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Making Sense of Algebraic Expressions

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. The Candy Shop.

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Making Sense of Algebraic Expressions

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  1. Making Sense of Algebraic Expressions

  2. 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.

  3. The Candy Shop • 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

  4. The Candy Shop • 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)

  5. x + y = 38x + 12y + 1 = 30 • 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

  6. Super Sized Sand • 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.

  7. Super Sized Sand • 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.

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