William H. Maxwell CTE High School
Mr. J. Badette, Principal
Department of Mathematics
Andrew Uwa, Assistant Principal
TASK 1
Name________________________
Topic: Solving Equations and Inequalities
Common Core Standards: A.CED.1, A.RE. 3
Unit 2- Solving Equations and Inequalities
October –November (5 Weeks 4days)
Lesson 22
Standards:
A.A.5, A.A.6
Common Core Standards:
A.CED.1
A.REI 1,3
Aim: How do we solve a two-step equation and use deductive reasoning to
Lesson 23
Standards:
A.N.1, A.A.5, A.A.22
Common Core Standards:
A.CED.1
A.REI 1,3
Aim: How do we solve equations containing like terms?
Lesson 24
Standards:
A.N.1, A.A.5,A.A.6, A.A.22
Common Core Standards:
A.CED.1
A.REI 1,3
Aim: How do we solve equations containing parentheses?
Lesson 25
Standards:
A.N.1, A.A.5, A.A.6,
A.A.22
Common Core Standards:
A.CED.1
A.REI 1,3
Aim: How do we solve equations containing variables on both sides?
Lesson 26
Standards:
A.N.1, A.A.5, A.A.6,
A.A.22
Common Core Standards:
A.CED.1, A.REI 1,3
Aim: How do we solve equations containing variables on both sides?
justify the steps?
PH Integrated Algebra: pp119 - 124
PH Integrated Algebra: pp126 - 132
(combining like terms)
(include verbal problems)
PH Integrated Algebra: pp126 - 132
(include verbal problems)
PH Integrated Algebra: pp134 - 139
(include verbal problems)
PH Integrated Algebra: pp134 - 139
(include verbal problems)
1
Lesson 27
Standards:
A.N.1, A.A.5, A.A.6,
A.A.22, A.G.2
Common Core Standards:
A.CED.1,4; A.REI 1,3
Aim: How do we transform formulas?
Lesson 28
Standards:
A.A.5
Common Core Standards:
A.REI.1, A.CED.1
Aim: How do we solve problems involving consecutive integers?
Lesson 29,30( 2days)
Standards:
A.A.5
Common Core Standards:
A.REI 1, A.CED.1
Aim: How do we solve verbal problems involving objects moving in same
Lesson 31
Standards:
A.A.5
Common Core Standards:
A.REI 1, A.CED.1
Aim: How do we solve verbal problems involving coins leading to linear
Lesson 32
Standards:
A.A.26, A.M.1, 2
Common Core Standards:
A.REI 1,3; N.Q.1,
Aim: How do we solve problems involving ratio and unit rate?
PH Integrated Algebra: pp140 - 141
(include verbal problems)
PH Integrated Algebra: pp162-165
(include even and odd consecutive integers)
and opposite
direction?
PH Integrated Algebra: pp 158 -165
equations?
PH Integrated Algebra: pp 158 -165
PH Integrated Algebra: pp 142 - 148
N.Q.2,N.Q.3
Lesson 33
Standards:
A.A.26, A.M.1, 2
Common Core Standards:
A.REI 1,3 ; N.Q.1,
Aim: How do we use proportions to solve verbal problems?
PH Integrated Algebra: pp 142 - 148
N.Q.2,N.Q.3
Lesson 34
Standards:
A.N.5
Common Core Standards:
A.CED 1,A.REI.1
Aim: How do we solve verbal problems involving percents?
PH Integrated Algebra: pp 16 6-167
(include verbal problems involving simple interest)
N.Q.1, N.Q.2,N.Q.3
Lesson 35
Standards:
A.M. 3
Common Core Standards:
A.CED 1,A.REI.1
Aim: How do we solve problems involving percent of change?
PH Integrated Algebra: pp 168 - 169
(include verbal problems)
2
Lesson 36
Standards:
A.M. 3
Common Core Standards:
A.CED 1,A.REI.1
Lesson 37,38(2 days)
Standards:
A.A.4,5,6; A.A.21,24
Common Core Standards:
A.CED 1, A.REI.3
Aim: How do we solve problems involving relative error?
Lesson 39
Standards:
A.A.4,5,6; A.A.21,24
Common Core Standards:
A.CED 1, A.REI.3
Lesson 40
Standards:
A.A. 5,6; A.A.24
Common Core Standards:
A.CED 1, A.REI.3
Aim: How do we solve verbal problems leading to linear inequalities in one
PH Integrated Algebra: pp 169 - 173
(include verbal problems)
Aim: How do we solve linear inequalities in one variable?
PH Integrated Algebra: pp 200 -225
(include writing inequalities given their graphs and graphing
solutions)
variable?
