Semester 2

Warm Up 3. −2 𝑥+9 =−10 1. 5𝑥=20 𝑥=4 𝑥=−4 2. 12+ 𝑥 2 =15 3. −2 𝑥+9 =−10 1. 5𝑥=20 𝑥=4 𝑥=−4 2. 12+ 𝑥 2 =15 4. 6 𝑥−4 =−3𝑥−6 𝑥=6 𝑥=2

How can we create equations to solve problems? Objective: SWBAT solve multi-step equations. 2.4.d.ii DOL: Given 3MC and 1 CR question, SW solve multi-step equations with 100% accuracy. Essential Question How can we create equations to solve problems? Why? We’re starting the semester with systems of equations, where we’ll need to use multiple equations to each problem.

Teacher Note The following CLT and DP slides are review slides that should be skippable by most classes. They’re here just in case any class is struggling a great deal. In groups on whiteboards, have students identify all like terms associated with a different variable, then check each other. Extension: Have students try combining like terms.

Combining Like Terms Variable: A symbol for a number we don’t know yet Coefficient: A number multiplied by a variable Like terms: Terms with the same variables and powers I used the variable ___. ____ is like terms with ____ because… In groups on whiteboards, have students identify all like terms associated with a different variable, then check each other. Extension: Have students try combining like terms.

Combining Like Terms 𝑝: 7𝑝+𝑝+12𝑝+10𝑝=30𝑝 𝑑: 2𝑑+8𝑑−5𝑑=5𝑑 Variable: A symbol for a number we don’t know yet Coefficient: A number multiplied by a variable Like terms: Terms with the same variables and powers 𝑝: 7𝑝+𝑝+12𝑝+10𝑝=30𝑝 𝑑: 2𝑑+8𝑑−5𝑑=5𝑑 𝑤: 2𝑤+4𝑤+3𝑤−13𝑤=−4𝑤 𝑡: 4𝑡=4𝑡 When we combine all like terms with the variable ______, we get _____ Students combine the same variables they have. When they’re done, they stand and find a partner from another group to check with.

Combining Like Terms We can simplify expressions by combining like terms Examples: 2𝑞+3𝑞=5𝑞 −6𝑘−3𝑘=−9𝑘 7+4𝑝−3𝑝=7+𝑝 14+5𝑥−15=5𝑥−1 1+𝑔−4𝑔+12=13−3𝑔 What’s the rule for combining like terms? Show you know: 5𝑡+8𝑡+3= Think-Share-Write

Combining Like Terms We can simplify expressions by combining like terms Examples: 2𝑞+3𝑞=5𝑞 −6𝑘−3𝑘=−9𝑘 7+4𝑝−3𝑝=7+𝑝 14+5𝑥−15=5𝑥−1 1+𝑔−4𝑔+12=13−3𝑔 To combine like terms, add or subtract the coefficients 𝟓𝒕+𝟖𝒕+𝟑=𝟏𝟑𝒕+𝟑 Think-Share-Write

Whiteboard check Heating Up 4𝑞+2𝑞 6𝑞 −5𝑑+3−2 −5𝑑+1 11𝑛+8𝑛−3𝑑+7𝑛−𝑑 26𝑛−4𝑑 On Fire −4𝑞+2𝑞+3 −2𝑞+3 5𝑘−8ℎ+4+2ℎ−11 5𝑘−6ℎ−7 −18−𝑏+ 𝑏 2 −4𝑏+21 𝑏 2 −5𝑏+3 Opt-in split by proficiency

Distributive Property We can simplify expressions by using the distributive property Examples: 2 𝑞+3 =2𝑞+6 6 𝑘−3 =6𝑘−18 7 −3𝑝−4 =−21𝑝−28 What’s the rule for distribution? Show you know: 3(2𝑡−4)= Think-Share-Write

Distributive Property We can simplify expressions by using the distributive property Examples: 2 𝑞+3 =2𝑞+6 6 𝑘−3 =6𝑘−18 7 −3𝑝−4 =−21𝑝−28 What’s the rule for distribution? Show you know: 3 2𝑡−4 =6𝑡−12 Think-Share-Write

