LEONA QSI Curriculum Map
Algebra 1B 2014-2015
Teacher:
Course Group: Algebra 1 A,B,C
Pre-Requisites: Algebra 1A
Course: Algebra 1B
Department: Math
Grade(s): 9-12
Unit 4:
Intro to
Functions
(8 days)
Patterns
Essential Questions:
How can a relationship be represented graphically?
How can a recursive pattern be represented graphically?
How can a graph be interpreted in context of the situation?
CCSS Standards
= Major □ = Supporting ○= Additional ★= Modeling
□N-Q.1, □N-Q.2, □N-Q.3, A-SSE.1a, A-SSE.1.b, ASSE.2, A-CED.1, A-CED.3, A-CED.4, A-REI.1,
A-REI.3
A-CED.A.2
Interpreting
Graphs
Intro to
Functions
A-REI.D.10
F-IF.A.1
Graphing
Families of
Functions
Understand that the graph of an
equation in two variables is the set of all its solutions plotted
in the coordinate plane, often forming a curve (which could
be a line).
Understand that a function from one set
(called the domain) to another set (called the range) assigns
to each element of the domain exactly one element of the
range. If f is a function and x is an element of its domain,
then f(x) denotes the output of f corresponding to the input x.
The graph of f is the graph of the equation y = f(x).
F-IF.A.2
Use function notation, evaluate functions
for inputs in their domains, and interpret statements that use
function notation in terms of a context.
F-IF.B.4
For a function that models a relationship
between two quantities, interpret key features of graphs and
tables in terms of the quantities, and sketch graphs showing
key features given a verbal description of the relationship.
Key features include: intercepts; intervals where the
functions is increasing, decreasing, positive, or negative;
relative maxima and minima; symmetries; end behavior; and
periodicity.
F-IF.B.5
Relate the domain of a function to its graph
and, where applicable, to the quantitative relationship it
describes. For example, if the function h(n) gives the number
of person-hours it takes to assemble n engines in a factory,
then the positive integers would be an appropriate domain
for the function.
□F-IF.C.7a,b
Graph functions expressed
symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated
cases. (★)
a. Graph linear and quadratic functions and show intercepts,
Coordinate Plane, x-axis, y-axis, Quadrant, Function, Relation, Arithmetic Sequence, Solutions,
Plotting, Points, Solution Set, Intersection, Linear Graph, Quadratic Graph, Absolute Value Graph,
Piecewise Graph, Exponential Graph, Square Root Graph, Polynomial Function, Table of Values,
Translation(Shift), Dilation(Shrink, Expand)
Core Content
(High School Standards)
Tier 3 Support
Identify the structure of patterns
and represent the pattern with an
expression.
Plotting Points in a
coordinate plane
Create equations in two or more
variables to represent relationships between quantities;
graph equations on coordinate axes with labels and scales.
Key Vocabulary: Ordered Pair, Linear Equation, Domain, Range, x-intercept, y-intercept,
Displaying data in
tables, graphs
Identify a function by looking at
domain and range in a table, data,
and a graph.
Domain and Range
Relate the domain of a function to
its graph and, where applicable, to
the quantitative relationship it
describes.
Compare rate of
change of linear
functions.
Represent constraints of domain
and range given a graph of a
function.
Interpret graphs in relation to a
context, and represent a situation
graphically
Identify families of graphs based
on attributes. ( linear, quadratic,
exponential, absolute value,
piecewise, and square root
functions)
Identify the effect on the graph of
replacing f(x) by f(x) +k, kf(x),
f(kx), and f (x+k) for specific
values of k (both positive and
negative)
Make conclusions about graphs in
Formal
Resources
1.
Identifying Patterns
http://illuminations.nctm.org/LessonDetail.aspx?
id=L881
2.
Patterns Activity
http://insidemathematics.org/problems-of-themonth/pom-growingstaircases.pdf
Dan Meyer: Pixel Pattern
http://threeacts.mrmeyer.com/pixelpattern/
Pre Test
Input output tables
Interpret and graph functions
including piecewise, linear,
absolute value, and step.
