Title of Lesson: Solving Decimal Equations
Subject: Algebra 1
Grade Level: 9th-10th
Teacher: Nathan Craig, Amy Norris
Objective(s):
 Solve linear equations that involve decimals.
 Solve real-life problems using linear equations.
SCSDE Curriculum Standard(s) Addressed:
 7-3: The student will demonstrate through the mathematical processes an understanding
of proportional relationships.
o Use inverse operations to solve two-step equations and two-step inequalities.
 8-3: The student will demonstrate through the mathematical processes an understanding
of equations, inequalities, and linear functions.
o Apply procedures to solve multistep equations.
NCTM Curriculum Standard(s) Addressed:
 Represent and analyze mathematical situations and structures using algebraic symbols
o Develop an initial conceptual understanding of different uses of variables.
o Use symbolic algebra to represent situations and to solve problems, especially
those that involve linear relationships.
 Understand meanings of operations and how they relate to one another
o Understand and use the inverse relationships of addition and subtraction,
multiplication and division, and squaring and finding square roots to simplify
computations and solve problems.
 Solve problems that arise in mathematics and in other contexts
Prerequisites:
 Checking Possible Solutions
 Simplifying like-terms
 Distribution Property
 Solving multi-step equations, and equations with variables on both sides
 Representing real-life problems with equations
Materials/Preparation:
 Multiple examples of algebraic as well as real-life equations using decimals, ranging
from easy to advanced.
 Graphing calculators, or simple calculators for decimal computation
Procedures:
1. Introduction activity-Give students several multistep equations with decimals as
constants, not as coefficients, allow students to try to solve in groups or pairs, tell them
they can use a calculator.
 Ask students what if anything is different from equations solved in the
previous lesson besides the decimal values, and if this changes their
strategies to solve the problem, or ability to isolate the variable to one
side.
2. Main Activity-Student should begin to understand that decimals do not affect the strategy
in solving the problem or ability to isolate the variable.
 Explain that linear equations can be solved the same way using decimals,
allow students to work a few problems with exact decimals answers.
 Give students several problems with solutions that are continuous
decimals, or decimals with more than 5 place values. Ask students
whether this is a reasonable answer, or is there an approximation they can
make of the decimal answer that better represents the solution. Allow
students to discuss and defend their answers.
 Remind students of their rules of rounding, and explain that in most
situations rounding to the hundredths place is the best representation of a
decimal answer for a linear equation.
 Continue with several examples involving multiple steps, with continuous
decimal answers to ensure students understand when and where to round.
3. Closure: Solving real-life problems, representing these equations using a verbal model.
Give each group a word problem and instruct each group to first write out all of its
components, and second to write out an equation verbally they believe represents the
equation. Check each group’s equation, do not say wrong or right, ask why students
constructed the equation the way they did, and then instruct them to solve and present to
the class. Discuss wrong and right answers.
Assessment:
 First assessment is based off of how receptive students are to topics discussed in
procedures, as to where more discussion or practice is needed. Mastery involves ability to
effectively solve equations with decimals, using simplifying, and inverse operations to
solve for a variable. Students should also be able to effectively set up equations with
decimals through real-life applications.
 Homework: 10-15 application problems, where students are required to setup and solve
equations with decimals. (2 or 3 challenging problems, assess how students respond)
Adaptations:
 By allowing students to talk with peers, or in groups, lower level ability students can
reinforce and discuss the concepts with their peers. Likewise group discussion leading
into class discussion can effectively present all problems students have with the concept.
Follow-up Lesson/Activities:
 Solving linear equations review, create a review sheet in which students are expected to
explain and define all the terms essential to solving linear equations. Also included in the
worksheet should be several algebraic problems from each section, as well as real-life
application problems. For one problem from each section have students explain in words
what they did to solve the problem and how each step they performed kept both sides of
the equation equal.
Reflection: