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Making Sense of Algebraic ExpressionsPowerPoint Presentation

Making Sense of Algebraic Expressions

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Making Sense of Algebraic Expressions

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Making Sense of Algebraic Expressions

Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1):

The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions based on contextual situations.

- A candy shop sells a box of chocolates for $30.
- It has $29 worth of chocolates plus $1 for the box.
- The box includes two kinds of candy: caramels and truffles.
- Lisa knows how much the different types of candies cost per pound and how many pounds are in a box.

https://www.illustrativemathematics.org/illustrations/389

- Lisa states:
- “If x is the number of pounds of caramels included in the box and y is the number of pounds of truffles in the box, then I can write the following equations based on what I know about one of these boxes:
- x + y = 3
- 8x + 12y + 1 = 30

- Based off of her equations, how many pounds of candy are in the box?
- 3 (x pounds of caramels and y pounds of truffles)

- What is the price per pound of the caramels?
- $8 (8 is the coefficient of x)

- What does the term 12y in the second equation represent?
- $12 per pound for truffles

- What does 8x + 12y + 1 in the second equation represent?
- This represents the total value of the box of chocolates: the value of caramels added to the value of the truffles added to the fixed cost of $1

- A company uses two different sized trucks to deliver sand.
- The first truck can transport x cubic yards.
- The second truck can transport y cubic yards.
- The first truck makes A trips to a job site.
- The second truck makes B trips to a job site.

- What do the following expressions represent in practical terms?
- A + B
- The number of trips both trucks make to the job site.

- x + y
- The amount of sand, in cubic yards, both trucks can transport together.

- xA + yB
- xAmeans the amount of sand in the first truck times the number of trips that truck makes.
- yB means the amount of sand in the second truck times the number of trips that truck makes.
- When you put them together, it is the amount of sand both trucks can deliver to the job site.