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Solving Single-Variable Equations with
Two Steps
Objectives: At
the end of the lesson, students will be able to solve two-step single-variable
equations.
Download as Microsoft Word
Documents or Inspiration File:
Instructional
Plan Template
Mathematics
Governor’s Institute 2005
Names of
group members: Barbara Lathroum, Lori
Pawluck, Davina Pike, and
Merle Reinford
Topic/Theme:
Solving Single-Variable Equations with Two Steps
Level: Algebra I
Time Element: 1 90-minute
period or 2 45-minute periods
NCTM
Standards Addressed:
Represent and
analyze mathematical situations and structures using algebraic symbols
PA Math Standards Addressed:
2.8.8.C Create and interpret expressions and equations that model problem situations
2.8.8.E Select
and use a strategy to solve an equation, explain solution, and check the
solution for accuracy
Math Assessment Anchors Addressed:
M8.D.2.1.1 Simplify an expression to solve an
equation
M8.D.2.1.2 Use substitution check solution
M8.D.2.1.3 Find the value of an expression by
substituting a value M8.D.2.2.2 Write and solve an equation for a given problem
situation.
R11.A.2 Demonstrate the ability to understand and interpret non-fiction text including textbooks.
Objectives: At the end of the lesson,
students will be able to solve two-step single-variable equations.
Instructional Strategies and Plan (include
strategies used to help different types of learners, i.e. auditory, visual,
etc):
Strategy: Modeling
problem will make necessary the solution of a two-step single-variable
equation.
Lesson Plan:
1. State the objective
for the students' learning.
2. Introduce the modeling problem involving a comparison of taxicab fares. Hand out a worksheet with to be completed by the student. On the worksheet, the students will
·
write equations for each
fare;
·
complete a table
·
plot points and graph
·
use the table to find out how far a given amount of money will
carry the passenger.
·
write the appropriate two-step questions and stop.
3. Finding the solutions algebraically.
·
Review of Vocabulary (from
pre-algebra) using a Frayer strategy: solution,
real number, addition property, subtraction property,
multiplication property, and division property
·
Review of properties will
include examples of one-step equations.
·
Examples of two-step
equations demonstrated by the teacher, guided by student input. A handout will include these sample problems
for the students to follow along and solve at their seats.
·
Student practice 2 or 3
more problems on handout.
·
Return to the equations
generated in the modeling exercise. Have
the students use the technique they have just learned to solve them. Discuss the results and the answer to the
modeling question.
4.
Handout open-ended question for kids to complete in class.
Materials/Resources: Model Worksheet
Practice
Worksheet
Open-Ended
Worksheet
Calculators
Interdisciplinary Connections:
1
2
Technology: TI-83+/84 Calculators
3
Other
Assessment Strategies:
1
Formative Evaluation
(checking student understanding during the lesson):
2
Summative Evaluation (How
will it be determined that the objectives were achieved?):
Correctives/Remediation:
Extensions/Enrichment:
Special Accommodations (special needs students)
1
Description of the Special
Needs student selected:
2
Accommodations to use with
this student:
Name _________________________ Date __________ Period ______________
You are new to
- Create equations that model the cost of each taxi company.
- C = 2.50x + 10
- C = 3.75x + 5
- C = 4.75x
- C = 3.75x for x£ 5 and 3.25(x-5) + 18.75 for x > 5
( for Fast Fran’s you will have to create 2 separate equations)
- Create tables for each taxi for the first 10 miles.
|
|
Speedy Sam's |
Miles |
Rapid Ron's |
Miles |
Zippy Zack's |
Miles |
Fast Fran's |
|
1 |
12.5 |
1 |
8.75 |
1 |
4.75 |
1 |
3.75 |
|
2 |
15 |
2 |
12.5 |
2 |
9.5 |
2 |
7.5 |
|
3 |
17.5 |
3 |
16.285 |
3 |
14.25 |
3 |
11.25 |
|
4 |
20 |
4 |
20 |
4 |
19 |
4 |
15 |
|
5 |
22.5 |
5 |
23.75 |
5 |
23.75 |
5 |
18.75 |
|
6 |
25 |
6 |
27.5 |
6 |
28.5 |
6 |
22 |
|
7 |
27.5 |
7 |
31.25 |
7 |
33.25 |
7 |
25.25 |
|
8 |
30 |
8 |
35 |
8 |
38 |
8 |
28 |
|
9 |
32.5 |
9 |
38.75 |
9 |
42.75 |
9 |
31.75 |
|
10 |
35 |
10 |
42.5 |
10 |
47.5 |
10 |
35 |
- Create a Data Plot Graph using each cab company.
ANSWER
- Answer the following questions using the data chart.
- Which is the best company for 3 miles? Explain why? Fast Fran’s
- Which is the best company for 4 miles? Explain why?
- Which is the best company for a short trip under 5 miles? Explain why?
- Which is the best company for a longer trip over 10 miles? Explain why?
E. Last Friday night your mother would not let you travel on the fan bus to see the football game at the rival school. So you and three of your other friends devised a plan to tell your parents that you are staying at each other’s houses. Upon breaking all your piggy banks everyone came up with a total of $125.25. After taking out the admission price of $5.25 each. You need to know how far that the remaining amount will get you and your buddies.
