IM Algebra 1 Supports Unit 2 Lesson 9

IM Algebra 1 Supports Unit 2 Lesson 9

"Same Situation, Different Symbols"

by Miss Copeland

​What are we doing?

Let’s think about the how and why of solving equations, and use those ideas to make problems easier.​

Fill in the Blanks

Fill in the Blanks

​9.2 Fizzy Drinks and Fast Driving

​9.2 Fizzy Drinks and Fast Driving

​9.2 Fizzy Drinks and Fast Driving

Fill in the Blanks

Fill in the Blanks

​9.2 Fizzy Drinks and Fast Driving

​9.2 Fizzy Drinks and Fast Driving

​9.2 Fizzy Drinks and Fast Driving

​9.3 Finding an Error

​Tyler is practicing finding different equivalent equations that match the story. For each of the problems below, he gets one equation right but the other equation wrong. For each one, explain the error, give the correct equivalent equation, and explain your reasoning.

Open Ended

​The yogurt at Sweet Delights costs $0.65 per pound and $0.10 per topping. The total cost of a purchase was $1.70. Let $$p$$   be the weight of the yogurt in pounds and  $$t$$   be the number of toppings bought.

Tyler’s first and correct equation:  $$0.65p+0.10t=1.70$$  

Tyler’s second and incorrect equation:  $$t=\left(1.70-0.65p\right)\cdot0.10$$  

What is the error?

​9.3 Finding an Error - Situation #1

​9.3 Finding an Error - Situation #1

Open Ended

​The perimeter of a rectangle (twice the sum of the length and width) is 13.5 inches. Let $$l$$    be the length of the rectangle and  $$w$$   be the width of the rectangle.

Tyler’s first and correct equation:  $$2\left(l+w\right)=13.5$$  

Tyler’s second and incorrect equation:  $$w=13.5-2l$$  

​What is the error?

​9.3 Finding an Error - Situation #2

​9.3 Finding an Error - Situation #2

Summary​

​Because all these equations describe the same relationship, just in different ways, they are equivalent.

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Equivalent equations can be found by thinking about the situation in different ways, as well as by applying acceptable moves for solving equations, such as adding the same amount to each side or multiplying each side by the same amount.

Open Ended

What are some things that you may have trouble with? If you're not struggling with it, then what did you learn today?