Download Equations and Inequalities

Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
Teacher:
Date(s): 9/22-9/29
Grade Level or Course: Foundations of Algebra
Content or Unit: Equations and Inequalities
STAGE 1: Desired Results ~ What will students be learning?
A.4The student will solve multistep linear and quadratic equations in two variables, including
a) solving literal equations (formulas) for a given variable;
b) justifying steps used in simplifying expressions and solving equations, using field properties
and axioms of
equality that are valid for the set of real numbers and its subsets;
d) solving multistep linear equations algebraically and graphically;
* Graphing calculators will be used both as a primary tool in solving problems and to verify
algebraic solutions.
Daily Lesson Objectives:
9/22-9/23
SOL/Learning
Objective
Students will identify and
model the properties of
numbers. Students will
practice studying using
flashcards.
9/24-9/25
Students will identify
algebraic operations,
determine their inverse
operation, and employ the
properties of equality.
Students will solve multistep
linear equations in one
variable.
9/26-9/29
Students will solve literal
equations (formulas) for a given
variable;
NOTE: Students with scores 79% or below will complete corrections and are required to retake the mastery check
during tutoring or Falcon 45. Students who score between 80and 99% are required to complete corrections. Students
who receive 100% join the Keep IT 600 board.
Richmond Public Schools 2014-15
1
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)







Essential Questions
& Understandings
/Big Ideas



How are the field properties and properties of equality of real numbers used to solve equations?
What is a literal equation?
How are equations modeled?
The coefficient is the numerical part of a term. A constant is a symbol representing a value that does not
change. Coefficients and constants as rational numbers will be emphasized.
In a linear equation, the exponent of the variable(s) is one. For example: x + 5 = 9 or y = 3x – 8.
A literal equation is an equation that shows the relationship between two or more variables. A formula is a
special type of literal equation.
Each step in the solution of the equation will be justified using the field properties of real numbers and the
properties of equations. These properties may be modeled using manipulative and pictorial representations.
Properties of Equality: reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication,
and division.
Field Properties of Real Numbers: closure, commutative, associative, inverse, identity, and distributive.
A solution to an equation is the value or set of values (solution set) that can be substituted to make the
equation true.
Set builder notation is used to represent solutions. If the solution is y=10 then in set notation the answer is
written {y: y=10} or
{y| y=10}.
NOTE: Always ask the questions: How do you know you’re right? How do you know you’re done?
Key Vocabulary
Coefficient, Constant, Formula, Linear Equation, Literal equation
Properties of equality: reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication, division
Field properties: closure, commutative, associative, inverse, identity, distributive
STAGE 2: Assessment Evidence ~ What is evidence of mastery?
1. Which statement(s) can be
justified using the distributive
property? Check all that apply.
