Practice · Solve graph values step by step from clues · Sensim Math

Variant 1 easy

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

Your answer

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

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

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 $4$ 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

Your answer

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

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

Your answer

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

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

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

Your answer

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

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 $3$ 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

Your answer

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

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 $5$ 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

Your answer

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

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 $8$ , 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

Your answer

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

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 $8$ , 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

Your answer

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

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

Your answer

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

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

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

Your answer

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!

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

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