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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. The Candy Shop.

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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
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

the candy shop1
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)
x y 3 8x 12y 1 30
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
super sized sand
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.
super sized sand1
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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