A
Mathematics
Georgia Standards of Excellence
Algebra 1 Parent Guide
Unit One
August 3 - August 26
All About Our Unit of Study
Relationships between Quantities and
Expressions
In unit 1, students are expected to solve problems
related to unit analysis and interpret the structure of
expressions. In real–world situations their answers will
usually be represented by numbers associated with units.
Units involve measurement and often require a
conversion. Measurement involves both precision and
accuracy.
In this unit students will:
• Use units of measure (linear, area, capacity, rates,
and time) as a way to understand problems.
• Interpret units in the context of the problem.
• Convert units and rates using dimensional analysis
(English–to–English and Metric–to– Metric without
conversion factor provided and between English
and Metric with conversion factor);
• Identify the different parts of the expression or
formula and explain their meaning.
• Decompose expressions and make sense of the
multiple factors and terms by explaining the
meaning of the individual parts.
• Understand similarities between the system of
polynomials and the system of integers.
• Understand that the basic properties of numbers
continue to hold with polynomials.
• Draw on analogies between polynomial arithmetic
and base–ten computation, focusing on properties
of operations, particularly the distributive property.
• Operate with polynomials with an emphasis on
expressions that simplify to linear or quadratic
forms.
• Rewrite (simplify) expressions involving radicals.
• Use and explain properties of rational and irrational
numbers.
• Explain why the sum or product of rational numbers
is rational; why the sum of a rational number and an
irrational number is irrational; and why the product
of a nonzero rational number and an irrational
number is irrational.
The Big Ideas of this Unit
Students should walk away from this unit
understanding that…
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Working with quantities and the relationships
between them provides grounding for work with
expressions, equations, and functions.
Polynomials are closed under the operations of
addition, subtraction and multiplication.
Expressions have parts that can be interpreted in
terms of a context, by viewing one or more of
their parts as a single entity.
Engage with Standards for Mathematical Practice (SMPs)
The Standards for Mathematical Practice (SMP) are practices that we want to develop in
students as they engage in mathematics.
Ask your child some of the following questions:
• Can you explain what the numbers and variables mean in this problem?
• How did you arrive at your answer?
• Why did you decide to use that math formula? Is there another way to do that problem?
• Does this method always work? How do you know?
• Where can you apply this mathematics in a real-world situation?
• How do you know that your solution is reasonable? How can you be sure?
• Are there other problems that are similar to this one?
• If I told you that I thought the answer was (offer a wrong answer), how would you convince me that I
was wrong?
Key Online Resources for Mathematics Learning
WebMATH provides quick homework help. http://webmath.com/index3.html
Lessons and games aligned to Common Core http://illuminations.nctm.org
Lessons covering various Algebra 1 topics https://www.purplemath.com/modules/index.htm
Video Lessons https://www.khanacademy.org/math/algebra
Regents Prep practice problems http://www.regentsprep.org/regents/math/algebra/math- algebra.htm
Key Terms to Know
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Algebra: The branch of mathematics that
deals with relationships between numbers,
utilizing letters and other symbols to represent
specific sets of numbers, or to describe a
pattern of relationships between numbers.
Coefficient: A number multiplied by a
variable.
Constant Term: A quantity that does not
change its value.
Expression: A mathematical phrase involving
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This is read as “the nth root of b”
Radicand: The value inside the radical symbol
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at least one variable and sometimes numbers
and operation symbols.
Factor: When two or more integers are
multiplied, each integer is a factor of the
product. "To factor" means to write the
number or term as a product of its factors.
Integer: The set of numbers ...,–3,–2,–
1,0,1,2,3,…
Irrational Number: A number whose
decimal form is nonterminating and
nonrepeating. Irrational numbers cannot be
written in the form a/b, where a and b are
integers (b cannot be zero). So all numbers
that are not rational are irrational.
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Rational number: A number expressible in the form a/b
or – a/b for some fraction a/b. The rational numbers
include the integers.
Term: A number, a variable, or a product of numbers and
variables.
Variable: A letter or symbol used to represent a number.
Volume: The amount of space occupied by an object.
Whole numbers: The numbers 0, 1, 2, 3, ….
Support Learning at Home
1. Engage your child in brain teasers, number games, and logic puzzles. Try sites such as illuminations.nctm.org or
cut-the-knot.org for exciting games that your child may enjoy.
2. Ask your child to teach you something new that they learned in math class each day. Require them to provide
examples and explain how they know what they know.
Sample Problems
Marla is a high school senior who is applying to college and wonders how many applications she
needed to send. Her counselor explained that with the excellent grade she received in chemistry
she would probably be accepted to one school out of every three to which she applied. She
immediately realized that for each application she would have to write 3 essays, and each essay
would require 2 hours of work. Of course writing essays is no simple matter. For each hour of
serious essay writing, she would need to expend 500 calories which she could derive from her
mother's apple pies [1 pie = 1000 calories]. Oh yes, mom makes a mini pie every 3 minutes that
Marla spends cleaning her room.
How many times would she have to clean her room in order to gain acceptance to 10 colleges?
Unit Factor Bank:
3 applications
1 accep tan ce
3 essays
1 application
2 hours
1 essay
500 calories
1 hour
1000 calories
1 pie
3 min cleaning
1 pie
“How many hours will it take to write enough essays to guarantee 10 acceptance letters?”
Say, “So, am I just turning 180 hours into minutes of cleaning now?...No, I need to consider the
number of minutes Marla needs to clean in order to get enough pies to generate the calories
needed to spend 180 hours writing essays.”