Solve graph values step by step from clues
3.MD.B.33.OA.A.3
Generated variants — 10
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (6 + 2 + 5 = 13), then add winter (4) to get 13 + 4 = 17 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (7 + 3 + 5 = 15), then add winter (6) to get 15 + 6 = 21 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (6 + 2 + 4 = 12), then add winter (6) to get 12 + 6 = 18 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (6 + 3 + 7 = 16), then add winter (6) to get 16 + 6 = 22 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (5 + 1 + 6 = 12), then add winter (4) to get 12 + 4 = 16 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (4 + 1 + 3 = 8), then add winter (3) to get 8 + 3 = 11 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (8 + 1 + 5 = 14), then add winter (5) to get 14 + 5 = 19 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (3 + 2 + 5 = 10), then add winter (4) to get 10 + 4 = 14 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (4 + 2 + 6 = 12), then add winter (6) to get 12 + 6 = 18 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.
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 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 to , one student per cell, and the horizontal axis lists the seasons (spring, summer, autumn, winter). The spring column has circles, summer has circles, and autumn has circles; the winter column is empty.
(1) How many students were born in summer?
(2) (Number of students born in winter) students
(3) (Total students surveyed) (spring) (summer) (autumn) (winter) students
Show solution
Understand
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.
- 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.
- The number of students born in winter.
- The total number of students surveyed.
- Each circle stands for 1 student.
- The total is the sum of all four seasons.
Plan
#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.
Execute
Review
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.
Add the three known seasons first (5 + 3 + 4 = 12), then add winter (6) to get 12 + 6 = 18 -- same total.
Standards · min grade 3
3.MD.B.3Draw and interpret scaled picture graphs and bar graphs — Reading season counts from the picture graph and summing them for the total.3.OA.A.3Solve multiplication and division word problems within 100 — Multiplying the summer count to find the winter count.