Linear Equations and Inequalities 7.EE.4b  Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

Think Pair Share 3 + p > 7 3 + p > 7 3 + p < 7 3 + p < 7 Explain the difference between these symbols. How does it change the meaning of each mathematical statement? 3 + p > 7 3 + p > 7 3 + p < 7 3 + p < 7 3 + p = 7

Scenario Grant is trying to make money to help pay for college by taking a job with Brian’s Bike Taxis of Baltimore. He has an agreement with Brian that he will rent the bike for $35.00 a night. He charges $3.75 for every mile he is transporting people.

Task Work with your group to determine how many miles he needs to ride with customers in order to make a profit. You will have 15 min. Each group member must record all problem-solving strategies in the class work section of their notebook. Record ALL attempts that your group explored; please don’t erase any even if they turn out to be wrong. As a group, choose one strategy that you used to solve the problem and post it on chart paper to share with the class.

GALLERY WALK You will have the opportunity to view all of the different ways that your classmates have solved the problem. It is your job to comment on their work. You need to make one accolade. They may have thought of something you did not, they may have explained something really clearly, or some other positive thing you noticed. You also need to make a suggestion of one thing the group might want to consider. Maybe something is not very clear or you thought of something that they could add that would strengthen the explanation of their strategy.

Time For Adjustments Read through all of the accolades and suggestions. Make any changes or additions that you think are appropriate. Re-Post your work for all to see.

Share Out You have 2-3 min to explain your strategy and the suggestions that others made for your group.

Summarize Which strategies did you like? Which would you choose to use in the future? Why? Which strategy makes the most sense to you?

Consider the Context Is it possible for Grant to make exactly 16 dollars? Why or why not? Use whatever strategy you would like to solve this problem.

Share Your Understanding Now that you have had some time to consider the context, share your understanding with your group.

Enough with the Hotdogs A car rental agency charges Shae’s family $25.00 plus $0.10 per mile that the car is driven. Shae wants to spend less than $35.00 on the car rental. How many miles can she drive the rental car?

Exit Ticket If Grant made $15 profit, how many miles did he ride? How would your equation change if I said Grant needed to make at least $15 a day, how many miles would he need to ride?

Day 3 Objective Students will use the graphing calculator to graph linear functions in order to determine how much money Grant will make transporting people around Baltimore.

Warm-up Pete was completing a science project about the life-cycle. In 6th grade he was 51 inches and grows 2 inches each year. How tall will he be by the time he graduates high school? Write an equation that represents his growth. x represents his grade. y represents his height in 12th grade. Graph your findings

Yesterday We determined that the linear equation for the money Grant makes transporting people was y = 3.75x – 35 Use the table we created yesterday to graph his data.

Interpreting our Graph In your groups answer the following questions: What do you notice about the shape of the graph? At what point does the line intersect the x-axis? At what point does the line intersect the y-axis? What do these intersections represent?

Closure Identify the x- and y-intercepts of Pete’s growth from 6th grade to his graduation (warm-up)