Download Unit 1 Lesson 1

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Campus: Clark Junior High and Princeton HS
Author(s): Lu, Ruckman, Patterson
Date Created / Revised: 07/13/15
Six Weeks Period: 1st
Grade Level & Course: Algebra 1
Timeline: 15 days
Unit 1 Title: Linear Expressions, Equations, and
Inequalities (one variable)
Lesson # 1
Stated Objectives:
TEK # and SE
A.1A - apply mathematics to problems arising in everyday life, society, and the workplace.
A.1B - use a problem-solving model that incorporates analyzing given information, formulating a
plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
A.1C - select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
A.1D – Communicate mathematical ideas, reasoning and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
A.1E – Create and use representations to organize, record, and communicate mathematical
ideas.
A.1F – analyze mathematical relationships to connect and communicate mathematical ideas;
and
A.1G – display, explain and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
A.5A – Solve linear equation in one variable, including those for which the application of the
distributive property is necessary and for which variable are included on both sides.
A.5B – Solve Linear Inequalities in one variable, including those for which the application of the
distributive property is necessary and for which variables are included on both sides.
A.10A – Add and subtract polynomials of degree one and degree two.
A. 10C – Determine the quotient of a polynomial of degree one and polynomial of degree two
when divided by a polynomial of degree one and polynomial of degree two when the degree of
the divisor does not exceed the degree of the dividend.
A. 10D – Rewrite polynomial expressions of degree one and degree two in equivalent forms
using the distributive property.
A. 12E – Factor, if possible, trinomials with real factors in the form ax^2 + bx + c, including
perfect square trinomials of degree two.
Key
Understandings
Students define polynomial expressions and perform operations (addition, subtraction, scalar
multiplication) with polynomials of degree one, including rewriting a polynomial to an equivalent
form when distributing by a rational scale factor. Students determine the quotient of a polynomial
of degree one divided by a polynomial of degree one. Students make connections between
expressions and equations, and solve linear equations in one variable, including variables on
both sides and the application of the distributive property. Students model both mathematical
and real-world problem situations using equations. Students solve linear inequalities in one
variable, including variables on both sides and the application of the distributive property.
Students model both mathematical and real-world problem situations using inequalities. Students
solve mathematic formulas (including solving for y), scientific formulas, and other literal
equations for a specified variable.
Misconceptions
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Some students may think that a constant term can be combined with a variable term
(e.g., 2x + 5 = 7x) rather than constant terms only combining with other constant terms
and like-variable terms combining with like-variable terms.
Some students may think that in the graph or table method of solving the equation,
the y-value is the answer rather than the x-value.
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Key Vocabulary
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Some students may think that the negative in front of the parentheses is distributed only
to the first term of the expression in parentheses rather than to all terms of the
expression in parentheses.
Some students may think that answers to both equations and inequalities are exact
answers rather than correctly identifying the solutions to equations as exact answers and
the solutions to inequalities as range of answers.
Some students may think that whenever a negative is involved, the order of the
inequality switches rather than only switching the order of inequality when multiplying or
dividing by a negative
Algebraic expression – a generalization that is a combination of variables, numbers
(constants and coefficients), and operators
Binomial – two terms; e.g., 4 – 2y, 3a + 1
Degree of polynomial – same as the degree of the term in the polynomial with the
highest degree
Degree of term – sum of the powers on the variables in the term
First degree polynomial – polynomial whose highest degree term contains one variable
with power of one
Linear equation in one variable – a mathematical statement composed of algebraic
and/or numeric expressions set equal to each other
Linear inequality in one variable – a mathematical statement composed of algebraic
and/or numeric expressions set apart by an inequality symbol
Literal equation – equation in which all or part of the terms are expressed in variables
such as two variable linear equations and mathematic and scientific formulas
Monomial – one term; e.g., –2.5x,
Polynomial expression – monomial or sum of monomials not including variables in the
denominator or under a radical
Trinomial – three terms; e.g., x2 + 2x + 1, a2 – 2ab – 8b2
Suggested Day
5E Model
Instructional Procedures
Day 1
Engage
August 25th
Objective: Connections to Algebra – Basic skills review.
(Engage, Explore, Explain, Extend/Elaborate, Evaluate)
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Integer computation skills evaluation
Variables in Algebra
Exponents and Powers
Closing statement: What is the purpose of the variable(s) in
an algebraic expression? Can variable be a symbol instead
of a letter?
