Download Pacing Guide Grade 8 Q3- Q4

Pacing Guide
VITAL INFORMATION
Teacher Name
Subject Area
Sanctus Yanni
Algebra 1
Date
Grade / class
Topic: Unit /
Chapter /
Section
Unit 3: Linear Equations and Inequalities.
Unit 4: Statistical Models
Unit 5: Linear Systems and Piecewise-Defined Functions.
Unit 6 Exponential Relationships
Unit 7 Polynomial Operations
February 2017- June 2017
Grade 8
Q3
W
Standard
Concept
1W
AREI.D.12
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 half-planes.
S-ID.B.5
Summarize categorical data for
two categories in two-way
frequency tables. Interpret relative
frequencies in the context of the
data (including joint, marginal, and
conditional relative frequencies).
Recognize possible associations
and trends in the data.
1W
S-ID.B.5
Skills
1) Graphing Linear Inequalities involving ≤ 𝑜𝑟 ≥
2) Graphing Linear Inequalities involving < 𝑜𝑟 >
3) Creating Models with Linear Inequalities.
1)
2)
3)
4)
5)
6)
Categorical Data and Frequencies.
Constructing Two-Way Frequency Tables.
Reading Two-Way Frequency Tables.
Relative frequencies.
Two-Way Relative Frequency Tables.
Conditional Relative Frequencies.
Assessment
Content
Describe and graph linear
inequalities with two
variables.
Ex: 30 + 5y ≥ 4x
Unit 3: Module7: Linear
Equations and Inequalities.
Count frequency for
categorical data.
Measure relative
frequency and conditional
relative frequency.
Using decimal, percent
and fractions.
Unit 4: Statistical Models.
Module 8: Multivariable
categorical Data.
7.3 Linear Inequalities in
Two Variables
8.1 Two-Way Frequency
Tables.
8.2 Relative Frequency
2W
S-ID.A.1
S-ID.A.2
SID.B.6C
S-ID.A.1
Represent data with plots on the
real number line (dot plots,
histograms, and box plots).
S-ID.A.2
Use statistics appropriate to the
shape of the data distribution to
compare center (median, mean)
and spread (interquartile range,
standard deviation) of two or more
different data sets.
S-ID.B.6C
Fit a linear function for a scatter
plot that suggests a linear
association.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
1W
2W
AREI.C.5
AREI.C.5
AREI.C.6
Exploring Data.
Measures of Center: Mean and Median.
Measures of Spread: Range and IQR.
Using Dot Plots to display Data.
Comparing Data Sets.
Comparing Data Distributions.
a. Symmetric, Skew-left, Skew-right.
Understanding Histograms.
Creating Histograms.
Estimating from Histograms.
Constructing Box Plots. (Box and whiskers)
Comparing Box Plots. (two Box plots)
Describing How Variables are related in Scatter Plots.
(negative, positive, no correlation)
Estimating the Correlation Coefficient of a Linear Fit.
(describe correlation negative/positive, weak/strong)
Fitting Linear Functions to Data. (Line of best fit)
Find mean, median, range
and IQR for a data set.
Describe data
distribution.
Decide whether a value is
an outlier.
Plot a line plot.
Graph a histogram
Make a box plot.
Describe a scatter plot.
Make a line of best fit.
Estimate a correlation
coefficient.
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.
1) Types of Systems of Linear Equations.
2) Solving Consistent, Independent Linear systems by
graphing. (solving by graphing,
consistent/inconsistent, Independent/dependent
systems)
3) Solving Special Linear Systems by Graphing.
(inconsistent)
4) Estimating solutions of linear systems by graphing.
5) Interpreting Graphs of linear systems to solve
problems. (word problems)
Graph a system of linear
equations.
Find the solution of a
system by graphing.
Estimate the solution
from the graph.
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.,
1) Exploring the substitution Method of solving Linear
systems.
2) Solving consistent, independent Linear systems by
substitution. (solving by substitution)
3) Solving Special Linear Systems by substitution.
(Proving no solution to parallel lines)
4) Solving Linear System Models by Substitution. (Word
Problems)
1) Exploring the Effects of adding Equations.
(Elimination)
Solve linear systems by
substitution.
Decide is one solution,
infinite solutions, or no
solutions.
Unit 4: Module 9: OneVariable Data Distributions.
9.1 Measures of center and
spread
9.2 Data distributions and
outliers.
9.3 Histograms and Box
Plots.
Unit 4: Module 10: Linear
Modeling and Regression.
10.1 Scatter Plots and Trend
Lines.
Unit 5: Linear Systems and
Piecewise-Defined
Functions.
Module 11: Solving Systems
of Linear Equations.
11.1 Solving Linear Systems
by Graphing.
Solve linear systems by
Elimination.
Solve linear systems by
multiplying first.
11.2 Solving Linear systems
by Substitution.
11.3 Solving Linear Systems
by adding or subtracting.
11.4 Solving Linear Systems
by Multiplying First.
with graphs), focusing on pairs of
linear equations in two variables.