Assessment
A function as a rule
Compare functions
by looking at
equations, tables
and graphs, and
focus primarily on
linear relationships
Calculate slope
given two points
using slope formula
and from a picture
using rise over run
Quizzes
Unit Test
Informal
3.
Checking for
Understanding
4.
Questioning
5.
Completion of
Project/Activity/
Assignments
Summarization
of Learning
Daily Exit Slip
http://visualpatterns.org/
Using patterns to write expressions: Chris Shore:
Pig Pen Algebra. See Appendix A
6. Graphing Patterns
http://www.shodor.org/interactivate/lessons/Intro
Arithmetic/
7. Identifying Types of Functions based on data
http://illuminations.nctm.org/LessonDetail.aspx?
id=L300
8. Dan Meyer: 25 Billion Apps
http://threeacts.mrmeyer.com/25billionapps/
9. Piecewise Functions
http://www.shodor.org/interactivate/lessons/Imp
ossibleGraphs/
10. Domain and Range Lesson
http://thescamdog.wordpress.com/2012/10/26/do
main-and-range-lesson/
11. https://app.box.com/s/cpd2ayhuxblhyaljyy7v
12. Vertical Line Test
http://www.shodor.org/interactivate/lessons/Vert
icalLineTest/
13. Comparing Linear to Quadratic Functions
http://insidemathematics.org/common-core-
Updated: 2/9/2016
LEONA QSI Curriculum Map
Algebra 1B 2014-2015
Teacher:
Course Group: Algebra 1 A,B,C
Pre-Requisites: Algebra 1A
Course: Algebra 1B
Department: Math
Grade(s): 9-12
maxima, and minima.
b. Graph square root, cube root, and piecewise-defined
functions, including step functions and absolute value
functions.
□F-IF.C.9 Compare properties of two functions each
relation to a context.
math-tasks/high-school/HS-F2007%20Graphs2007.pdf
Graph a situation based on given
data, table, or function.
14. Matching Functions Equations, Tables, Graphs
http://insidemathematics.org/common-coremath-tasks/high-school/HS-F2008%20Sorting%20Functions.pdf
represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For
example, given a graph of one quadratic function and an
algebraic expression for another, say which has the larger
maximum.
□F-BF.A.1a
15. 13. Various Functions
http://illuminations.nctm.org/LessonDetail.aspx?
ID=L768
16. Functions in Everyday Situations
http://map.mathshell.org/materials/lessons.php?t
askid=430&subpage=concept
Write a function that describes a
relationship between two quantities.
a. Determine an explicit expression, a recursive process, or
steps for calculation from a context.
○F-BF.B.3 Identify the effect on the graph of
replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for
specific values of k (both positive and negative); find the
value of k given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using
technology. Include recognizing even and odd functions
from their graphs and algebraic expressions for them.
17. Comparing Key Components of Linear
Equations
http://illuminations.nctm.org/LessonDetail.aspx?
id=L629
18. Graphing Stories
http://www.graphingstories.com/
19. Desmos Calculator
https://www.desmos.com/calculator
Mathematical Practices
MP.1-8
20. Sample Task Items:
http://www.illustrativemathematics.org/standards
/hs
21. Mathalicious-Domino Effect
Unit 5:
Linear
Functions
(15 days)
Essential Questions:
How do you identify key features of a graph and interpret it in terms of the
context?
How can you compare functions and their relationships to each other?
CCSS Standards
= Major □ = Supporting ○= Additional ★= Modeling
□N-Q.1, □N-Q.2, □N-Q.3,
Arithmetic
SSE.2, A-CED.1,
A-SSE.1a, A-SSE.1.b, AA-CED.3, A-CED.4, A-REI.1,
Core Content
(High School Standards)
Understand arithmetic sequences
in explicit and recursive notation.
Key Vocabulary: Ordered Pair, Linear Equation, Domain, Range, x-intercept, y-intercept,
Coordinate Plane, x-axis, y-axis, Quadrant, Function, Relation, Solutions, Plotting, Points, Solution Set,
Intersection, Linear Graph, Table of Values, Translation(Shift), Dilation(Shrink, Expand), Slope, SlopeIntercept Form, Point-Slope Form, Standard Form, Parallel Functions, Perpendicular Function
Tier 3 Support
Slope as a rate of
change and
Assessment
Formal
Resources
1. Application of Slope as Rate of Change
http://illuminations.nctm.org/LessonDetail.aspx?
