← Solve graph values step by step from clues · Solve a Table or Graph Step by Step from Clues

Solve graph values step by step from clues · 10 practice problems

3.MD.B.33.OA.A.3

Generated variants — 10

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

Variant 1 easy answer: 17 students

A class surveyed which season each student was born in and recorded the results in a picture graph. The number of students born in winter is $2$ times the number born in summer. Find the total number of students surveyed.

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $6$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $6$ circles, summer has $2$ circles, and autumn has $5$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times2=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 6, summer 2, autumn 5, and winter blank. The number born in winter is 2 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 6 students, summer = 2 students, autumn = 5 students (read from the graph).
Winter = 2 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 2 circles, so 2 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 2 times summer: 2 x 2 = 4 students born in winter.

2 \times 2 = 4

'2 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 6 + 2 + 5 + 4 = 17 students.

6 + 2 + 5 + 4 = 17

The whole survey is just the sum of every season's count.

Answer: 17 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (6, 2, 5, 4) and their sum 17 is a believable class size; winter (4) is indeed 2 times summer (2), matching the rule.

Another way: Add the three known seasons first (6 + 2 + 5 = 13), then add winter (4) to get 13 + 4 = 17 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 2 medium answer: 18 students

A class surveyed which season each student was born in and recorded the results in a picture graph. The number of students born in winter is $3$ times the number born in summer. Find the total number of students surveyed.

Number of students by season of birth

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times3=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 6, summer 2, autumn 4, and winter blank. The number born in winter is 3 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 6 students, summer = 2 students, autumn = 4 students (read from the graph).
Winter = 3 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 2 circles, so 2 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 3 times summer: 2 x 3 = 6 students born in winter.

2 \times 3 = 6

'3 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 6 + 2 + 4 + 6 = 18 students.

6 + 2 + 4 + 6 = 18

The whole survey is just the sum of every season's count.

Answer: 18 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (6, 2, 4, 6) and their sum 18 is a believable class size; winter (6) is indeed 3 times summer (2), matching the rule.

Another way: Add the three known seasons first (6 + 2 + 4 = 12), then add winter (6) to get 12 + 6 = 18 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 3 medium answer: 16 students

A class surveyed which season each student was born in and recorded the results in a picture graph. The number of students born in winter is $4$ times the number born in summer. Find the total number of students surveyed.

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $6$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $5$ circles, summer has $1$ circles, and autumn has $6$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times4=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 5, summer 1, autumn 6, and winter blank. The number born in winter is 4 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 5 students, summer = 1 students, autumn = 6 students (read from the graph).
Winter = 4 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 1 circles, so 1 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 4 times summer: 1 x 4 = 4 students born in winter.

1 \times 4 = 4

'4 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 5 + 1 + 6 + 4 = 16 students.

5 + 1 + 6 + 4 = 16

The whole survey is just the sum of every season's count.

Answer: 16 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (5, 1, 6, 4) and their sum 16 is a believable class size; winter (4) is indeed 4 times summer (1), matching the rule.

Another way: Add the three known seasons first (5 + 1 + 6 = 12), then add winter (4) to get 12 + 4 = 16 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 4 easy answer: 11 students

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $6$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $4$ circles, summer has $1$ circles, and autumn has $3$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times3=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 4, summer 1, autumn 3, and winter blank. The number born in winter is 3 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 4 students, summer = 1 students, autumn = 3 students (read from the graph).
Winter = 3 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 1 circles, so 1 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 3 times summer: 1 x 3 = 3 students born in winter.

1 \times 3 = 3

'3 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 4 + 1 + 3 + 3 = 11 students.

4 + 1 + 3 + 3 = 11

The whole survey is just the sum of every season's count.

Answer: 11 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (4, 1, 3, 3) and their sum 11 is a believable class size; winter (3) is indeed 3 times summer (1), matching the rule.

Another way: Add the three known seasons first (4 + 1 + 3 = 8), then add winter (3) to get 8 + 3 = 11 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 5 medium answer: 14 students

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $6$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $3$ circles, summer has $2$ circles, and autumn has $5$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times2=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 3, summer 2, autumn 5, and winter blank. The number born in winter is 2 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 3 students, summer = 2 students, autumn = 5 students (read from the graph).
Winter = 2 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 2 circles, so 2 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 2 times summer: 2 x 2 = 4 students born in winter.

2 \times 2 = 4

'2 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 3 + 2 + 5 + 4 = 14 students.

3 + 2 + 5 + 4 = 14

The whole survey is just the sum of every season's count.

Answer: 14 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (3, 2, 5, 4) and their sum 14 is a believable class size; winter (4) is indeed 2 times summer (2), matching the rule.

Another way: Add the three known seasons first (3 + 2 + 5 = 10), then add winter (4) to get 10 + 4 = 14 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 6 easy answer: 18 students

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $6$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $5$ circles, summer has $3$ circles, and autumn has $4$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times2=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 5, summer 3, autumn 4, and winter blank. The number born in winter is 2 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 5 students, summer = 3 students, autumn = 4 students (read from the graph).
Winter = 2 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 3 circles, so 3 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 2 times summer: 3 x 2 = 6 students born in winter.

3 \times 2 = 6

'2 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 5 + 3 + 4 + 6 = 18 students.

5 + 3 + 4 + 6 = 18

The whole survey is just the sum of every season's count.

Answer: 18 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (5, 3, 4, 6) and their sum 18 is a believable class size; winter (6) is indeed 2 times summer (3), matching the rule.

Another way: Add the three known seasons first (5 + 3 + 4 = 12), then add winter (6) to get 12 + 6 = 18 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 7 medium answer: 21 students

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $8$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $7$ circles, summer has $3$ circles, and autumn has $5$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times2=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 7, summer 3, autumn 5, and winter blank. The number born in winter is 2 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 7 students, summer = 3 students, autumn = 5 students (read from the graph).
Winter = 2 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 3 circles, so 3 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 2 times summer: 3 x 2 = 6 students born in winter.

3 \times 2 = 6

'2 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 7 + 3 + 5 + 6 = 21 students.

7 + 3 + 5 + 6 = 21

The whole survey is just the sum of every season's count.

Answer: 21 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (7, 3, 5, 6) and their sum 21 is a believable class size; winter (6) is indeed 2 times summer (3), matching the rule.

Another way: Add the three known seasons first (7 + 3 + 5 = 15), then add winter (6) to get 15 + 6 = 21 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 8 hard answer: 22 students

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $8$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $6$ circles, summer has $3$ circles, and autumn has $7$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times2=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 6, summer 3, autumn 7, and winter blank. The number born in winter is 2 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 6 students, summer = 3 students, autumn = 7 students (read from the graph).
Winter = 2 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 3 circles, so 3 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 2 times summer: 3 x 2 = 6 students born in winter.

3 \times 2 = 6

'2 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 6 + 3 + 7 + 6 = 22 students.

6 + 3 + 7 + 6 = 22

The whole survey is just the sum of every season's count.

Answer: 22 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (6, 3, 7, 6) and their sum 22 is a believable class size; winter (6) is indeed 2 times summer (3), matching the rule.

Another way: Add the three known seasons first (6 + 3 + 7 = 16), then add winter (6) to get 16 + 6 = 22 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 9 hard answer: 19 students

A class surveyed which season each student was born in and recorded the results in a picture graph. The number of students born in winter is $5$ times the number born in summer. Find the total number of students surveyed.

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $8$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $8$ circles, summer has $1$ circles, and autumn has $5$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times5=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 8, summer 1, autumn 5, and winter blank. The number born in winter is 5 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 8 students, summer = 1 students, autumn = 5 students (read from the graph).
Winter = 5 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 1 circles, so 1 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 5 times summer: 1 x 5 = 5 students born in winter.

1 \times 5 = 5

'5 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 8 + 1 + 5 + 5 = 19 students.

8 + 1 + 5 + 5 = 19

The whole survey is just the sum of every season's count.

Answer: 19 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (8, 1, 5, 5) and their sum 19 is a believable class size; winter (5) is indeed 5 times summer (1), matching the rule.

Another way: Add the three known seasons first (8 + 1 + 5 = 14), then add winter (5) to get 14 + 5 = 19 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!

Variant 10 hard answer: 18 students

Number of students by season of birth

The vertical axis shows the number of students from $1$ to $8$ , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has $4$ circles, summer has $2$ circles, and autumn has $6$ circles; the winter column is empty.

(1) How many students were born in summer?

(2) (Number of students born in winter) $=\square\times3=\square$ students

(3) (Total students surveyed) $=$ (spring) $+$ (summer) $+$ (autumn) $+$ (winter) $=\square$ students

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by birth season: spring 4, summer 2, autumn 6, and winter blank. The number born in winter is 3 times the number born in summer. I need the total number of students surveyed.

Givens

Spring = 4 students, summer = 2 students, autumn = 6 students (read from the graph).
Winter = 3 times summer.
Winter's column is empty and must be worked out.

Unknowns

The number of students born in winter.
The total number of students surveyed.

Constraints

Each circle stands for 1 student.
The total is the sum of all four seasons.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Solve the knowable pieces in order: read summer, use the multiplying rule to get winter, then add all four seasons for the total. Reading circle counts off the graph supports each step.

3 · Execute3 carry out the plan

1Read summer

#1 Draw a Diagram 3.MD.B.3

The summer column has 2 circles, so 2 students were born in summer.

Counting a column's circles is direct picture-graph reading.

2Find winter

#7 Identify Subproblems 3.OA.A.3

Winter is 3 times summer: 2 x 3 = 6 students born in winter.

2 \times 3 = 6

'3 times' means multiply the summer count -- a Grade 3 multiplication idea.

3Add up the total

#7 Identify Subproblems 3.MD.B.3

Total = spring + summer + autumn + winter = 4 + 2 + 6 + 6 = 18 students.

4 + 2 + 6 + 6 = 18

The whole survey is just the sum of every season's count.

Answer: 18 students

4 · Reviewdoes it hold up?

All season counts are small whole numbers (4, 2, 6, 6) and their sum 18 is a believable class size; winter (6) is indeed 3 times summer (2), matching the rule.

Another way: Add the three known seasons first (4 + 2 + 6 = 12), then add winter (6) to get 12 + 6 = 18 -- same total.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.

💡Takeaway. This only needs Grade 3 multiplying and adding the columns -- solve the knowable parts first!