Expressions and Equations – Apply and extend previous understandings
of arithmetic to algebraic expressions.
TEACHERS: Terri Pemberton
SUBJECT: 6th Grade Math
STANDARD:
 6.EE.2.c – Evaluate expressions at specific values for their variables.
OBJECTIVE (EXPLICIT):
 Solve expressions for a given value of a variable including those used in formulas.
EVIDENCE OF MASTERY (MEASURABLE):
SUB-OBJECTIVES, SWBAT (SEQUENCED FROM BASIC TO COMPLEX):
 Evaluate an algebraic expression for a given value.
 Substitute values in formulas (perimeter and area) to solve real-world problems.
KEY VOCABULARY:
Substitute
Evaluate
Order of operations
MATERIALS:
20 - Color tiles (represent variable terms)
30 - Color chips (units)
White boards & markers
BEFORE
ENGAGE (MAKE CONTENT AND LEARNING RELEVANT TO REAL LIFE AND CONNECT TO
STUDENT INTEREST) It takes 4 minutes for the cook to create a burger at Bob’s Burger Barn
once it is ordered. If 5 people have placed their order before Tommy, how long will it take Tommy
to get his burger?
TEACHER WILL:
STUDENT WILL:
1. Ask students to create an
1. Create an expression for the cost of x
expression that would find the cost
number of sundaes at $3 each with
of sundaes for x number of people
shoulder partner.
if the sundaes cost $3.
2. Share their expression with the class.
2. Ask students to share their
3. Using a white board, substitute the
expressions and write them on the
given values for the variable to
board.
determine the cost depending on the
3. Ask students to “substitute”
number of people ordering sundaes.
different values for the variable to
4. Brainstorm other uses for expressions
determine the total cost of sundaes
where simply substituting a value can
depending on the number of people
change the answer.
ordering them.
4. Ask students to brainstorm other
uses for expressions where simply
substituting a value can change the
answer (guide them towards finding
perimeter and area).
DURING
TEACHER WILL:
STUDENT WILL:
1. Distribute bags of color tiles and
1. Separate tiles and chips.
chips and remind students that the
2. Follow along with teacher to create a
tiles represent terms with a variable
visual representation of “3x” using
and the chips represent units.
chips and tiles.
2. Model how “3 times a number x”
3. Use tiles and chips to create a model.
would look using tiles and chips.
4. Count the chips to find the solution.
(Place 3 tiles under document
5. Use chips and tiles to solve additional
camera)
examples then write the expression
3. Tell students that we are going to
and its solution on a sheet of paper.
substitute 4 for x so that we can
6. With shoulder partner, identify what
evaluate the expression. (Replace
the variables represent in the
each of the 3 tiles with 4 chips
perimeter and area.
each.)
7. With shoulder partner, find the
4. Count the tiles.
perimeter and area of the square
5. Guide additional examples for
drawn on the board. Be able to
evaluating each expression using
explain how substitution was used in
order of operations (see attached
each expression to evaluate each
for sample):
formula. Discuss a real world
o 15 + x for x = 6.
example for how finding the perimeter
o 2f – 3 for f = 5.
and area of a shape could be useful.
o 24 ÷ b for b = 3 (guide
8. Use pictures and numbers to
students to separate 24 into
complete additional practice
groups of 3)
worksheet.
o 7x for x = 3
9. Discuss the importance of the
6. Review the perimeter and area
expression or formula in regards to
formulas for rectangles and
the value being substituted for the
squares and ask students what the
variable.
variables represent. (P = s+s+s+s
or 4s; A = lw or 𝑠 2 )
7. Draw a square. Tell them that one
side is 5 feet long and ask them to
use the formulas to find perimeter
and area. Ask students to come up
with a real world example for how
finding the perimeter and area of a
shape could be useful.
8. Hand out worksheets with
additional practice (attached)
9. Bring students back together and
guide them to discover that as the
number being substituted into an
expression or a formula changes so
does the answer, but the
expression or formula does not.
AFTER
TEACHER WILL:
STUDENT WILL:
 Ask students the engage question
 With your shoulder partner, discuss
from above. With shoulder partner
the answer to the engage question.
discuss an answer. How would
your time differ if there were 3
 Discuss how the time will differ
people ahead of you? 6? 7?
depending on the number of people
 Ask students to write a real-word
ahead of you.
problem using a coefficient,
operation and variable. Then, pick
 Create an expression for a real world
a value for the variable to prove
situation. Write a journal entry
their algebraic expression works.
explaining how you use substitution to
 Additional practice problems:
evaluate your expression for a variety
https://www.georgiastandards.org/C
of values of your variable.
ommonCore/Common%20Core%20Frame
works/CCGPS_Math_6_6thGrade_
Unit3SE.pdf pgs. 14-17
Examples for student work that can be put in notebook or on a blank piece of paper:
Expression: 15 + x for x = 6 Expression: 2f – 3 for f = 5
Picture:
Picture:
OOOOOOOOOOOOOOO
- OOO
+
OOOOOO = 21
OOOOO OOOOO – OOO = 7
Solution: 15 + 6 = 21
Solution: 2(5) – 3 = 7
Name ______________________________________ Block_____ Date_________ ____
(Practice Worksheet 6.EE.2.c)
Directions: Solve each expression for the given variable. Use pictures and numbers for
each problem.
1. 8x – 4; when x = 4
Picture:
Numbers:
2. (7 + c) ÷ 4; when c = 5
Picture:
Numbers:
3. 8b – (b + 4); when b = 4
Picture:
Numbers:
4. 𝑥 2 + 3y - (z + 4); when x = 2, y = 4, and z = 6.
Pictures:
Numbers:
Answer the following questions keeping in mind the perimeter and area formulas.
5. The length of a rectangle is 5 feet and the width is 3 feet. Draw and label the
rectangle, then find the perimeter and area. Make sure you label your answers.
Picture:
Perimeter:
Area:
6. The area of square is 3 square inches. Draw and label a picture of the square. Then,
find the perimeter of the square.
Picture:
Perimeter:
7. Find the area and perimeter for the given rectangle.
5 in.
5 in.
Perimeter:
8 in.
8. Explain how you were able to find the perimeter and area for #7.
Area: