Name: Date: Algebra I - Unit 3, Lesson 4: Writing and Graphing Inequalities to Represent Constraints

Transcription

1 Name: Date: Algebra I - Unit 3, Lesson 4: Writing and Graphing Inequalities to Represent Constraints Agenda: Math Minute 48 (5 min, including checking and tracking work) Put away any graded work Review from Thursday Intro to Pampering and Feeding Time & Instructions Review Expectations Work on Task Discussion of Work & Notes Exit Ticket Closing & LNT Year/Unit LTs: I model real world and math situations with systems of linear equations or inequalities. I make my thinking visible. Daily LTs: I can write inequalities in two variables based on a real world problem. I can graph inequalities in two variables and show the solution. I maintain an organized binder and complete classroom tasks. Review from Thursday Fill this in from Thursday s Work Write down one of the inequalities created using Carlos method: Write down one of the inequalities created using Clarita s method: THE SCENARIO: Pampering and Feeding Time We are continuing our work with the pet sitters, Carlos and Clarita. We will add in some further constraints today. Carlos and Clarita have been worried about space and start-up costs for their pet sitters business, but realize they also have a limit on the amount of time they have for taking care of the animals they board. To keep thingsfair, they have agreed on the following time constraints. Feeding time: Carlos and Clarita estimate that cats will require 6 minutes each twice a day morning and evening to feed them and to clean their litter boxes, for a total of 12 minutes per day for each cat. Dogs will require 10 minutes twice a day to feed and walk, for a total of 20 minutes per day for each dog. Carlos can spend up to 8 hours each day for the morning and evening feedings, but needs the middle of the day off for baseball practice and games. Pampering Time: The twins plan to spend 16 minutes each day brushing and petting each cat, and 20 minutes each day bathing or playing with each dog. Clarita needs time off in the morning for swim team and evening for her art class, but she can spend up to 8 hours during the middle of the day to pamper and play with the pets. YOUR WORK Write inequalities for each of these additional time constraints. Plot and shade the solution set for each constraint on separate coordinate grids. Be sure to title each graph, label axes, and label the inequality graphed. Hint: make sure that your data is in the same units. 1

2 Feeding Time: Method chosen: Work shown to create inequality: Feeding Time Inequality: 2

3 Feeding time boundary equation: Feeding time boundary equation table: Dogs Cats On your graph of the feeding time inequality, how did you determine which half plane to shade in? 3

4 Feeding Time Inequality Graph 4

5 Pampering Time Method chosen: Work shown to create inequality: Pampering Time Inequality: 5

6 Pampering time boundary equation: Pampering time boundary equation table: Dogs Cats On your graph of the pampering time inequality, how did you determine which half plane to shade in? 6

7 Pampering Time Inequality Graph 7

8 DISCUSSION/NOTES Half planes extend in the non-bounded directions indefinitely. Could we have negative values satisfy the inequalities (not the real-world scenarios) we wrote today? Why or why not? Could we have negative values satisfy the real-world scenarios we worked on today? Why or why not? EXIT TICKET On loose leaf, write the following: Your name Algebra I Your Section (8A or 8B) The date The question: create a series of steps that another student could follow to write and graph an inequality in two variables. The answer to the above question 8