Download Author - Princeton ISD

Campus: Huddleston
Author(s): Charles, Pappas, Segleski,
Stovall
Date Created / Revised: 10-4-14
Six Weeks Period: 3rd
Grade Level & Course: 6th Grade Math
Timeline: 13 days
Unit Title: Unit 6: Equivalent Expressions and
One-Variable Equations
Stated Objectives:
TEK # and SE
Lesson # 1 0f
1
(1) Mathematical process standards. The student uses mathematical processes to acquire and
demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
(C) 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;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical
ideas;
(F) analyze mathematical relationships to connect and communicate mathematical
ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
(7) Expressions, equations, and relationships. The student applies mathematical process
standards to develop concepts of expressions and equations. The student is expected to:
(A) generate equivalent numerical expressions using order of operations, including
whole number exponents and prime factorization;
(B) distinguish between expressions and equations verbally, numerically, and
algebraically;
(C) determine if two expressions are equivalent using concrete models, pictorial models,
and algebraic representations; and
(D) generate equivalent expressions using the properties of operations: inverse, identity,
commutative, associative, and distributive properties.
(9) Expressions, equations, and relationships. The student applies mathematical process
standards to use equations and inequalities to represent situations. The student is expected to:
(A) write one-variable, one-step equations and inequalities to represent constraints or
conditions within problems;
(B) represent solutions for one-variable, one-step equations and inequalities on number
lines; and
(C) write corresponding real-world problems given one-variable, one-step equations or
inequalities.
(10) Expressions, equations, and relationships. The student applies mathematical process
standards to use equations and inequalities to solve problems. The student is expected to:
(A) model and solve one-variable, one-step equations and inequalities that represent
problems, including geometric concepts; and
(B) determine if the given value(s) make(s) one-variable, one-step equations or
inequalities true.
See Instructional Focus Document (IFD) for TEK Specificity
Key
Understandings
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Misconceptions
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Key Vocabulary
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Numerical expressions can be represented in different forms while still having
the same values.
Concrete models, pictorial models, and algebraic representations can be used to
determine if two expressions are equivalent.
Properties of operations may be used to generate equivalent expressions.
Real-world problems may be written when given an equation.
Equations that represent problems may be solved using concrete, pictorial, and
algebraic models.
An equation remains true when the equation is evaluated with the solution of the
equation.
Some students may think that a constant term can be combined with a variable term
(e.g., x + 5 = 6x).
Some students may think variables are letters representing an object as opposed to
representing a number or quantity of objects.
Some students think of exponents as the multiplication of the base with the exponent
(e.g. 4³ = 4(3)), rather than powers of the base (e.g., 4³ = (4)(4)(4)).
Some students may think that the order of the variable and the constant is not important
in subtraction expressions (e.g., x – 7 is not equal to 7 – x).
Coefficient – a number that is multiplied by a variable(s)
Constant – a fixed value that does not appear with a variable(s)
Equation – a mathematical statement composed of algebraic and/or numeric
expressions set equal to each other
Exponent – in the expression xy, x is called the base and y is called the exponent. The
exponent determines the number of times the base is multiplied by itself.
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Expression – a mathematical phrase, with no equal sign, that may contain a number(s),
a variable(s), and/or an operator(s)
Order of operations – the rules of which calculations are performed first when
simplifying an expression
Prime factorization – the process of decomposing a composite number as a unique
product of prime factors
Rational numbers – the set of numbers that can be expressed as a fraction ,
where a and b are integers and b ≠ 0, which includes the subsets of integers, whole
numbers, and counting (natural) numbers (e.g., -3, 0, 2, – ,
, etc.). The set of
rational numbers is denoted by the symbol Q.
Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
Variable – a letter or symbol that represents a number
Suggested Day
5E Model
Instructional Procedures
Day 1
Engage
Explain
Explore
Goal: Prime Factorization with Exponents
Day 2/3
Engage
Explain
Explore
Goal: Order of Operations (with Integers)
Day 4
Explore
Explain
Goal: Writing Algebraic Expressions
Materials, Resources, Notes
(Engage, Explore, Explain, Extend/Elaborate, Evaluate)
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Pizzazz C-16 & C-17
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Hopscotch Foldable
Chalk
Texas Go Math
CSI – Order of
Operations
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Sequence Cards
Activity: Brain Pop Video – Prime Factorization
Record Notes in Journal making sure to emphasize exponents
Practice – Pizzazz C-16 & C-17
Record Notes in Journal – Hopscotch Foldable; emphasize that
the “P” will represent more than just Parentheses as they go
through later grades
Practice the chant a couple of times inside with the motions
“Parenthesis, Exponents, Multiplication & Division – from
LEFT to RIGHT, LEFT to the RIGHT, Addition &
Subtraction from the LEFT to the RIGHT, the LEFT to the
RIGHT”
Activity – Go outside and have students re-create the PEMDAS
hopscotch; practice the chant and motions
Practice 1 – Texas Go Math: Lesson 6.3 Guided and
Independent Practice
Practice 2 – CSI Around the Room for Order of Operations with
Integers
Record Notes in Journal; practice writing a couple as a whole
class
Activity – Use sequence cards to find the rule and write the rule
as an expression
Day 5
Engage
Explore
Explain
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Pizzazz B-76 & C-77
“I Have Who Has” –
Algebraic
Expressions
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Index Cards
String/Yarn
Measuring Up
Goal: Writing Algebraic Equations
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Activity: Algebraic Equation Match; students will match graphs
and tables to equations
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Algebraic Equation
Match
Measuring Up
Goal: Evaluating Algebraic Expressions
Record Notes in Journal – go over vocabulary related to
expressions and how to evaluate algebraic expressions;
emphasize when a number is next to a variable (or next to
parentheses) that it means to multiply
Activity – “I Have Who Has” Zip Line Race
Practice – Pizzazz B-76 & C-77
Day 6
Engage
Explore
Explain
Goal: Equivalent Algebraic Expressions
Review Algebraic Expressions
Activity: Each student will receive an index card necklace and will
have to find another student in the class who has an expression
that is equivalent to their necklace
Practice – Measuring Up: Equivalent Numerical Expressions (pg.
142)
Day 7/8
Engage
Practice: Measuring Up – Writing Equations from Tables (pg.
130)
Day 9/10
Engage
Explore
Explain
Goal: Solving Addition and Subtraction Equations
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Activity – Use balance scales (borrow from science department)
to have students explore what happens when adding and taking
away objects to each side of the scales
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Balance Scales
(science dept.)
Pizzazz E-71 & E-72
Record Notes in Journal and practice a few as a whole class;
emphasize that the equal sign is like a balance scale (when I
move to the opposite side of the equation that I must use the
opposite operation)
Practice – Pizzazz E-71 & E-72
Day 11/12
Explore
Explain
Goal: Multiplication and Division Equations
Record Notes in Journal and practice as a whole class; review all
types of equations and expressions
Activity – Around the Room (with a partner)
Practice: Pizzazz E-73 & E-74
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Around the Room Equations
Day 13
Explore
Explain
Goal: Review Expressions and Equations
Practice: Pizzazz B-77 & E-75
Algebraic Expressions and Equations and Word Problems
Handout
Accommodations
for Special
Populations
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Pizzazz B-77 & E-75
Algebraic
Expressions and
Equations and Word
Problems Handout
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.