Red Springs High School
Math I Pacing Guide
2013-2014
1
Table of Contents
Course Outline ..................................................................................................... 3
Testing Information.............................................................................................. 4
Common Core Mathematical Practices ............................................................... 5
RSHS Math I Pacing Guide.................................................................................. 7
Sample Questions From Unpacking Document ................................................ 27
North Carolina Math I Standard Course of Study ............................................. 34
Assessments: Teachers should monitor and assess students daily. Suggestions for Summative Formative Assessments: Projects, Tests,
Quizzes...Suggestions for Formative Assessments: Exit slip, group work, labs, drills, discussions, journal entries/student reflection,
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Course Outline
Unit
Total Number of days
Preview: Fractions, Decimals, and Percents
1. Tools of Algebra
2. One Variable Equations & Inequalities
3. Introduction to Functions
4. Linear Functions/Linear Regression
Mid-Term
5. Systems of Equations & Inequalities
6. Coordinate Geometry
7. Polynomials
8. Quadratic Functions
9. Exponential Functions
10.1-Variable Statistics
11.Circles and Volume
EOC Review
Final Exams
Total:
4
7
7
10
6
2
7
5
7
7
7
6
4
6
5
90
Assessments: Teachers should monitor and assess students daily. Suggestions for Summative Formative Assessments: Projects, Tests,
Quizzes...Suggestions for Formative Assessments: Exit slip, group work, labs, drills, discussions, journal entries/student reflection,
*******Adjustments will be made accordingly.*******
3
Testing information
Conceptual Category Weight Distributions for Algebra I/Integrated I
Number and Quantity
5-10%
Algebra
22-27%
Functions
35-40%
Geometry
10-15%
Statistics and Probability
15-20%
Total
100%
In addition to the content standards, the CCSS includes eight Standards for Mathematical Practice that cross domains, grade levels,
and high school courses. Assessment items written for specific content standards will, as much as possible, also link to one or more of
the mathematical practices.
Assessments: Teachers should monitor and assess students daily. Suggestions for Summative Formative Assessments: Projects, Tests,
Quizzes...Suggestions for Formative Assessments: Exit slip, group work, labs, drills, discussions, journal entries/student reflection,
etc……
4
COMMON CORE STATE STANDARDS FOR MATHEMATICS Standards for Mathematical Practice
Mathematical Practice
DO STUDENTS:
MP 1: Make sense of problems and
persevere in solving them.
MP 2: Reason abstractly and
quantitatively.
MP 3: Construct viable arguments and
critique the reasoning of others.
MP 4: Model with mathematics.
5
 Use multiple representations (verbal descriptions, symbolic, tables,
graphs, etc.)?
 Check their answers using different methods?
 Continually ask, “Does this make sense?”
 Understand the approaches of others and identify correspondences
between different approaches?
 Make sense of quantities and their relationships in problem situations?
 Decontextualize a problem?
 Contextualize a problem?
 Create a coherent representation of the problem, consider the units
involved, and attend to the meaning of quantities?
 Make conjectures and build a logical progression of statements to explore
the truth of their conjectures?
 Analyze situations and recognize and use counter examples?
 Justify their conclusions communicate them to others, and respond to
arguments of others?
 Hear or read arguments of others, and decide whether they make
sense, and ask useful questions to clarify or improve the argument?
 Apply the mathematics they know to solve problems in everyday life?
 Apply what they know and make assumptions and approximations to
simplify a complicated situation as an initial approach?
 Identify important quantities in a practical situation?
 Analyze relationships mathematically to draw conclusions?
 Interpret their mathematical results in the context of the situation and
reflect on whether the results make sense?
MP 5: Use appropriate tools
strategically.
MP 6: Attend to precision.
MP 7: Look for and make use of
structure.
MP 8: Look for and express regularity
in repeated reasoning.
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 Consider the available tools when solving mathematical problems?
 Know the tools appropriate for their grade or course to make sound
decisions about when each of these tools might be helpful?
 Identify relevant external mathematical resources and use them to
pose or solve problems?
 Use technological tools to explore and deepen their understanding of
concepts?
 Communicate precisely to others?
 Use clear definitions?
 Use the equal sign consistently and appropriately?
 Calculate accurately and efficiently?
 Look closely to determine a pattern or structure?
 Utilize properties?
 Decompose and recombine numbers and expressions?
 Understand equivalence?
 Notice if calculations are repeated, and look both for general methods
and for shortcuts?
 Maintain oversight of the process, while attending to the details?
