Study Island
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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. |
| |
|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. |
| |
|The stations and additional questions are given. |
| |
|Station 1 |
|The graph shows how much food is needed for a polar bear over a certain number of days. |
|[pic] |
|Interpret the points (0,0) and (1,4) in the context of the situation. |
| |
| |
|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. |
| |
|Bird Exhibits |
|Volunteers |
| |
|6 |
|2 |
| |
|9 |
|3 |
| |
|12 |
|4 |
| |
| |
|Model the relationship shown in the table using an equation. |
| |
|Station 4 |
|The graph shows the height of the zoo’s giraffe over the past 5 years. |
|[pic] |
|Model the relationship shown on the graph with a linear equation. |
| |
| |
|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. |
| |
|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 |
| |
|75 |
|2 |
| |
|94 |
|4 |
| |
| |
| |
| |
|Describe any patterns. Based on the list, predict how many people will enter the zoo 8 hours after 9:00 am. |
| |
|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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