Day 2
Explore/Explain
August 26th
Objective: Connections to Algebra – Basic skills review.
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Expression, Equations and Inequalities
Distributive Property
Terms, like terms.
Closing statement: What is the difference between
expression, equation and inequality?
Materials, Resources, Notes
Day 3
Explore/Explain
August 27th
1. Objective: Students solve one-step equations using
concrete models, algebraic methods, graphs, and tables.
Students compare and contrast the various methods and
verify the reasonableness of the solution.
2.
3. Explanation of use of Algebra Tiles. Work through very few
examples (x+3=7, x – 5= 3)
4.
5. In pairs, students can complete One-Step Equations
6. and teacher will facilitate a class discussion on using algebra
tiles, pictorial models, graphs and tables in the graphing
calculator, and algebraic methods to model and solve a one-step
equation.
algebra tiles
graphing calculator
Handout: One-Step
Equations (1 per student)
Websites:
http://tinyurl.com/kokqf7w
Clarify any misconceptions and instruct students to correct their
handouts.
Ask:
What representations were used to model solving one-step
equations?(concrete, algebraic, graphic and tabular)
How are these models similar? How are they different? Answers
may vary. The concrete and algebraic reflect the same step by
step modeling, whereas the graphic and tabular models a visual
solution that is not necessarily step by step; etc. When using the
tiles or algebraic representation, what was the first step in
solving? Answers may vary. Isolate the variable using inverse
operations; etc.
Where is the solution found in the table? (The x value where the
y values are equal.)
Where is the solution found on the graph? (The x value at the
point of intersection.)
Homework from the book (TBD)
Closing statement: From what you learned today, which
method(s) is easier for you to solve one-step equation?
Day 4
Explore/Explain
August 28th
7. Objective: Students solve two-step equations using
concrete models, algebraic methods, graphs, and tables.
Students compare and contrast the various methods and
verify the reasonableness of the solution.
Two-Step Equations
algebra tiles
graphing calculator with
display
Place students in pairs or groups to complete Two-Step
Equations
Facilitate a class discussion on solving two-step equations using
concrete models, algebraic methods, graphs, and tables.
Allow students time to complete the problems, and monitor
students to assess understanding and clarify any misconceptions
and instruct students to correct their handouts.
Ask:
How are these models similar? How are they different? Answers
Websites:
Khan Academy
http://tinyurl.com/kzsfscn
Modeling solving equations
with manipulatives
http://tinyurl.com/6c4qgds
may vary. The concrete and algebraic reflect the same step by
step modeling, whereas the graphic and tabular models a visual
solution that is not necessarily step by step; etc.
When using the tiles or algebraic representation, what was the
first step in solving? Answers may vary. Identify the constant and
use inverse operations; etc.
What is the next step? Answers may vary. Solve for x (changing
leading coefficient to be one) by using inverse operations; etc.
When using the graphic representation, where did you find the
solution in the table? (The x value where the y values are equal.)
Where is the solution in the graph? (The x value at the point of
intersection.)
Class discussion of student results, clarifying any
misconceptions.
Homework from the book (TBD)
Closing statement: From what you learned today, which
method(s) is easier for you to solve two-step equation?
Day 5
Explore/Explain
August 31st
Objective: Students use concrete models to visually simplify
algebraic expressions. i.e. Simplification of expressions,
Distributive property, Commutative property, Associative
property
Book work (TBD)
Algebra tiles
Algebra Scavenger Hunt
(TBD)
Homework from the book (TBD) with concentration on the use of
Algebra tiles
Ask:
What tiles can be combined and why? Answers may vary. The x
tiles can combine together and the unit tiles can combine
together; etc.
Which tiles cannot be combined and why? Answers may vary.
The x tiles and the unit tiles cannot combine together; etc.
What is a zero pair? Answers may vary. The same number of
positive and negative tiles combined; etc.
How does a zero pair effect the simplified expression? Answers
may vary. It cancels out some of the variables and units to
simplify the expression; etc.
Students complete the Algebra Scavenger Hunt of Properties.
Closing statement: Please create an algebraic expression of
your own for your partner to simplify it.