 Continually evaluate the reasonableness of their intermediate result?
Math I Pacing Guide 2013-2014
MATH I PACING GUIDE
The pacing guide should be used along with the Math I NCSCOS, the Math I unpacking document
Additional Sample Questions are located at the end of the pacing guide document
*Indicates Modeling Standards
To Be Addressed Through-out the Course When Appropriate
● N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret
units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
● N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.
● N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities
Unit 1: Tools of Algebra – 7 days(includes preview)
Standard: A-APR.1
Learning Targets
1. Basic Math
- Integers, Multiplication, Long Division,
Operations with Decimals, Fractions, Mixed
Numbers and Percents
2. Algebraic Expressions
- Translating algebraic to verbal and vice
versa
3. Order of Operations/Evaluate Expressions
4. Simplifying Expressions
- Distributive Property and Combining
Like Terms
- Introduction to simple Polynomials
5. Assessment
7
Glencoe Algebra I
1-1
1-2
2-1 to 2-4
1-5, 1-6
Vocabulary
Additive Inverse
Multiplicative Inverse
Reciprocal
Algebraic Expression
Constant
Coefficient
Exponent
Base
Equivalent Expressions
Evaluate Integers
Like Terms
Order of Operations
Real Number
Absolute Value Simplify
Term
Variable
Verbal Expression
Sample Question/Clarification
Unit 2- Equations and Inequalities
7 days
Standards: A-REI.1, A-REI.3
Learning Targets
1. Multi-Step Equations
2. Ratios, Proportions, Rates, and
Conversions
- Compare ratios
- Solve Proportions(include
multi-step)
- Use Proportions to model and
solve problems – Convert Units
3. One/Two and multi-step inequalities
4. Literal Equations (Focus on Geometric
formulas)
- Use units assigned to quantities in a
problem and identify which variable they
correspond to in a formula.
5. Unit Assessment (Equations and
Inequalities with and without calculator)
8
Vocabulary
Equations
Solution of an Equation
Formula
Glencoe Algebra I
Inverse Operations
3-1 to 3-3 3-4 and 3-5 6Literal Equations
1 to 6-3 8-5
Proportions
3-8
Unit Analysis
Properties of Equality
Inequality
Solution of Inequality
Sample Problem/Clarification
Students should understand
solving equations and inequalities
as a process of reasoning and
explain the reasoning to justify a
method and/or solution.
Solve 5(x3)3x55 for x. Justify
the steps using properties.
A salesperson earns $700 per
month plus 20% of sales. Write
an equation to find the minimum
amount of sales needed to receive
a salary of at least $2500 per
month.
A parking garage charges $1 for
the first half-hour and $0.60 for
each additional half-hour or
portion thereof. If you have only
$6.00 in cash, write an inequality
and solve it to find how long you
can park.
Compare solving an inequality in
one variable to solving an
equation in one variable.
If HkA(T1T2),
L
Solve for T2.
When finding the area of a circle
using the formula Ar2 ,which
unit of measure would be
appropriate for the radius? Solve
for r.
Solve AxBC for x. What are
the restrictions on A?
Unit 3: Introduction to Functions-10 days
Standards: A-REI.10, F-BF.1, F-BF.3, F-LE.2, F-IF.2, F-IF. 3, F-IF.5, F-IF.6
Sample Questions/Clarification
Learning Targets
Vocabulary
A concert hall has 58 seats in row
1. Review of Coordinate Plane
Graph
1, 62 seats in row 2, 66 seats in
- Label parts i.e. origin, axes, quadrants - Plot
Dependant Variable
row 3, and so on. The concert hall
ordered pairs
Domain
has 34 rows of seats. Write a
2. Using Graphs to Relate Two Quantities Function
recursive formula to find the
Analyze and Interpret Graph
Function Notation
number of seats in each row. How
- Match table to a graph (vice versa)
Independent Variable
Glencoe Algebra I
many seats in row 5? Write the
- Sketch a graph
Linear Function
1-8, 4-1 4-3, 4-4, 4-6 p.
explicit formula to determine
3. Patterns and Linear Functions
Non-Linear
278-279, 531, 556 4-6
which row has 94 seats.
– Represent a Geometric Relationship
Function
a. Table
Range
Which of the following points are
b. Words
Relation
on the graph of the equation
c. Equations d. Graphs
Sequence
– Represent a Linear Function a. Table
Vertical Line Test
2xy6?
b. Words
Term of a Sequence
c. Equations
Arithmetic Sequence
(0, 5), (1, 4), (-4, 14), (3,0)
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d. Graph
4. Patterns and Non-Linear Functions
- Classify Functions ( Linear vs. Non-Linear) a.
