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.
4
3
In addition to
level 3.0 and
above and
beyond what
was taught in
class, the
student may:
·
Make
connection with
other concepts
in math
·
Make
connection with
other content
areas.
The student will be
able to use
properties of rational
and irrational
numbers to write,
simplify, and
interpret expressions
on contextual
situations.
- justify the sums and
products of rational
and irrational
numbers
-interpret expressions
within the context of
a problem
2
1
0
The student will
With help
Even with
be able to use
from the
help, the
properties of
teacher, the student has
rational and
student has no success
irrational
partial
with real
numbers to
success with
number
write and
real number expressions.
simplify express expressions.
ions based on
contextual
situations.
-identify parts
of an
expression as
related to the
context and to
each part
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 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
• 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
• 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 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
• xA means 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.