Day 6
Explore/Explain
Sept 1st
Objective: Students use prior knowledge to compare oneand two-step equations of the previous unit with the multi-
MATERIALS
 algebra tiles (1 set per
student)
step equations addressed in this unit. Students predict how
the properties for simplifying expressions can be applied to
solve multi-step equations.
Explore/Explain: Students solve multi-step equations using
concrete models, tables, graphs, and algebraic methods.
1. Place students in pairs. Distribute handout: Multi-Step
Equations and a set of algebra tiles to each student.
2. Refer students to Sample problem 1 on handout: Multi-Step
Equations.
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graphing calculator (1
per student)
graphing calculator
with display (1 per
teacher)
cardstock (4 sheets per
2 students)
scissors (1 per
teacher)
plastic zip bag (quart
size) (1 per 2 students)
3. Instruct students to work with their partner to complete Sample
problems 2 – 3.
4. Distribute handout: Math Detective to each student. Instruct
students to work with their partner to complete the handout.
Closing statement: What is the key operation to solve all
kind of equations?
Day 7
Explore/Explain
Sept 2nd
Objective: Students solve multi-step equations using
concrete models, tables, graphs, and algebraic methods.
1. Prior to instruction, create card set: Math Detective Cards by
copying on cardstock, laminating, cutting apart, and placing in
plastic zip bags. One card set will be given to each pair of
students.
MATERIALS
 algebra tiles (1 set per
student)
 graphing calculator (1
per student)
 graphing calculator
with display (1 per
teacher)
2. Place students with the same partner from the previous day.
Distribute card set: Math Detective Cards to each pair of
students. Instruct students to use the cards to check and correct
their answers on handout: Math Detective.
3. Refer students to Sample problem 4 on handout: Multi-Step
Equations.
4. Instruct students to work with their partner to complete Sample
problems 5 – 7.
5. Instruct students to work independently to complete the
Practice problems on handout: Multi-Step Equations.
Closing statement: What is the difference among one-step,
two-step and multi-step equation?
Day 8
Explore/Explain
Sept 3rd
Objective: Students continue to solve multi-step equations
using algebraic methods.
1. Place students in pairs. Distribute handout: Scrambled
“Egg”Quations, scissors, and glue to each pair of students.
2. Instruct students to work with their partner to complete the
activity, putting both names on the answer sheets on pages 1 –
2. The remaining pages are cut up to glue in the appropriate
places on the answer sheets.
MATERIALS
 scissors (1 per 2
students)
 glue (1 per 2 students)
 graphing calculator (1
per student)
3. Distribute handout: Multi-Step Equations Practice Problems.
Instruct students to work independently to complete the handout.
Closing statement: Is algebraic method the best way to
solve multi-step equations?
Day 9
Explore/Explain
Sept 4th
Objective: Students solve inequalities using concrete
models, tables, graphs, and algebraic methods.
1. Place students in pairs. Distribute handout: Solving
Inequalities and a set of algebra tiles to each student.
Refer students to page 1. Display teacher resource: Solving
Inequalities, and facilitate a class discussion on methods of
solving inequalities and their solutions.
MATERIALS
 algebra tiles (1 set per
student)
 graphing calculator (1
per student)
 graphing calculator
with display (1 per
teacher)
2. Refer students to Sample problems 1 – 4 on handout: Solving
Inequalities. Prior to filling in the tables on the handout, instruct
students to solve the inequality using algebra tiles, then put the
symbolic solution in the table, and finally enter functions into y1
and y2 of the graphing calculator to analyze the graphs and
tables.
3. Instruct students to work with their partner to complete the
Guided Practice problems 1 – 2 on handout: Solving Inequalities.
These problems may be completed as homework, if necessary.
Closing statement: discuss with your partner to give an
example for “why we need an inequality?”
Day 10
Explore/Explain
Sept 8th
Objective: Students solve inequalities using concrete
models, tables, graphs, and algebraic methods.
1. Facilitate a class discussion to debrief Guided Practice
problems on handout: Solving Inequalities.
MATERIALS
 graphing calculator (1
per student)
 graphing calculator
with display (1 per
teacher)
2. Place students in pairs. Refer students to Sample problems 5
– 6 on handout: Solving Inequalities
3. Model solving inequalities involving special cases using
Sample problems 5 – 6. Facilitate a class discussion of student
responses, clarifying any misconceptions.
