Download Algebra I Unit 2

Algebra I
Unit 2
Title
Suggested Time Frame
st
Understanding Functions
1 & 2 Six Weeks
Suggested Duration – 18 days
Guiding Questions
Big Ideas/Enduring Understandings
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A function represents a dependence of one quantity on another.
A function can be described in a variety of ways.
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How can you use functions to solve real-world problems?
How are patterns and sequences used to solve real-world
problems?
Vertical Alignment Expectations
TEA Vertical Alignment Grades 5-8, Algebra 1
Sample Assessment Question
COMING SOON…………..
The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper
depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the
suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the
district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material.
CISD Math – ALG 1 – Unit 2
Updated July 7, 2015
Ongoing TEKS
Math Processing Skills
A.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
The student is expected to:
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Focus is on application
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Students should assess which tool to apply rather than trying only one or all
(E) create and use representations to organize, record, and communicate
mathematical ideas;
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Students should evaluate the effectiveness of representations to ensure they are
communicating mathematical ideas clearly
Students are expected to use appropriate mathematical vocabulary and
phrasing when communicating ideas
(F) analyze mathematical relationships to connect and communicate
mathematical ideas; and
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Students are expected to form conjectures based on patterns or sets of
examples and non-examples
(G) display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication
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Precise mathematical language is expected.
(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;
CISD Math – ALG 1 – Unit 2
Updated July 7, 2015
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Knowledge and Skills
with Student
Expectations
A.2 Linear functions,
equations, and
inequalities. The
student applies the
mathematical
process standards
when using
properties of linear
functions to write
and represent in
multiple ways, with
and without
technology, linear
equations,
inequalities, and
systmes of
equations. The
student is expected
to:
(A) determine the
domain and range of
a linear function in
mathematical
problems; determine
reasonable domain
and range values for
real-world situations,
both continuous and
CISD Math – ALG 1 – Unit 2
Updated July 7, 2015
District Specificity/ Examples
Vocabulary
Suggested Resources
Resources listed and categorized
to indicate suggested uses. Any
additional resources must be
aligned with the TEKS.
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A.2(A)
The student should be able to read and write domain and range in set
notation. {x|-3<x<4}
The student should be able to read graphs with points of discontinuity.
Misconceptions
The student may confuse x and y values.
The student may confuse which inequality symbol to use (< or >, > or ≥,
etc.)
The student may have trouble recognizing whether a real-world
situation should be represented with discrete or continuous variables.
The student may confuse domain and range on the graph and see
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Between
Between, inclusive
Closed circle
Continuous
Discrete
Domain
Equation
Function
Graph
Greater than (>)
Greater than or
equal to (≥)
Inequality
Less than (<)
Less than or equal to
(≤)
Linear
Open circle
Point-slope form
Range
Slope
Slope-intercept form
Strictly between
Table
Verbal description
X-values
Y-intercept
Y-values
HMH Algebra I
Unit 2
Web Resources:
Region XI: Livebinder
NCTM: Illuminations
discrete; and
represent domain
and range using
inequalities.
domain as the “height” of the graph and the range as the “width” of
the graph.
Including, but not limited to:
1. Use the definition of a function to determine whether a relationship
is a function given a table, graph or words.
2. Given the function f(x), identify x as an element of the domain, the
input, and f(x) is an element in the range, the output.
3. Know that the graph of the function, f, is the graph of the equation
y=f(x).
4. When a relation is determined to be a function, use f(x) notation.
5. Evaluate functions for inputs in their domain.
6. Interpret statements that use function notation in terms of the
context in which they are used.
7. Given the graph of a function, determine the practical domain of the
function as it relates to the numerical relationship it describes.
A.2(C)
Write a linear equation from a table.
Write a linear equation from a graph.
Write a linear equation from a verbal description.
(C) write linear
equations in two
variables given a
table of values, a
graph, and a verbal
description.
CISD Math – ALG 1 – Unit 2
Updated July 7, 2015
Misconceptions
The student may confuse the y-intercept with the x-intercept.
The student may switch values for x and y in the slope formula, or in
the point-slope form of a linear equation.
The student may confuse the signs of a line’s slope or y-intercept
(positive or negative).
Understand that all solutions to an equation in two variables are
contained on the graph of that equation.
Example 1:
The graph below represents the cost of gum packs as a unit rate of $2
dollars for every pack of gum. The unit rate is represented as $2/pack.
Represent the relationship using a table and an equation.
A.12 Number and
algebraic methods.
The student applies
the mathematical
process standards
CISD Math – ALG 1 – Unit 2
Updated July 7, 2015
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Define
Domain
Element
Function
Funtion notation
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and algebraic
methods to write,
solve, analyze, and
evaluate equations,
relations, and
functions. The
student is expected
to:
A.12(A)
Define a function as a relation where each element in the domain is
(A) decide whether
paired with one element in the range.
relations
Apply the definition in multiple representations.
represented verbally, Recognize a function from a graph – including the vertical line test.
tabularly, graphically, Symbolically, relations are functions if they can be written as a single
and symbolically
equation in “y=” form. For example, 4x + 2y = 10 is a function because
define a function.
it can be rewritten as y = -2x + 5; however, the relation x2 + y2 = 25 is
not a function because it cannot be written as one single equation in
“y=” form.
Misconceptions
Students may have difficulty recognizing that a relation is still a
function when y is repeated.
Students may also have difficulty recognizing when points (both x, and
y) are repeated – same x with the same y.
Clear concept of “function” needs to be understood. For every input (x)
there is exactly one output (y).
Example 1:
A tree grows 20 cm every year. The following table compares the tree’s
age to its height. Does this represent a function?
CISD Math – ALG 1 – Unit 2
Updated July 7, 2015
Input
Output
Range
Relation
Example 2:
Does the following graph represent a function?
Solution:
No, because for each input (x) there are two outputs (y).
(B) evaluate
functions, expressed
in function notation,
given one or more
CISD Math – ALG 1 – Unit 2
Updated July 7, 2015
A.12(B)
Function notation is the process of evaluating a function with values
from its domain.
elements in their
domains.
Misconception: When students see f(x)=3, they want to plug in
different values for x, such as x=2, x=5, etc., and claim that f(2)=2,
f(5)=5.
Example 1:
Evaluate the range of the following function when the domain is
-2,-1,0,1, and 2.
CISD Math – ALG 1 – Unit 2
Updated July 7, 2015