Algebra I | Unit 1 2 3 4 5 6 7
In this unit, your student will analyze constraints on different quantities. For example, the amount you spend on groceries may be limited by your budget. To qualify for a sports team, you may need to practice at least a certain number of hours, or lift at least a certain number of pounds. Here are some ways to write constraints using mathematical notation: w<20. An apartment building only allows dogs that weigh less than 20 pounds. m+g+b=4. A casserole recipe calls for four cups of vegetables. You have mushrooms, green beans, and broccoli. 12.5c+15a=1,000. In order for a concert to be performed, the artists need to be sure of 1,000 in ticket sales. Tickets for children under 18 are 12.50 and tickets for adults are 15.5n + 10d = 150. You need 1.50 in coins for a parking meter. You have a bunch of nickels and dimes in your pocket. For this last situation, we can see that using more dimes to make $1.50 means that we can use fewer nickels, and vice-versa. A graph allows us to see this relationship even more clearly.
Each point on the graph represents a combination of nickels and dimes that totals $1.50. For example, if you use 8 nickels, you will need 11 dimes.
Priya is saving money to go on an overnight school trip. The cost of the trip is 360. She has a job at a convenience store, which pays 9 per hour, and sometimes babysits for a family in her neighborhood, which pays 12 per hour. The equation 9x + 12y = 360 represents all the combinations of hours Priya could work at each job and earn a total of 360. Here is a graph showing those combinations.
IM Algebra 1 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).