Do Now Use the information in the table to determine whether the rule works for the given input-output pair. Write “Yes” if the rule works for the input-output pair and “No” if it does not. Write the rule that works for all pairs. Students will be able to create and solve equations involving real world problems. Common Core Learning Standard: A-REI-3 It is recommended that packets of the PowerPoint slides be printed and handed out for students to follow along with and to complete the given problems. A maximum of 3 slides per page is suggested.

Modeling Using Equations Let’s practice looking for a pattern and describing it in words. Believe it or not, there is a relationship between input and output in the tables below. Write an input-output rule in words to describe each relationship. Input Output apple e egg g hour r and d eight t Input Output sing 16 chair 25 is 4 a 1 revolve 49 Ask student volunteers to explain their reasoning behind their verbal representation.

Let’s look for more rules!!! Find a rule for each input-output table. State your rule in two different ways: (1) as a sentence; and (2) as an equation. x Process y -0.5 7.5 8 0.5 8.5 1 9 1.5 9.5 x Process y 7 3 4 5 2 -5 12 -1 8 Ask student volunteers to show and explain their process and rule representations.

Link to the Real World Rule: How can you use your rule to Mia is ordering CDs from an online store. Each CD costs $5, and the shipping fee is $10, no matter how many CDs she orders. For example, if she orders 3 CDs, then the payment will be $25. Find four more possibilities for the number of CDs ordered. Fill in the table below. Then write a rule relating the number of CDs ordered, C, to the payment amount, P. C Process P 3 25 Rule: Ask student volunteers to show and explain their process and rule representations. How can you use your rule to determine how much it will cost if Mia orders 25 CDs?

Now You Try!! Romero and his brother Nelson love to play video games. Right now, Romero’s score is 11 less than 2 times Nelson’s score. For example, if Nelson has 80 points, than Romero has 149 points. Find four more possibilities for the brothers’ scores and fill in the table below. Then write a rule relating Romero’s score, R, to Nelson’s score, N. N Process R 80 149 Rule: How many points will Romero have if Nelson has 5072 points? Ask student volunteers to show and explain their process and rule representations. Explain how you used your rule to find Romero’s score.

Now You Try!! Wes mows lawns in the summer. He charges the same fixed amount for each lawn that he mows. As of today, he has earned $36 after mowing 3 lawns. Create an input-output table using the headings “Number of lawns mowed” for the input and “Amount of money in dollars” for the output. Fill in the appropriate values for Wes’ situation. Then fill in several other rows of information that fit the situation. For example, what if he mows 8 lawns? Use any patterns you see in your input-output table to find a rule relating the number of lawns mowed and the amount of money in dollars. Have students work on this problem in pairs. Ask different pairs to volunteer to show and explain their process and rule representations. Compare similarities/differences. c. Explain how you know that your rule works. d. Wes wants to go to a 2-day music festival. Tickets for the festival cost $190. How many lawns will Wes need to mow this summer to earn enough money to buy a ticket? Show how you got your answer.

More Modeling Using Equations Before looking at more situations where we can use equations to find solutions, let’s review some helpful guidelines: Be sure to read carefully. Define your variable(s) according to the situation. Set-up an equation. Solve.

Let’s try one together. x + x + 1 = 45 2x + 1 = 45 - 1 - 1 2x = 44 2 2 Find two consecutive integers whose sum is 45. Let x = the first number 1. Read carefully. Let x + 1 = the second number 2. Define the variables. x + x + 1 = 45 3. Set up equation. 2x + 1 = 45 4. Solve. - 1 - 1 Use a Think Aloud strategy while reviewing this slide. 2x = 44 2 2 x = 22 The first number is 22, and the second number is 23. x + 1 = 23

Now you try! Find three consecutive integers whose sum is – 147. Have students work on this problem in pairs. Ask different pairs to volunteer to show and explain their process and rule representations. Compare similarities/differences.

Let’s try another one together. In the championship game, Chris scored 5 points less than Dwayne, and LeBron scored 1 point more than twice as many as Dwayne. If LeBron scored 20 points more than Chris, how many points were scored by each player? Let: Dwayne = x Chris = x – 5 LeBron = 2x + 1 2x + 1 = x – 5 + 20 2x + 1 = x + 15 - x - x x + 1 = 15 - 1 - 1 Use a Think Aloud strategy while reviewing this slide. In the championship game, Dwayne scored 14 points, Chris scored 9 points, and LeBron scored 29 points. x = 14 x – 5 = 9 2x + 1 = 29

Now you try! The second of three numbers is 8 more than the first, and the third number is 3 less than 3 times the first. If the third number is 15 more than the second, find the three numbers. Have students work on this problem in pairs. Ask different pairs to volunteer to show and explain their process and rule representations. Compare similarities/differences.