Assessment Part 1
☐ The cost of 4 bagels and 4
bottles of juice is equal to 4
times the cost of one bagel and
one bottle of juice.
☐ The cost of 4 bagels and 4
bottles of juice is equal to the
Richmond Public Schools 2014-15
Solve for 𝒙:
𝟓
𝟐𝟎) = 𝟔 (𝟏𝟐 − 𝟔𝒙)
𝟐
𝟓
(𝟏𝟎𝒙 −
Express your answer as a
whole number,
𝟏
Solve 𝑽 = 𝟑 𝝅𝒓𝟐 𝒉 for 𝒉.
= 𝟑𝑽𝝅𝒓𝟐
𝟑𝑽
B. 𝒉 =
𝟐
A. 𝒉
C. 𝒉
=
D. 𝒉
=
𝝅𝒓
𝟑𝑽𝝅
𝒓𝟐
𝝅𝒓𝟐
𝟑𝑽
2
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
cost of 4 bottles of juice and 4
bagels.
☐ Four times the cost of one
tub of peanut butter, one
bagel, and one bottle of juice is
equal to the cost of 4 tubs of
peanut butter, 4 bagels, and 4
bottles of juice.
☐ The cost of 4 bagels, 4
bottles of juice, and 4 tubs of
peanut butter is equal to the
cost of 4 tubs of peanut butter,
4 bottles of juice, and 4 bagels.
☐ The cost of 4 bagels and 4
bottles of juice is equal to the
cost of one bottle of juice and
one bagel plus $4.
Possible
misconceptions or
learning gaps
Solve for x
2(2x + 3) = (3)(4 + x)
Solve Q = 3a + 5ac for a.
a=
i
n
Write your answer in the box
t
provided (type
on SOL)
j
j
j
j
e
g
e
r
,
FROM A.1 students are struggling with Undoing fractions- teach students to
#1 difference between squared and
get rid of fractions first by multiply
square roots translation and entering
every term by denominator
calculator (reteach with warm-up and
homework)
Students are confused with
#2, students are struggle with
understanding when to add fractions
vocabulary ex difference – student
verses the multiplication of its
indicated operation as (+), product
inverse.
and quotient (student indicated them a
combination of incorrect operations)
and Turnaround words and parenthesis
words. Flash cards were made for
common mistakes and students used
incorrect practice problems to create
any other flashcards.
STAGE 3: Learning Plan ~ What are the strategies and activities you plan to use?
Richmond Public Schools 2014-15
3
Lesson Plan Template
Snapshot/Warm-up
(Stages adapted from the UBD model by McTighe and Wiggins)
Day 1 SOL (A.1)
Give the operation for
following words
1. difference
2. product
3. quotient
4. times the difference
of
5. subtracted from
6. squared
7. cube root
8. at least
9. at most
10.half of
Day 2 SOL (A.1)
1.
What is the value of
2
3x - y 3 27 if x = -1 and y
= 3?
2.
A consulting engineer
bills his customers $75 for
each hour he works. If a
client’s bill is $785, which
equation could be used to
find the number of hours
worked?
3.
Write an algebraic
expression for
the sum of the cube of a
number and 5.
Richmond Public Schools 2014-15
Day 1 (10 one-step
equations) no calculator
Ex.
X + 5 = 10
x/5 = 10
x - 5 = 10
5x = 10
Day 2 SOL (A.1)
SOL (A.1)
1. Translate into an
algebraic expression:
The cube root of 64, less
the product of three and
the square root of x
2. Translate into a verbal
expression:
3 2x - 3 x
3. Write a verbal
expression for the
Day 1 (Properties)
Name the following
Algebraic Properties:
1. (4 + 5) + 9 = 4 + (5
+ 9)
2. 5(x – y) = 5x – 5y
3. A + (-A) = 0
4. 𝐰 ∙ 𝐠 ∙ 𝐭 = 𝐠 ∙ 𝐭 ∙ 𝐰
Day 2 (REAL Numbers)
Place in order according to
Mnemonic:
Rhina (rational)
Is (Integer)
Winning (Whole)
Now (Natural)
Irrational (island by itself)
And give a fact about each
1. rational- add fractions
2. integer- add negative
#
3. whole- add 0
4. natural- counting
numbers
5. irrational4
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
4.
Write a verbal
expression for the
algebraic expression
5.