Updated: 2/9/2016
LEONA QSI Curriculum Map
Algebra 1B 2014-2015
Teacher:
Course Group: Algebra 1 A,B,C
Pre-Requisites: Algebra 1A
Course: Algebra 1B
Department: Math
Grade(s): 9-12
Sequences
Rate of
Change &
Slope
A-REI.3
,
F-IF.1,
F.-IF.2,
F-IF.4,
F-IF.5, □F-IF.9,
□F-BF.1a, ○F-BF.3
A-CED.A.2 Create equations in two or more
variables to represent relationships between quantities;
graph equations on coordinate axes with labels and scales.
Direct
Variation
A-REI.D.10 Understand that the graph of an
equation in two variables is the set of all its solutions plotted
in the coordinate plane, often forming a curve (which could
be a line).
Linear
Functions in
a Context
A-REI.D.12 Graph the solutions to a linear
inequality in two variables as a half-plane (excluding the
boundary in the case of a strict inequality), and
graph the solution set to a system of linear inequalities in
two variables as the intersection of the corresponding halfplanes.
Using Forms
of Functions
Parallel and
Perpendicular
Lines
Write and
Apply Linear
Functions
Graphing
Linear
Inequalities
Application
of
Inequalities
F-BF.B.2 Write arithmetic and geometric sequences
both recursively and with an explicit formula; use them to
model situations, and translate between the two forms.
Write or construct arithmetic and
sequences with an explicit or
recursive formula and use them to
model situations.
Graphing linear
equations
Interpret the rate of change in a
context or in comparison to other
graphs.
Graph data points
and data from a
table
Calculate the rate of change over a
specific interval, identify if the
rate of change in constant,
increasing, or decreasing across
the graph.
Positive/Negative/N
o correlation
Make connections between rate of
change and the meaning of the
slope of a graph.
F-IF.B.6 Calculate and interpret the average rate of
change of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of change from a
graph. (★)
Understand and compare the
relationship of direct variation
functions
and show key features of the graph, by hand in simple cases
and using technology for more complicated cases. (★)
a. Graph linear and quadratic functions and show intercepts,
maxima, and minima.
□F-LE.A.1a, b, c
Distinguish between situations that can be modeled with
linear functions and with exponential functions. (★)
a. Prove that linear functions grow by equal differences over
equal intervals, and that exponential functions grow
by equal factors over equal intervals.
b. Recognize situations in which one quantity changes at a
constant rate per unit interval relative to another.
c. Recognize situations in which a quantity grows or decays
by a constant percent rate per unit interval relative to
another.
□F-LE.A.2 Construct linear and exponential functions,
including arithmetic and geometric sequences, given a
graph, a description of a relationship, or two input-output
pairs (include reading these from a table.) (★)
X and Y intercepts
of linear equations
Recognize that sequences are
functions
F-IF.A.3 Recognize that sequences are functions,
sometimes defined recursively, whose domain is a subset
of the integers. For example, the Fibonacci sequence is
defined recursively by F(0) = F(1) = 1, f(n +1) = f(n) + f (n – 1)
for n ≥ 1.
□F-IF.C.7a Graph functions expressed symbolically
calculating the slope
given two points.
Graph a function given
symbolically or with in a context.