Tables
b. Words
c. Equations
d. Graphs
5. Graph a Function Rule
- Linear and Non-Linear (calculator active and
inactive) - Calculate and interpret the average rate
of change
6. Write a Function Rule
- Write and Evaluate Linear and Non-Linear
7. Formalizing Relations and Functions
 - Identify Domain and Range
 - Make a Mapping
 - Is it a Function?
 - Vertical Line Test
 - Evaluate a function {use function
notation f(x)}
 Rate of Change
 Calculate and interpret the average rate of
change using function notation 8.
Sequences and Functions
 - Extend Sequences
 - Identify an Arithmetic Sequence
 - Use the pattern to write a rule for
Arithmetic
Sequence (emphasize additive relationship)
 - Recursive to Explicit (vice versa)
9. Assessment
10
Common Difference
What is the average rate at which
this bicycle rider traveled from 4
to 10 minutes of her ride?
Discuss appropriate domains for
problems in context (real world
problems) i.e. 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.
Evaluate f(2)for f(x)x5. 2x
Unit 4: Linear Functions and Regression-6 days
Standards: F-BF.1, F-BF.2, S-ID.6, S-ID.7, S-ID.8, S-ID.9, G-CO.1, G-GPE.5, F-IF.4, F-IF.5, F-IF.7, N-Q.1, N-Q.3
Sample Problem/Clarification
Learning Targets
Vocabulary
If h(n) gives the number of
1. Find Slope in context of real world
Linear Equation
person hours it
problems
Parallel Lines
takes to assemble n engines in a
2. Slope-Intercept Form
Perpendicular Lines
factory, what would be an
-Effects of Slope and Y-intercept on the graph Rate of Change
appropriate domain?
Identify Slope and Y- intercept
Slope
What is the sum of the squared
-Write equation given m and b, two points, or
Slope Intercept Form
residuals of the linear model that
graph
Standard Form
represents the situation described
-Use Slope-Intercept form to model real world
Trend Line
above? Can you find a different
problems
X-Intercept
line that gives a smaller sum?
3. Standard Form
Y-Intercept
Explain.
o - Find X-Intercept and YLinear Regression
Below is the data for the 1919
Intercept
Line of Best Fit
Glencoe Algebra I
o - Graph using Intercepts
5-1, 5-7 5-3 to 5-5 5-6 Correlation Coefficient season and World Series batting
averages for nine White Sox
o Writing the equation of a line
5-4,5-7
Residual
players.
using two points to point-slope
Horizontal Line
a. Create a scatter plot for the
and to slope-intercept form(vice
Vertical Line
data provided. Is there a linear
versa)
Linear
association? Explain.
o - Transform Standard Equation to
Parent Function
b. What is the Least Squares
Slope-Intercept Form (vice versa)
Opposite
Regression Line that models this
o - Use Standard Form to model
Reciprocal
data?
real world problems
Scatter Plot
c. How do you know this
4. Parallel and Perpendicular Lines
Positive Correlation
equation is the line of best fit to
o - Write an Equation for Parallel
Negative Correlation
model the data?
and Perpendicular Lines
No Correlation
o - Classify Lines as Perpendicular,
Causation
Season batting World Series
Parallel, or Neither
Translation
average
batting average
11
o
- Solve a real world problem
5. Scatter Plot and Trend Lines
- Collect real data using different measuring
tools (Choose a level of accuracy appropriate to
limitations on measurement when reporting
quantities)
 - Make a Scatter Plot, choose appropriate
scale, describe Correlation
 - Write an Equation of a Trend Line and
make predictions (calculator inactive)
 - Find Line of Best Fit and Linear
Regression (calculator active)
 - Find and Interpret Correlation
Coefficient
 - Interpret Slope and Y-Intercept in
context of the problem
 - Identify if a relationship is causal
 - Find difference between observed and
predicted (residuals) and graph
6. Assessment
Benchmark-1 day
Unit 5: System of Equations and Inequalities-7 days
Standards: A-REI.6, A-CED.3
Vocabulary
Learning Targets
Consistent
Glencoe
1. Solve system of equations by graphing.
Dependent
Algebra I
 - Write a system and solve
7-1
Elimination Method
 - Systems with infinite and no
7-2 to 7-4 7-5
Inconsistent
solutions
Independent
12
.319
.279
.275
.290
.351
.302
.256
,282
.296
.226
.250
.192
.233
.375
.056
.080
.304
.324
Sample Problem/Clarification
How do you find the solution to
an equation graphically?
Solve the system by
elimination/substitution, checking




- Solve equation by graphing to find
the intersection point and interpret for
answer.
Write and Solve (Word Problems)
Choose appropriate method
Must know how to solve by hand for
calculator inactive Applications
2. Graph Linear Inequalities
 - Identify Solutions
 - Write an Inequality from graph 5.
System of Inequalities
 - Graph a system
 - Write a system from graph
 - Use a system to model and solve
(Linear programming is not the intent at
this level)
 - Find max values and interpret
solutions (Linear programming is not
the intent at this level)
3. Assessment
13
Linear Inequality
your solution by graphing using
Solution of an inequality technology.
Solutions of a system of If 3x 5,let y 3x and y 5 then
Linear Equations
use 12 the intersection to find the
Solutions of a system of solution.
Linear Inequalities
Substitution Method
Solve the following equations by
graphing. Give your answer to
the nearest tenth.
3(2x)6x7 10x5x8
How do we use a graph to
represent the solutions to a linear
inequality? Why do we use a
graph instead of listing the
solutions (as we do when solving
equations)?
Decide whether the boundary line
should be included for the
following inequalities. How
many solutions does each
inequality have?
3x  4 y  7 y  2x  6 3x  4
y1
Unit 6: Coordinate Geometry-5 days
Standards: G-CO.1, G-GPE.4, G-GPE.6, G-GPE.7
Learning Targets
1. Simplifying and operating with radicals
(add, subtract, multiply)
2. Finding Distance between two points
(Distance Formula)
- Using Distance to find Perimeter and Area on
Coordinate Plane
3. Find the Midpoint or Endpoint of a line
segment (directed line)
- Use real world applications
4. Classify Quadrilaterals (Parallelogram,
Rhombus, Square, and Rectangles)
- Use Distance, Midpoint, Parallel and
Perpendicularity (include geometric
definitions) to prove classification
5. Assessment
14
Glencoe
Algebra I
11-1, 11-2 113
11-5
Vocabulary
Radicals
Radicand
Square Root
Cube Root
Line Segment
Distance
Midpoint
Pythagorean Theorem
Polygon
Quadrilateral
Parallelogram
Rhombus
Square
Rectangles
Diagonals
Radius
Diameter
Endpoint
Circle
Center of a Circle
Altitude
Prime Factorization
Sample Problem/Clarification
The coordinates for a
quadrilateral are (3,0), (1,3),
(-3,1) and (0, -2). Determine the
type of quadrilateral showing all
work. Identify the properties used
to determine your classification.
Unit 7: Polynomials-7 days
Standards: N-RN.1, N-RN.2, A-SSE.1, A-APR.1
Learning Targets
1. Adding and subtracting polynomials
 - Finding Perimeter
 - Finding difference between
perimeters and areas
2. Laws of Exponents
Vocabulary
- Multiplying, Dividing, Zero, Negative, Power
Binomial,
to a Power and Rational (At the Math 1 level, Glencoe
Degree of a Monomial Degree of
focus on fractional exponents with a numerator Algebra I
a Polynomial Difference of
of 1)
8-5
Squares Monomial
3. Multiplying Polynomials
8-1, 8-2, 8- 3
Polynomial
 - Include Special Products
8-6, 8-7
Trinomial, Factor Greatest
 - Area applications
Common Factor
4. Factoring Greatest Common Factor
(using reverse Distributive Property)
5. Factoring Trinomials ( x2  bx  c ) Emphasize equivalent expressions
6. Factoring Perfect Squares
7. Assessment
Unit 8: Quadratic Functions-7 days
Standards: A-SSE.3, A-SSE.1, F-IF.8, F-IF.4
Vocabulary
Learning Targets
Axis of Symmetry
*Use function notation and equation notation
Maximum
Glencoe
throughout the unit.
Minimum
Algebra I
1. Quadratic Graphs and Their Properties
10-1 10-2
Parabola
o - Identify a vertex and axis of
Quadratic Function
symmetry
Quadratic Equation
15
Sample Problem/Clarification
Understand that the denominator of
the rational exponent is the root
index and the numerator is the
exponent of the radicand.
For example,
Students should investigate the
meaning of rational exponents by
examining the pattern:
24 16
22 4
21 2 1
22 ?
Using the connection between
rational exponents and radicals,
determine the value of x:
Sample Question/Clarification
Compare the graph of a quadratic
function to the equation of another
quadratic function and determine
which has the lowest minimum.