y3 x
algebraic expression 7(p
– 11)2.
2
+5 .
b
What is the value of

2
if x = 512 and y =
-3?
4. What is the value of
x(5 + y)2 if x = -
2
and y
3
= -8?
5.
What is the value of
3
 4x+8 

 - 3 216 when x =
 4x+4 


-4?
Instructional
Strategies
I use math 360—Students become the
performers and I am he audience. The
student’s work on the walls around the
room (white boards) and the teacher
stands in the middle, where she can
observe students closely. I can see
where their misunderstandings are and
correct them instantly. Students
usually form social network of learning
during this up-tempo, active learning
experience helping one another grow
with learning with my support and real
time correction.
Richmond Public Schools 2014-15
I am also using a combination of the
Model-lead-test strategy and
Systematic strategy in my direct
instruction described below.
Direct instruction will include pacing
the lesson, allowing adequate
processing and feedback time,
encouraging frequent student
responses, and listening and
monitoring throughout the lesson.
Model-lead-test strategy instruction
(MLT): 3 stage process for teaching
students to independently use
learning strategies: 1) teacher
models correct use of strategy; 2)
teacher leads students to practice
Math 360
Model-Lead-Test
Systematic instruction
Visual Representations
Cooperative Learning
Math Stations
Kinesthetic Learning
5
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
correct use; 3) teacher tests’
students’ independent use of it.
Once students attain a score of 80%
correct on two consecutive
assessments, instruction on the
strategy stops.
Systematic instruction
(This method focuses on teaching
students how to learn. The teacher
models strategy use for students
using memory devices, strategy
steps in everyday language, strategy
steps in order, and strategy steps
that prompt students to use
cognitive abilities)
Cooperative Learning
Math Stations
Kinesthetic Learning
Reciprocal Peer Tutoring
“I do…”
I will provide background and notes on
the all properties and the students will
receive a precut/typed foldable with
properties to study
Notes on properties pg 31 in INB
Teaching and
Learning Activities
Richmond Public Schools 2014-15
Teacher will explain that an
equation consist of 2 algebraic
expression connected (related) by
an equal sign. Class will discuss
what it means to balance
something. Students will then be
asked to model balancing
something. Example: If I put a
glove on one hand I must put a
glove on my other hand to keep me
balanced. Students will review four
properties of equality and model
them on the Right side of their INB.
Teacher will model how to solve
multi-step equations using the
“do/undo” method and the “U-turn”
method (Interactive PowerPoint
Presentation).
Use same method as linear
equations to demonstrate the
similarity with literal equations
Teacher will use model how to solve
literal equations using the “do/undo”
method and the “U-turn” method
(Interactive PowerPoint Presentation).
Student will be given a solving
equations foldable outlining the
following steps:
7. Any grouping () {} [] or || ?
Use Distributive Property to
simplify
8. Any fractions? Multiply all
terms in equation by any
denominators
9. Any like-terms? Check both
sides of the equal sign
6
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
Foldable on properties on pg 32 in INB
Student will be given a solving
linear equations foldable outlining
the following steps:
1. Any grouping () {} [] or ||
? Use Distributive Property
to simplify
2. Any fractions? Multiply all
terms in equation by any
denominators
3. Any like-terms? Check
both sides of the equal sign
4. Get variable on one side
of equal sign and
everything else on the other
side of the equal sign
5. Does the variable have a
coefficient? Divide by any
coefficients.
6. Is the variable on one side
of the equal sign by itself?
Yea!!! we’re done :o)
10. Get variable on one side of
equal sign and everything
else on the other side of the
equal sign
11. Does the variable have a
coefficient? Divide by any
coefficients.
12. Is the variable on one side of
the equal sign by itself? Yea!!!
we’re done :o)
Ex V=lwh solve for w
A= ½ bh
Day 2 teacher will model 3 problems to
justify steps
Richmond Public Schools 2014-15
7
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
“We do…”
Day 1 teacher will work 3 distributive
problems
Day 2 We will play spin to win to learn
the properties. I will spin the wheel
and the students will indicate when to
stop the wheel. The money value and
property is written with the suggested
answer. Next after written the students
will raise hand to offer the answer. A
“correct” explosion will appear if they
get it right and a red X appears if they
incorrect and next student can answer.
The student with top score wins.
Richmond Public Schools 2014-15
Teacher will put an equation on the
board and ask the students to walk
her/him through solving it.
Equation will have a variable on
both sides of the equal sign and the
same coefficient. When the
variables cancel each other out,
class will discuss Infinite solutions
and No Solution equations
We will draw a line down our paper
and we will work a one step on one
side and a one step literal on the other.
Second problem move to a 2-step on
