6.EE.4 Expressions and Equations – Apply and extend previous
understandings of arithmetic to algebraic expressions.
TEACHERS: Terri Pemberton
SUBJECT:6th Grade Math
STANDARD:
 6.EE.4 Identify when two expressions are equivalent.
OBJECTIVE (EXPLICIT):
 Prove whether or not two expressions are equal using models and numbers.
EVIDENCE OF MASTERY (MEASURABLE):
SUB-OBJECTIVES, SWBAT (SEQUENCED FROM BASIC TO COMPLEX):
 I can determine whether two expressions are equivalent by using the same value to
evaluate both expressions.
KEY VOCABULARY:
MATERIALS:
Equivalent expressions
20 - Color tiles (represent variable terms)
20 - Color chips (constant)
White boards & markers
Equivalent Expressions handout with
answer key
http://www.graniteschools.org/depart/teachi
nglearning/curriculuminstruction/math/elem
entarymathematics/K6%20Support%20Doc
uments/6th%20Grade%20Support/Equivale
nt%20Expressions.pdf
BEFORE
ENGAGE (MAKE CONTENT AND LEARNING RELEVANT TO REAL LIFE AND CONNECT TO
STUDENT INTEREST) If two things are the same, do they always look the same?
TEACHER WILL:
 Ask students if the expressions 3y +
4 and y+y+y + 4 are equal? Explain
their answer and reasoning.
 Ask students to prove their answer
by plugging in a value for the
variable.
 Tell students that they are going to
be proving whether or not two
expressions are equal using tiles
and chips and then coming up with
a “short-cut” for proving
equivalency.
STUDENT WILL:
 Think-Pair-Share with their shoulder
partner whether or not they think the
two expressions are equal. Be able
to explain their answer.
 Using their whiteboards, pick a
value for the variable and prove
whether or not they were correct in
their reasoning.
DURING
AFTER
TEACHER WILL:
STUDENT WILL:
 Distribute tiles and chips to each pair
 Follow along with the teacher as the
of students and the equivalent
tiles and chips are being set up for
expressions handout.
each expression.
 Model using chips and tiles to set up
 Replace each of the tiles with 2
the expressions 3y + 4 and y+y+y +
chips each for both expressions.
4.(see model)
 Count chips for both expressions
and determine if they have the same
 Tell students to let y = 2 and replace
each tile with 2 chips.
number of chips for each expression.
 Count the chips on both sides. Ask
 Follow along and set up the second
student if they have an equal
example.
number of chips on either side.
 Replace tiles with chips as directed.
 Set up another example this time
 Count chips to see if expressions are
using exponents: 5𝑥 3 + 2 and 5x +
equal.
5x + 5x + 2. Remind students that a
 Complete Equivalent Expressions
number raised to a power means to
worksheet by first using tiles ands
multiply. Tell students that x = 2.
and chips to prove it, then using
(see model)
numbers to complete the worksheet.
 Distribute Equivalent Expressions
 Be able to explain how they were
handout (linked) and instruct
able to solve each expression
students to use tiles and chips to
numerically.
prove equivalency, then, use
numbers to complete the worksheet.
 Bring students back together and
discuss answers found on the
worksheet. Ask them how they were
able to solve each expression using
numbers after proving equivalency?
Guide them into discovering that if
you substitute and use order of
operations that you should be able to
solve both expressions numerically.
TEACHER WILL:
 Ask students to work in pairs on the
engage problem.
 Tell students that their homework is
to pick two problems from the
Equivalent Expression worksheet
that were FALSE and change one of
the expressions so that they are
equal expressions. Write 3 to 4
sentences for each problem
explaining how they were able to
STUDENT WILL:
 Work in pairs on the engage problem
to come up with things that are the
same but may not look the same.
 Pick two problems from the
Equivalent Expression worksheet
that were FALSE and change one of
the expressions so that they are
equal expressions. Write 3 to 4
sentences for each problem
explaining how they were able to
change one of the expressions.
Then, use pictures to prove
equivalency.
change one of the expressions.
Then, use pictures to prove
equivalency.
Example without chips and tiles:
5𝒙𝟑 + 2
5 * 2 * 2 * 2 +2
40 + 2 = 42
5x + 5x + 5x + 2
5*2+5*2+5*2+2
10+10+10+2 = 32
when x = 2