The height of a ball t seconds after it
is kicked vertically depends upon the
o
- Graph (how does a affect the
graph)
o - Graph (how does c affect the
graph)
o - Falling Object Model (no
initial velocity)
2. Quadratic Functions
- Graph (by hand and in the calc.) – Identify
and Interpret key features: Intercepts,
Intervals of Increasing and Decreasing, where
the Function is Positive and Negative, and
Maximum and Minimum
- Interpret a, b, c, vertex, y-intercept, and xintercepts (zeros) in the context of a real world
problem (i.e Projectile Motion, Profit)
3. Solve Quadratic Equations
 - Graphing
 - Using Square Roots
 - Factoring 4. Assessment
Solution of a quadratic equation
Zeros
X- Intercepts
Vertex
Increasing
Decreasing
Positive
Negative
Zero Product Property
initial height and velocity of the ball
and on the downward pull of gravity.
Suppose the ball leaves the kicker’s
foot at an initial height of 0.7 m with
initial upward velocity of 22m/sec.
Write an algebraic equation relating
flight time t in seconds and height h
in meters for this punt.
Unit 9: Exponential Function-7 days
Standards: A-CED.1, A-CED.2, F-IF.3, F-IF.4, F-BF.1, F-BF.2, F-IF.6, F-IF.8, F-IF.9, F-LE.1, F-LE.2, F-LE.3, F-LE.5
Learning Targets
1. Sequences from Graphs, Words, and
Tables -Recursive (use next, now
notation) and Explicit formulas
- Connect and emphasize that
geometric sequences are examples of
exponential functions (emphasize
multiplicative relationship)
16
Glencoe
Algebra I
10-5, 10-6
Vocabulary
Compound Interest
Decay Factor
Exponential Decay
Exponential Function
Exponential Growth
Growth Factor
Decay Factor
Sample Problem/Clarification
The value, NEXT, of a particular car
is related to the previous year’s value
NOW, by the function
NEXT=NOW(1-.015).
a) Identify the factors.
b) What does NOW represent in the
context of this problem?
2. Identify an Exponential Function from
Table, Graph, Function, and Words
o - Distinguish between
situations that can be modeled
with linear functions and
exponential function
o - Compare properties of two
given functions (linear,
quadratic, or exponential).
Could be given as verbal
expressions, tables, graphs or
equations.
3. Evaluate an Exponential Function
4. Graph an Exponential Function
o - Identify as increasing or
decreasing, growth or decay
o - Determine growth or decay
factor, intercepts, and end
behavior
5. Use an Exponential Function to model,
solve, and make predictions
o - Exponential growth, decay,
and Compound Interest
o - Interpret the different parts of
the function in context of the
problem
o - Determine Domain and Range
6. Assessment
17
End Behavior
Geometric Sequence
c) Which statement best describes the
change in the car’s value from one
year to the next? i) The value is
decreasing by 15%.
ii) The value is increasing by 15%.
iii) The value is decreasing by 85%.
iv) The value is increasing by 85%.
Unit 10: One-Variable Statistics-6 days
Standards: N-Q.1, N-Q.2, S-ID.1, S-ID.2, S-ID.3, S-ID.5
Learning Targets
1. Frequency tables and Relative frequency
tables
-Make a frequency table
- Make and Interpret a Histogram
- Compare Sets of Data (peek, spread, centers,
shape, and outliers)
2. Measures of Central Tendency and
Measures of Variation (Dispersion)
- Find Mean, Median, Mode and determine
when to use each
-Find Range
-Find Standard Deviation
3. Box and Whiskers
- Summarize Data using Min, Q1, Median, Q3,
Max - Make and Interpret Box and Whisker
Plots
- Find Interquartile Range
-Analyze Data in Box and Whisker Plot
4. Assessment
18
Vocabulary
Measure of Central Tendency
Outlier
Quartile
Frequency
Frequency Table
Histogram
Glencoe
Mean
Algebra I
Median
13-3 13-4
Mode
13-5
Measure of Dispersion
Range
Standard Deviation
Inter Quartile Range
Box and Whiskers
Univariate
Shape of a Histogram
Sample Question/Clarification
Why does the shape of the
distribution of incomes for
professional athletes tend to be
skewed to the right?
Why does the shape of the
distribution of test scores on a
really easy test tend to be skewed to
the left?
Why does the shape of the
distribution of heights of the
students at your school tend to be
symmetrical?
19