4. Instruct students to work independently to complete the
Practice problems on handout: Solving Inequalities.
This may be completed as homework, if necessary.
Closing statement: Are the solution(s) for equation and
inequality different in some ways?
Day 11
Explore/Explain
Sept 9th
Objective: Students continue to solve inequalities using a
card game.
1. Prior to instruction, create card set: Unbalanced Inequalities by
copying on cardstock, laminating, cutting out, and placing in
plastic zip bags. One card set will be needed for each pair of
students.
2. Facilitate a class discussion to debrief the Practice problems
from handout: Solving Inequalities.
MATERIALS
 graphing calculator (1
per student)
 cardstock (2 sheets per
2 students)
 scissors (1 per
teacher)
plastic zip bag (quart size)
(1 per 2 students)
3. Place students in pairs. Distribute handout: Unbalanced
Inequalities Recording Sheet to each student. Distribute a card
set: Unbalanced Inequalities to each pair of students. Instruct
students to work with their partner using the card set to complete
the table on the handout.
Closing statement: do you think both equation and
inequality always has solution(s)?
Day 12
Explore/Explain
Sept 10th
Objective: Students explore and explain verbal statements
and inequalities.
1. Instruct students to work on Inequality Connection
independently. Facilitate a class discussion to debrief and check
for student understanding.
2. Place students in pairs. Facilitate a class discussion of Seeing
Inequalities page 1. Instruct students to work with their partner to
complete problems A – G.
3. Divide the class into 8 groups, and assign each group 1 of the
Guided Practice problems 1 – 9 on handout: Seeing Inequalities
to each group. Instruct each group to write an expression to
represent their assigned problem situation.
MATERIALS
 graphing calculator (1
per student)
 graphing calculator
with display (1 per
teacher)
TEACHER NOTE
Students connect verbal
statements and symbolic
inequalities. This skill is
used in applications of
equations and inequalities.
4. Instruct students to work independently on Practice problems 1
– 10 on handout: Seeing Inequalities.
Closing statement: Discuss with your partner to create a
real-life word problem that is in inequality situation.
Day 13
Elaborate
Sept 11th
Objective: Students set up verbal problems involving
consecutive integers into equations and inequalities.
Students solve the equations and inequalities using
methods of choice. Students justify answers in terms of the
problem situation.
MATERIALS
 graphing calculator (1
per student)
 graphing calculator
with display (1 per
teacher)
1. Facilitate a class discussion over Seeing Inequalities.
2. Place students in pairs. Refer students to page 1 of Equations
and Inequalities with Consecutive Numbers, and facilitate a class
discussion on consecutive numbers. Instruct students to work
with their partner to complete problems 1 – 2.
3. Instruct students to work with their partner to complete
problems 3 – 7 on handout: Equations and Inequalities with
Consecutive Numbers.
4. Instruct students to work independently to complete Practice
problems 1 – 6 on handout: Equations and Inequalities with
Consecutive Numbers.
Closing statement: How are algebraic operations used to
solve equations and inequalities?
Day 14
Elaborate
Sept 14th
Objective: Students set up verbal problems involving ratios
into an algebraic equation. Students solve the equations
using methods of choice. Students justify answers in terms
MATERIALS
 graphing calculator (1
per student)
of the problem situation.
1. Facilitate a class discussion over Equations and Inequalities
with
Consecutive Numbers.
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graphing calculator
with display (1 per
teacher)
2. Place students in pairs to complete the sample problems and
Guided Practice problem 1-3 from Problem Solving with Ratios
handout.
3. Facilitate a class discussion of student results, clarifying any
misconceptions.
4. Instruct students to work independently on Practice problems
1–8 on handout: Problem Solving with Ratios.
Closing statement: Why must solutions be justified in terms
of problem situations?
Day 15
Evaluate
Sept 15th
Evaluate:
1. Facilitate a class discussion to debrief Practice Problems on
handout: Problem Solving with Rates.
MATERIALS
graphing calculator (1 per
student)
2. Assess student understanding of related concepts and
processes by using the Performance Indicator(s) aligned to this
lesson.
3. Assessment.
Accommodations
for Special
Populations
Accommodations for instruction will be provided as stated on each student’s (IEP)
Individual Education Plan for special education, 504, at risk, and ESL/Bilingual.