Students will simplify algebraic expressions using properties
Main Curriculum Tie:
Mathematics - Pre-Algebra
Standard 3 Objective 2
Evaluate, simplify, and solve algebraic expressions, equations, and inequalities.
Background For Teachers:
Enduring Understanding (Big Ideas):
The order of operations and properties
help us simplifying expressions
- How do you know when an algebraic expression
is in simplest form?
Simplify algebraic expressions
Order of operations, commutative property,
associative property, identity property, distributive
property, like terms, algebraic expression, simplify
Ways to Gain/Maintain Attention (Primacy):
Contest, predicting, music, technology,
stories, analogy, manipulative, writing, movement, cooperative discussion, journaling
Starter: Accessing prior knowledge
- Which of these representations does not tell us to multiply?
- 6 • 7
- 8 x 10
- Use Mental Math to compute. (hint: use properties to make it easier)
- 3 + (17 + 138)
- 1( ½ + 4 + ½ )
- 5 x 26 x 2
- 2(13) + 2(7)
- 5(3 + 10)
- 231 • 8 • 0
- Compute using the correct order for operations:
3 + 5²[9 – 3(-1 + 4)]
When correcting number 2 and 3 on the starter, have students explain their thinking.
As they do, review the commutative, associative, identity, 0, and distributive
properties. Have them get out and review their properties foldable from
September, Lesson 7. Sing the Properties Song (attached) to review.
Lesson Segment 1: How do the order of operations and properties help me
simplify algebraic expressions?
In our language we often simplify expressions. For example, we could say, “Hi there.
How are you doing? Or, we could say, “Hey, Sup?” The meaning is the same, but the
second expression is much shorter and simpler than the original expression.
In mathematics we want to write expressions as simply as possible, but do not want to
change their meaning or value. We want the simplified expression to be equivalent to
the original, longer expression.
When we say “simplify the expression” we mean to make the expression more simple
to understand or look at without changing the value of the expression. In the problems
for # 2 on the starter you used the properties to simplify the expressions. In problem
# 3, you used the order of operations to simplify the expression.
As you ask the following questions to mobilize student knowledge from past lessons,
have student record the problems on Smart Pals or on a paper.
Q. When we say two expressions are equivalent what does that mean? For example
when we say 3 + 1 is equivalent to 4 (or 3 + 1 = 4), what does that mean?
The equal sign tells us one expression is equivalent to the other or in other words, the
expressions have the same value.
Q. If two expressions are equivalent, must they always look exactly the same? What
makes you think so?
Show examples: 2 + 6 = 6 + 2, 3(2 • 5) = (3 • 2)5, 3(5 + 6) = 3 • 5 + 3 • 6
Q. How can we know whether two expressions are equivalent if they don’t look alike?
One way to verify that two expressions are equivalent, is to simplify each expression.
Example 1: 2 + 6 = 6 + 2
2 + 6 simplified is 8
6 + 2 simplified is 8
8 = 8.
So, 2 + 6 = 6 + 2
Example 2: 3(2 • 5) = (3 • 2)5
3(2 • 5) is 3(10) =30
(3 • 2)5 is (6)5 = 30
30 – 30
So, 3(2 • 5) = (3 • 2)5
Example: 3(5 + 6) = 3 • 5 + 3 • 6
3(11) = 33
3 • 5 + 3 • 6 is 15 + 18 = 33
33 = 33
So, 3(5 + 6) = 3 • 5 + 3 • 6
Tell students these ideas about equivalency and simplifying apply with variables as well
as numbers. We use properties to simplify algebraic expressions. When we simplify an
algebraic expression using properties, we can compare the original expression with the
simplified expression to make sure they are equivalent. A simplified expression is
always equivalent to the original. The way to compare the value of two algebraic
expressions is to substitute values for the variable(s) and evaluate each as we did in
our lesson a couple of days ago.
Lesson Segment 2: How do you know when an algebraic expression is in
Using Algeblocks and the Basic Mat have students go through these steps for each
problem on the Simplifying Algebraic Expressions worksheet. As appropriate use the
vocabulary such as “like terms” and the names of properties to help them describe
what they are doing.
- Set up the expression on the Basic Mat
- Use zero pairs from the integer rules and simplify the expression to find out the
total on the mat after taking away any zero pairs.
- Use the TI-73 to check to make sure the original expression is equivalent to the
An algebraic expression is simplified when a) parentheses have been multiplied through
and b) all like terms and units have been combined through adding or subtracting.
Practice: In order to simplify correctly students must use integer operations rules and
must be able to work with decimals and fractions, so assign text practice as needed.
When practice is tedious or mundane, I play a game with the students such as the
following Boxes Game.
Object: Draw the most boxes for your
Procedure: Divide class into two
teams. Have students all work on a
problem. Call on a person to explain
how they did the problem. If the
student explains correctly, he/she goes
to the board and draw two segments,
each connecting one point to another.
The perimeter of the box may be used
as line segments, so one box could be
made in any corner using only two line
segments. The student puts a letter or
number to represent the team in the
box. For each box the student draws
in that turn, one more line segment
must be drawn somewhere on the
observation, questioning, writing, mental math,
student response cards
This lesson plan was created by Linda Bolin
Created Date :
May 07 2009 14:34 PM