30 - 6 - 6 = 18 students.

30 - 6 - 6 = 18

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 6. If we take those extra 6 away from the 18, the rest splits into two equal summer-sized parts: (18 - 6) / 2 = 6, so summer = 6.

(18 - 6) \div 2 = 12 \div 2 = 6

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 6 more than summer, so winter = 6 + 6 = 12.

6 + 6 = 12

Adding the known difference back gives the larger count.

Answer: 12 students

Review

Check the whole table: 6 + 6 (summer) + 6 (fall) + 12 (winter) = 30, matching the total, and winter 12 is exactly 6 more than summer 6.

Guess and Check: try summer 5/winter 11 -> 6+5+6+11=28 (too small); summer 6/winter 12 -> 30 (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 18 into two parts differing by 6 to get summer and winter.

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

Variant 6 answer: 10 students

Jiho'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	$3$		$8$		$29$

Show solution

Understand

A class table shows 3 like spring, 8 like fall, the total is 29, and the summer and winter counts are blank. Winter is 2 more than summer. We find how many like winter.

Givens

Spring = 3, Fall = 8.
Total students = 29.
Winter = Summer + 2.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 29 - 3 - 8 = 18 students.

29 - 3 - 8 = 18

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 18, the rest splits into two equal summer-sized parts: (18 - 2) / 2 = 8, so summer = 8.

(18 - 2) \div 2 = 16 \div 2 = 8

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 = 8 + 2 = 10.

8 + 2 = 10

Adding the known difference back gives the larger count.

Answer: 10 students

Review

Check the whole table: 3 + 8 (summer) + 8 (fall) + 10 (winter) = 29, matching the total, and winter 10 is exactly 2 more than summer 8.

Guess and Check: try summer 7/winter 9 -> 3+7+8+9=27 (too small); summer 8/winter 10 -> 29 (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 18 into two parts differing by 2 to get summer and winter.

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

Variant 7 answer: 9 students

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 the total.
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 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 'more' clue - all Grade 3!

Variant 8 answer: 9 students

Minji's class surveyed their favorite seasons and recorded the results in a table. If the number of students who like winter is $4$ 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	$5$		$6$		$25$

Show solution

Understand

A class table shows 5 like spring, 6 like fall, the total is 25, and the summer and winter counts are blank. Winter is 4 more than summer. We find how many like winter.

Givens

Spring = 5, Fall = 6.
Total students = 25.
Winter = Summer + 4.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 25 - 5 - 6 = 14 students.

25 - 5 - 6 = 14

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 4. If we take those extra 4 away from the 14, the rest splits into two equal summer-sized parts: (14 - 4) / 2 = 5, so summer = 5.

(14 - 4) \div 2 = 10 \div 2 = 5

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 4 more than summer, so winter = 5 + 4 = 9.

5 + 4 = 9

Adding the known difference back gives the larger count.

Answer: 9 students

Review

Check the whole table: 5 + 5 (summer) + 6 (fall) + 9 (winter) = 25, matching the total, and winter 9 is exactly 4 more than summer 5.

Guess and Check: try summer 4/winter 8 -> 5+4+6+8=23 (too small); summer 5/winter 9 -> 25 (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 14 into two parts differing by 4 to get summer and winter.

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

Variant 9 answer: 10 students

Arin'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	$8$		$7$		$33$

Show solution

Understand

A class table shows 8 like spring, 7 like fall, the total is 33, and the summer and winter counts are blank. Winter is 2 more than summer. We find how many like winter.

Givens

Spring = 8, Fall = 7.
Total students = 33.
Winter = Summer + 2.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 33 - 8 - 7 = 18 students.

33 - 8 - 7 = 18

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 18, the rest splits into two equal summer-sized parts: (18 - 2) / 2 = 8, so summer = 8.

(18 - 2) \div 2 = 16 \div 2 = 8

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 = 8 + 2 = 10.

8 + 2 = 10

Adding the known difference back gives the larger count.

Answer: 10 students

Review

Check the whole table: 8 + 8 (summer) + 7 (fall) + 10 (winter) = 33, matching the total, and winter 10 is exactly 2 more than summer 8.

Guess and Check: try summer 7/winter 9 -> 8+7+7+9=31 (too small); summer 8/winter 10 -> 33 (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 18 into two parts differing by 2 to get summer and winter.

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

Variant 10 answer: 8 students

Nari's class surveyed their favorite seasons and recorded the results in a table. If the number of students who like winter is $4$ 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	$3$		$6$		$21$

Show solution

Understand

A class table shows 3 like spring, 6 like fall, the total is 21, and the summer and winter counts are blank. Winter is 4 more than summer. We find how many like winter.

Givens

Spring = 3, Fall = 6.
Total students = 21.
Winter = Summer + 4.

Unknowns

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

Constraints

All four season counts must add to the total.
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 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 21 - 3 - 6 = 12 students.

21 - 3 - 6 = 12

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 4. If we take those extra 4 away from the 12, the rest splits into two equal summer-sized parts: (12 - 4) / 2 = 4, so summer = 4.

(12 - 4) \div 2 = 8 \div 2 = 4

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 4 more than summer, so winter = 4 + 4 = 8.

4 + 4 = 8

Adding the known difference back gives the larger count.

Answer: 8 students

Review

Check the whole table: 3 + 4 (summer) + 6 (fall) + 8 (winter) = 21, matching the total, and winter 8 is exactly 4 more than summer 4.

Guess and Check: try summer 3/winter 7 -> 3+3+6+7=19 (too small); summer 4/winter 8 -> 21 (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 12 into two parts differing by 4 to get summer and winter.

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