one side and literal 2 step on the other
side
We will continue showing equations on
left and literals on right for 10
problems.
Students will be ask to solve 5 for
understanding.
8
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
x + 5 = 10
X+W= P
2x + 5 = 10
2x + A = T
Game paper in back of INB. WE place
all practice in back of journal. (Work
from back to front with practice work.
CW for classwork and HW for
homework
“Students do…”
DAY 1 Students will practice using the
properties in a matching activity with a
partner. The teacher will print and give
each group a copy. Each student will
be creating a worksheet to record their
work as they match the cards. The
teacher will group students of 2. The
timer will be set for 15 minutes (more
if needed). Students will write down
and solve the problem using
Richmond Public Schools 2014-15
Identify the algebraic operation
and determine the inverse
operation. Do not solve
1.
2.
3.
4.
5.
3r = 20
y – 4 = 15
4=s+2
x + 16 = 30
𝒎
=𝟒
𝟑
6. 90 = 45(g)
.Once
students understand
literal equations, they will
complete literal project. The
students will create a literal
equations poster of their
name. The students will use
formulas related to real word.
Also the student will include 4
9
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
properties. When the timer goes off,
they will review the answers with
another group and given 6 min to
correct their work. . As student are
moving about the teacher will be
listening and prompting students with
questions.
DAY 2 Students will complete 4
problems independently after the
teacher models 3 problems.
Student complete 10 distributive
property problems
7. p ∙ 6 = 18
8. 4 = z ÷ 4
9. − w = 4
10. -9 + f = 10
Students will work in groups
on the Multistep Equations
Math Lib
pictures that describe them.
L
Y
= A/W (A= L X W) solve for L
= (c – Ax)/B (Ax + By = C)
solve for y
N
= V/(l X W) If letter does not
Have a formula take a
geometry formula and replace letter
N = height in V= lwh
8
Students must use
letters. A
combination of first and last if
needed.
Richmond Public Schools 2014-15
10
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
Higher Level Thinking
Differentiation
Technology Use
A rectangle has a width of 52
units and perimeter of 200 units.
Find the length.
Hint1: Perimeter is the sum
of all the sides
P=200
Students will enter the answers to
their snapshots using Socrative
Student either on their phone, my
tablet, or my computer.
TI-84 calculators will be utilized.
Connections to other subject areas
and/or authentic applications
Geography --- using D= rt
To travel from SOLclocations
52
l
l
52
9/229/23
Think-PairShare
Flexible
Grouping
Tiered
Instruction
l + 52 + l + 52 = 200
9/229/23
Hint2: Gather like terms on
the left side of the equation
2l + 104 = 200
9/229/23
Hint 3: Gather constants on
right side
2l + 104 – 104 = 200 – 104
2l = 96
Hint4: isolate the variable
2l/2 = 96/2
l = 48 units
Check your work
9/249/25
Think-PairShare
9/249/25
. Michael has $66 in his account.
He saving $4.20 per week. How
long does it take to him to save
#339?
Richmond Public Schools 2014-15
Using Geometry formulas to solve
9/24- literal equations
9/25
11
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
Hint1: Add up the money boy
has now to the amount of
money he needs and equate
it to his goal.
66 + 4.20w = 339
Hint2: Gather the constants
on both sides
66+4.20w -66 = 339-66
4.20w = 273
Hint3: Now, isolate the
variable
4.20w/4.20 = 273/4.20
w= 65
Hint4: check your answer
9/269/29
Think-PairShare
Flexible
Grouping
Tiered
Instruction
Checking for
Understanding
Lesson Closure &
Student
Summarizing of
their Learning
9/269/29
Make up your own equation word
problem.
Share with a friend to solve.
9/269/29
Mon and Tues (Property drills)
Wed and Thurs (Retake A.1)
Fri and Mon (Equations drills)
STAGE 4: Closure ~ What did the students master & what are they missing?
TEAMS- Students will summarize what is important from today’s lesson
INDIVIDUALLY – Students will take a sticky note
and place it on the Ticket Out The Door.
Comments to the teacher about the lesson
may be written on the sticky note and question or struggling skill.
The teacher will use this information to adjust plans for the next lesson.
Richmond Public Schools 2014-15
12
Lesson Plan Template
(Stages adapted from the UBD model by McTighe and Wiggins)
Weekly practice problems
Pg 2 1-10 translation
Pg 4 38-43 evaluation
Pg 6 9-12 real numbers
Pg 9 7-24 evaluation
Pg 10 22-33 evaluation
Pg 12 41-48 evaluation
Pg 14 49-54 translation
Pg 23 1-10 like yerms
Assessment Part 2
Day 1 Review properties
Race to finish (25
versions) each student
given a different version
first 5 to finish win
Problems are to be complete and
taped into back of INB. No particular
order of pages to be completed.
Students may choose to work on
week skills or choose to work aall
strong skills first to ensure mastery.
Solve the following
equations for x.
1. 𝟔𝒙 + 𝟑𝟎 − 𝟏𝟓𝒙 + 𝟔 = 𝟏𝟖
2. −𝟔(𝒙 − 𝟏) = 𝟏𝟎𝟖
3. −𝟒(𝒙 + 𝟐) − 𝟑𝒙 = 𝟐𝟎
4. 𝟑(𝒙 − 𝟐) − (𝒙 + 𝟓) = 𝟏𝟕
Day 2 Weekly Workbook pages
from day 1
Day 2 weekly Workbook
pages from day 1
Teacher Reflection / Effectiveness of Learning
Teachers will reflect on the student learning and use assessment data to determine if students have mastered the material.
Richmond Public Schools 2014-15
13