PH Integrated Algebra: pp 200 -225
( include AT LEAST and AT MOST )
Aim: How do we solve compound inequalities?
PH Integrated Algebra: pp 227 -232
3
Integrated Algebra Performance Task
The Road Trip!
You have decided to go on a road trip over summer with some friends. You have three separate trips you want
to take during the 2 months of summer break.
One is to a town a distance of 90 miles to see an old friend.
Another trip is to a shopping mall 120 miles away.
And the third is to see a concert in a city 250 miles away.
Finances are tight and you need to hire a car for the trip. There are three car hire companies for you to choose
from.
 Budget Car Rental charges a base fee of $50 and then 20c per mile
 Enterprise Car Rental charges a base fee of $20 and then 30c per mile
 National Car Rental charges 40c per mile with no base fee
Question 1
Construct a table with the costs for each company for distances up to 500 miles. You should
include at least 5 different distances but more would be helpful.
Question 2
a) Write a mathematical equation to show the cost of hiring a car for each company.
b) What are the slopes and y-intercepts of these of these linear equations?
Question 3
Which car rental place would you choose for each of your trips? Explain your choice in light of
your answers to questions 1 & 2.
(Hint: For what distances is Budget’s Car Rental the cheapest? What about Enterprise Car Rental?
What about National Car Rental?)
Question 4 At what trip distance would Budget Car Rental and Enterprise Car Rental cost the
same?
Question 5 At what trip distance would Enterprise Car Rental and National Car Rental cost the
same?
Question 6
At what trip distance would Budget Car Rental and National Car Rental cost the same?
Question 7 Graph On the same set of axes; draw a graph for each car rental company. The horizontal axis is
distance and the vertical axis is cost. Make sure your graph is large and that the horizontal axis
extends to at least 500 miles.
Question 8
Find the coordinates of the intersection of the lines and label them.
Question 9
Comment of the significance of these points.
Enjoy your trip!
4
Common Core learning Standards
Reasoning with Equations & Inequalities
A-RE I Understand solving equations as a process of reasoning and explain the reasoning.
1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step,
starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution
method
A-RE I Solve equations and inequalities in one variable.
3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters
A-RE I Represent and solve equations and inequalities graphically.
10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane,
often forming a curve (which could be a line)
11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the
solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make
tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational,
absolute value, exponential, and logarithmic functions.★
5
Rubrics
25 points
Student constructed 3
correct tables. Student
included 5 different
distances.
20 points
15 points
10 points
Student constructed 2
correct tables.
Student included 4
different distances.
Student constructed
1 correct table.
Student included 5
different distances.
Student constructed
1 correct table.
Student included
only 2 different
distances.
Writing
Equation
Student correctly wrote
equations for all 3
companies. Student
correctly identifies the
slopes and y-intercepts
of these of these linear
equations.
Student correctly
wrote equations for
2 companies.
Student correctly
identifies at least 2
of the slopes and yintercepts of these of
these linear
equations.
Student wrote
correctly equation 1
companies.
Student correctly
identifies at least 1
of the slopes and yintercepts of these
of these linear
equations.
Student wrote
correct equation for
3 companies.
However, student
did not correctly
identify the slopes
and y-intercepts of
these linear
equations.
Constructing
Graph
Student correctly drew
a graph for each car
rental company. The
horizontal axis
extended to at least 500
miles. Student correctly
plotted points for each
line. Students found the
coordinates of the
intersection of the lines
and labeled them.
Student correctly
drew a graph for 2
car rental company.
The horizontal axis
extended to at least
500 miles. Student
correctly plotted
points for each line.
Students found the
coordinates of the
intersection of the
lines and labeled
them.
Student correctly
drew a graph for at
least 1 car rental
company. The
horizontal axis
extended to at least
500 miles. Student
correctly plotted
points for 1 line.
Students found the
coordinates of the
intersection of the
lines and labeled
them.
Student correctly
drew a graph for at
least 1 car rental
company. The
horizontal axis
extended to at least
500 miles. Student
correctly plotted
points for 1 line.
Students found the
coordinates of the
intersection of the
lines and labeled
them.
Question
Response and
Critical
Thinking
Student clearly
explained reasoning for
choice of car rental
company. Student
identified the
significance of the
coordinates of the
intersection of the
lines.
Student explained
reasoning for choice
of car rental
company. Student
did not identify the
significance of the
coordinates of the
intersection of the
lines.
Student did not
clearly explained
reasoning for
choice of car rental
company. Student
did identify the
significance of the
coordinates of the
intersection of the
lines.
Student clearly
explained reasoning
for choice of car
rental company.
Student identified
the significance of
the coordinates of
the intersection of
the lines.
Table
6
7