Identify the
properties of
rectangles
Pre Test
Quizzes
Unit Test
Informal
Checking for
Understanding
id=L668
2. Direct/Indirect Variation
http://illuminations.nctm.org/LessonDetail.aspx?
id=L729
3. Negative Slope Application and Meaningful
Intercepts
http://illuminations.nctm.org/LessonDetail.aspx?
id=L682
Questioning
Completion of
Project/Activity/
Assignments
Summarization
of Learning
Daily Exit Slip
4. Application of Slope, Coordinates
http://www.thirteen.org/get-the-math/thechallenges/math-in-videogames/take-thechallenge/17/
5. Dan Meyer: Taco Cart
http://threeacts.mrmeyer.com/tacocart/
6. Chris Shore: tic tacs and kisses
http://mathprojects.com/2012/04/03/tic-tacs-andkisses/
7. Chris Shore: Rising Water
http://mathprojects.com/2012/04/03/rising-water/
8. Chris Shore: Monster Cars
http://mathprojects.com/2012/04/03/monstercars/
Compare attributes of linear
graphs in relation to the parent
function f(x) = x. Relate vertical
translations to the y intercept of a
linear equation.
Make conclusions and identify the
relationship between parallel and
perpendicular linear functions.
9. Chris Shore: 4X4 Matching: See Appendix A
10. Robert Kaplinsky: Speeding Ticket
http://robertkaplinsky.com/work/finlandspeeding-ticket/
Interpret solutions within a linear
equation with two variables.
12. Interactive
http://www.classzone.com/cz/books/algebra_1_2
011_na/get_chapter_group.htm?cin=5&rg=anim
ated_math&at=animations&npos=2&spos=5&va
r=animations
Explain the meaning of slope, xintercepts, and y intercepts in
11. Slope Intercept Form
http://illuminations.nctm.org/LessonDetail.aspx?
ID=L769
Updated: 2/9/2016
Course: Algebra 1B
Department: Math
Grade(s): 9-12
LEONA QSI Curriculum Map
Algebra 1B 2014-2015
Teacher:
Course Group: Algebra 1 A,B,C
Pre-Requisites: Algebra 1A
relation to a context.
□F-LE.A.3
Observe using graphs and tables that a
quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more
generally) as a polynomial function. (★)
□F-LE.B.5
Interpret the parameters in a linear or
exponential function in terms of a context. (★)
G-GPE.B.5
Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given
point).
Mathematical Practices
MP.1-8
Calculate x and y intercepts and
make conclusions regarding their
meaning in relation to a context, or
in comparison to other graphs.
Given data in a table decide if a
linear model is adequate to
represent the data.
13. Graphing Stories
http://www.graphingstories.com/
14. Desmos Calculator
https://www.desmos.com/calculator
15. Sample Task Items:
http://www.illustrativemathematics.org/standards
/hs
Explore simple linear functions by
engaging in hands-on experiments.
Compare and understand the
reasoning for different forms of
linear functions.
Construct linear functions
symbolically given specific
restraints or attributes.
Construct linear functions
symbolically to represent a context
or situation.
Identify and compare linear
functions that are parallel and
perpendicular
Construct linear functions based
on parallel and perpendicular
restraints.
Apply understanding of graphing
two variables with linear
inequalities.
Interpret solutions within regions
of inequalities with two variables.
Updated: 2/9/2016
LEONA QSI Curriculum Map
Algebra 1B 2014-2015
Teacher:
Course Group: Algebra 1 A,B,C
Pre-Requisites: Algebra 1A
Course: Algebra 1B
Department: Math
Grade(s): 9-12
Unit 6:
Systems of
Equations
(7 days)
Essential Questions:
How can the solutions to a system be represented and interpreted?
In what ways can a system be solved?
CCSS Standards
= Major □ = Supporting ○= Additional ★= Modeling
□N-Q.1, □N-Q.2, □N-Q.3,
Foundations
of Linear
Systems
Applications
of Systems
Systems of
Linear
Inequalities
SSE.2, A-CED.1,
A-REI.3
,
F-IF.1,
A-SSE.1a, A-SSE.1.b, AA-CED.3, A-CED.4, A-REI.1,
F.-IF.2,
F-IF.4,
A-CED.A.2 Create equations in two or more
variables to represent relationships between quantities;
graph equations on coordinate axes with labels and scales.
○A-REI.C.5
Prove that, given a system of two
equations in two variables, replacing one equation by the
sum of that equation and a multiple of the other produces a
system with the same solutions.
○ A-REI.C.6
Solve systems of linear equations
exactly and approximately (e.g., with graphs), focusing on
pairs of linear equations in two variables.