We Do 4(2𝑥+4) 8𝑥+16 −5(𝑑+3) −5𝑑−15 8𝑛−10 2 4𝑛−5 Opt-in split by proficiency

Whiteboard check Heating Up 4(2𝑡+4) 8𝑡+16 −5(3𝑑+4) −15𝑑−20 On Fire −(2𝑞−7) −2𝑞+7 (−4𝑘+8) −2 2𝑘−4 We could replace this with a Quiz-Quiz-Trade

Independent Work On Fire Heating Up −4𝑞−2 3𝑞+3 =−26 4𝑞+2 𝑞−4 =16 𝑞=2 𝑞=4 −4 2𝑑+10 =−2𝑑−4 𝑑=−6 11𝑛−8 𝑛−2 =7+𝑛−𝑛 𝑛=−3 On Fire −4𝑞−2 3𝑞+3 =−26 𝑞=2 9𝑑−12 −3 =28−11𝑑 𝑑=3 − 12𝑛−6 6 +4 2−4𝑛 =−6𝑛+57 𝑛=−4 Opt-in split by proficiency Answers are shown intentionally. The goal is for students to verify they can reach the correct answer.

Independent Work If you feel comfortable with a section, skip ahead to the next one Answers are shown intentionally. The goal is for students to verify they can reach the correct answer.

Beating the Competition About 4.9 million households had computer Brand A. The use of Brand A grew at an average rate of 0.275 million households a year. In 2001, about 2.5 million households used Brand B computers. The use of Brand B computers grew at an average rate of 0.7 million households a year. How long will it take for the two types of computer to be in the same number of households? What year is this?

Beating the Competition About 4.9 million households had computer Brand A. The use of Brand A grew at an average rate of 0.275 million households a year. In 2001, about 2.5 million households used Brand B computers. The use of Brand B computers grew at an average rate of 0.7 million households a year. How long will it take for the two types of computer to be in the same number of households? What year is this? 4.9 + 0.275y = 2.5 + 0.7y Y = 5.6 years This will happen in the year 2006

Dishing It Up Moe Tell starts washing dishes at the Greasy Spoon Café. Fifteen minutes later Fran Tick joins Moe, and both wash until all the dishes are done. Moe washes 9 dishes per minute and Fran washes 16 dishes per minute. Together, they need to wash 760 dishes. Write an equation that can represent the total number of dishes washed.

Dishing It Up Moe Tell starts washing dishes at the Greasy Spoon Café. Fifteen minutes later Fran Tick joins Moe, and both wash until all the dishes are done. Moe washes 9 dishes per minute and Fran washes 16 dishes per minute. Together, they need to wash 760 dishes. Moe: 9 dishes per minute 9𝑚 Fran: 16 dishes per minute, but only after 15 minutes 16 𝑚−15 Final equation: 9𝑚+16 𝑚−15 =760

Plumbing Out Nick O’Time, the plumber, charges $30 per hour. His brother Ivan, the plumber’s helper, charges $20 per hour. Nick starts working on a job. Four hours later Ivan joins him and both work until the job is finished. They want to earn at least $470. Write an inequality to represent how much they make based on how many hours they work.

Plumbing Out Nick O’Time, the plumber, charges $30 per hour. His brother Ivan, the plumber’s helper, charges $20 per hour. Nick starts working on a job. Four hours later Ivan joins him and both work until the job is finished. They want to earn at least $470. Nick: $30 per hour 30ℎ Ivan: $20 per hour, but starts 4 hours later 20 ℎ−4 Final equation: 30ℎ+20(ℎ−4)≥470

On the Run A cougar spots a fawn 132 meters away. The cougar starts toward the fawn at a speed of 18 meters per second. At the same instant the fawn starts running away at 11 meters per second. Write an equation to determine how long it will take for the cougar to catch the fawn.

The cougar closes in at 7 meters per second. On the Run A cougar spots a fawn 133 meters away. The cougar starts toward the fawn at a speed of 18 meters per second. At the same instant the fawn starts running away at 11 meters per second. Cougar: 18𝑠 Fawn: 11𝑠 Final equation: 18𝑠−11𝑠=133 7𝑠=133 𝑠=19 The cougar closes in at 7 meters per second. The cougar catches the fawn after 19 seconds…if it can hold that speed.

DOL

DOL