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|Math Topic: Proportional Relationships |Grade Level: 7 |

|Standard: 7.RP.A.2.A, 7.RP.A.2.C, 7.RP.A.2.D |Task Depth of Knowledge: 3 |

|Activity Duration: 2 class periods |Audience: small group/whole class |

|Resources Needed: board, space for stations, graph paper (optional), writing utensils, paper |

|Primary Mathematical Practice Target: |

|Math Practice Standard 3 |

|Construct viable arguments and critique the reasoning of others. |

|Secondary Mathematical Practice Target(s): |

|Math Practice Standard 2 – Reason abstractly and quantitatively. |

|Task Description |

|In this activity, students are presented with various situations in a single context and asked to determine whether the situation represents a|

|proportional relationship and to identify the constant of proportionality. Students are provided a variety of representations, including |

|tables, graphs, verbal descriptions, lists, and equations. Students must explain their reasoning and justify their conclusions. Students |

|critique and review one another’s work. Students present their findings to the class using ratio language. This task may be used as an |

|introduction or a culmination to displaying proportional relationships in a variety of representations. |

|Task Timeline |

|Day 1: Introduction (5 min): Teacher introduces situations, and presents the questions that need to be answered at each station. |

|Day 1: Small group work (35-40 min): Students go station-to-station answering questions on their own paper. |

|Day 2: Small group discussion (15 min): Students plan to share responses, how they reached their answers, and create summary statements about |

|an assigned station. |

|Day 2: Small group presentations (30-35 min): Each group presents. Optional – the board can be used for students who want to display |

|equations, graphs, tables, etc. Groups that reached a different conclusion should share and explain why their conclusion is different. |

| Task Procedures |

|In small groups, students will go to 6 stations to answer questions. Present the context that the students are volunteers at the zoo. |

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|At each station, students will answer the following: |

|Is the situation describing a proportional relationship? If so, identify the constant of proportionality. If not, explain why. |

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|The stations and additional questions are given. |

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|Station 1 |

|The graph shows how much food is needed for a polar bear over a certain number of days. |

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|Interpret the points (0,0) and (1,4) in the context of the situation. |

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|Station 2 |

|At the petting zoo, 5 goats and 8 sheep are let out to interact with kids. The next day, 6 goats and 9 sheep are let out. The third day , 7 |

|goats and 10 sheep are let out. |

|Create a 1st quadrant graph, and plot the coordinate pairs described, where x represents the number of goats and y represents the number of |

|sheep. |

| |

|Station 3 |

|The table below shows the number of bird exhibits and the number of volunteers at the Bird Sanctuary. |

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|Bird Exhibits |

|Volunteers |

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|6 |

|2 |

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|9 |

|3 |

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|12 |

|4 |

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|Model the relationship shown in the table using an equation. |

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|Station 4 |

|The graph shows the height of the zoo’s giraffe over the past 5 years. |

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|Model the relationship shown on the graph with a linear equation. |

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|Station 5 |

|The cost per entrance ticket to the zoo can be modeled by the following equation, where c represents the total cost and n represents the |

|number of tickets bought. |

|c = 16n |

|Interpret and summarize the equation in context by finding the unit rate. Then, solve the equation for 15 tickets and for a total cost of |

|$128. |

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|Station 6 |

|The list below shows how many people were entering the zoo per hour on a Saturday morning. |

|People |

|Hours after 9:00 am |

| |

|55 |

|0 |

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|75 |

|2 |

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|94 |

|4 |

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|Describe any patterns. Based on the list, predict how many people will enter the zoo 8 hours after 9:00 am. |

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|The teacher will assign each group one station. For that station, each group will share with the class how they reached their answers and |

|provide a statement that justifies whether the situation is proportional or not. |

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