A-REI.D.10 Understand that the graph of an
equation in two variables is the set of all its solutions plotted
in the coordinate plane, often forming a curve (which could
be a line).
A-REI.D.11 Explain why the x-coordinates of the
points where the graphs of the equations y = f(x) and y =
g(x) intersect are the solutions of the equation f(x) = g(x);
find the solutions approximately, e.g., using technology to
graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or
g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
A-REI.D.12 Graph the solutions to a linear
inequality in two variables as a half-plane (excluding the
boundary in the case of a strict inequality), and
graph the solution set to a system of linear inequalities in
two variables as the intersection of the corresponding halfplanes.
Coordinate Plane, x-axis, y-axis, Quadrant, Function, Relation, Solutions, Plotting, Points, Solution Set,
Intersection, Linear Graph, Table of Values, Translation(Shift), Dilation(Shrink, Expand), Slope, SlopeIntercept Form, Point-Slope Form, Standard Form, Parallel Functions, Perpendicular Function, Infinite
Solutions (Dependent/Consistent), No Solution (Independent/Inconsistent), Coinciding Lines
Core Content
(High School Standards)
Tier 3 Support
Interpret the solutions to a system
of equations.
Substitute values for
variables and
determine if it is a
solution to the
equation
F-IF.5, □F-IF.9,
□F-BF.1a, ○F-BF.3
Key Vocabulary: Ordered Pair, Linear Equation, Domain, Range, x-intercept, y-intercept,
Make conclusions relating the
system of equations in relation to a
context.
Solve for a solution to a system of
equations exactly and
approximately using various
methods and strategies.
Graph and solve systems of linear
equations
Identify the constraints of a
solution within a system of
equations or inequalities and in
relation to a context.
Interpret solutions within regions
between systems of graphed
inequalities with two variables.
Model a system of equations by
determining the appropriate
equations or inequalities for the
solution set.
Identifying the
solution to a system
by visualizing on
the coordinate
plane.
Identifying when a
system has one,
none, or infinite
solutions.
Assessment
Resources
1.
Systems of Equations Graphing
http://illuminations.nctm.org/LessonDetail.aspx?
ID=L770
2.
Application Systems of Equations -Cell Phone
Plan
http://illuminations.nctm.org/LessonDetail.aspx?
id=L780
3.
Completion of
Project/Activity/
Assignments
Interactive
http://www.classzone.com/cz/books/algebra_1_2
011_na/get_chapter_group.htm?cin=7&rg=anim
ated_math&at=animations&npos=3&spos=7&va
r=animations
4.
Dan Meyer: Ditch Diggers
http://threeacts.mrmeyer.com/ditchdiggers/
Summarization
of Learning
5.
Dan Meyer: Dueling Discounts
http://threeacts.mrmeyer.com/duelingdiscounts/
6.
Chris Shore: Tortoise and the Hair
http://mathprojects.com/2012/04/03/the-tortoiseand-the-hare/
7.
Chris Shore: Mixture Problems
http://mathprojects.com/2012/04/03/stixtureproblems/
8.
Chris Shore: Monster Cars
http://mathprojects.com/2012/04/03/monstercars/
9.
Desmos Calculator
https://www.desmos.com/calculator
Formal
Pre Test
Quizzes
Unit Test
Informal
Checking for
Understanding
Questioning
Daily Exit Slip
□F-IF.C.7a Graph functions expressed symbolically
and show key features of the graph, by hand in simple cases
and using technology for more complicated cases. (★)
a. Graph linear and quadratic functions and show intercepts,
maxima, and minima.
10. Graphing Stories
Updated: 2/9/2016
Course: Algebra 1B
Department: Math
Grade(s): 9-12
Mathematical Practices
MP.1-8
LEONA QSI Curriculum Map
Algebra 1B 2014-2015
Teacher:
Course Group: Algebra 1 A,B,C
Pre-Requisites: Algebra 1A
http://www.graphingstories.com/
11. Sample Task Items:
http://www.illustrativemathematics.org/standards
/hs
12. Mathalicious - Date lines
Updated: 2/9/2016