2W
ACED.A.3
AREI.D.12
A-CED.A.3
Represent constraints by equations
or inequalities, and by systems of
equations and/or inequalities, and
interpret solutions as viable or
nonviable options in a modeling
context. For example, represent
inequalities describing nutritional
and cost constraints on
combinations of different foods.
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 half-planes.
2) Solving Special Linear Systems by Adding or
Subtracting.
3) Solving Linear System Models by Adding or
Subtracting. (Word Problems
1) Understanding Linear Systems and Multiplication.
2) Solving Linear Systems by Multiplying First.
3) Solving Linear system models by multiplying first.
(Word Problems)
1) Creating Linear System Models by changing
Parameters.
2) Creating Linear System Models from Verbal
Descriptions.
3) Creating Linear System Models from Tables.
4) Creating Linear System Models from Graphs.
5) Determining Solutions of Systems of Linear
Inequalities.
6) Solving Systems of Linear Inequalities by Graphing.
7) Graphing Systems of Inequalities with Parallel
Boundary Lines.
8) Modeling Real-world constraints with Systems.
9) Modeling Real-world constraints with systems of
linear equations.
10) Modeling Real-world constraints with systems of
Linear inequalities.
Interpret word problem
to a system of linear
equations.
Create a system of linear
equation from a table or
from a graph.
Graph a system of linear
inequalities and find the
solution.
Unit 5: Module 12:
Modeling with Linear
Systems.
12.1 Creating Systems of
Linear Equations.
12.2 Graphing Systems of
Linear Inequalities.
12.3 Modeling with linear
systems.
Q4
2W
1.5W
AREI.B.3
FIF.C.7B
NRN.A.1
NRN.A.2
A-REI.B.3
Solve linear equations and
inequalities in one variable,
including equations with
coefficients represented by
letters.
F-IF.C.7B
Graph square root, cube
root, and piecewise-defined
functions,
including step functions and
absolute value functions.
N-RN.A.1
Explain how the definition
of the meaning of rational
exponents follows from
extending the properties of
integer
exponents to those values,
allowing for a notation for
radicals
in terms of rational
exponents.
N-RN.A.2
Rewrite expressions
involving radicals and
rational exponents
1)
2)
3)
4)
5)
Exploring Piecewise-defined function Models.
Evaluating Piecewise-defined functions.
Graphing Piecewise-defined functions.
Modeling with piecewise-defined functions.
Building piecewise-defined functions from graphs.
1) Understanding the Parent Absolute Value Function.
2) Graphing Translations of Absolute Value Functions.
(𝑔(𝑥) = |𝑥 − ℎ| + 𝑘)
3) Constructing Functions for Given Graphs of Absolute
Value Functions.
4) Solving Absolute Value Equations Graphically.
(Disjunction “x= or x=”)
5) Solving Absolute Value Equations Algebraically.
6) Absolute Value Equations with Fewer than Two
Solutions.
7) Visualizing the solution set of an absolute value
inequality.
8) Solving Absolute Value Inequalities Graphically.
9) Solving Absolute Value Inequalities Algebraically.
10) Solving a real-world problem with absolute value
inequalities.
Understanding Integer Exponents.
1) Exploring Rational Exponents. 〖(a〗^(1/2))
2) Simplifying Numerical Expressions with n^th roots.
3) Simplifying Numerical Expressions with rational exponents.
1) Exploring Operations with Rational and Irrational
Numbers.
2) Simplifying Multivariable Expressions Containing
Radicals. (22 ∗ 22 )
3) Simplifying Multivariable Expressions Containing
Rational Exponents.
4) Simplifying Real-World Expressions with Rational
Exponents.
Evaluate a piecewise
function for a given value.
Graph piecewise function.
Write and equation for a
piecewise graph.
Unit 5: module 13: PiecewiseDefined Functions.
Graph absolute value
function.
Write an equation from
graph.
13.2 Absolute Value Functions
and Transformations.
Solve absolute value
equations.
13.1 Understanding piecewisedefined functions.
13.3 Solving Absolute Value
Equations.
13.4 Solving Absolute Value
Inequalities.
Solve absolute value
inequalities.
Evaluate exponential
expressions.
Simplify exponential
expressions.
Simplify algebraic
exponential expressions.
Unit 6: Exponential
Relationships.
Module 14: Rational Exponents
and Radicals.
14.1 Understanding Rational
Exponents and Radicals.
14.2 Simplifying Expressions
with Rational Exponents and
Radicals.
2.5
W
2W
ASSE.A.1a
AAPR.A.1
AAPR.A.1
using the properties of
exponents
A-SSE.A.1a
Interpret expressions that
represent a quantity in
terms of its
context.
A-APR.A.1
Understand that
polynomials form a system
analogous to
the integers, namely, they
are closed under the
operations of
addition, subtraction, and
multiplication; add,
subtract, and
multiply polynomials.
A-APR.A.1
Understand that
polynomials form a system
analogous to
the integers, namely, they
are closed under the
operations of
addition, subtraction, and
multiplication; add,
subtract, and
multiply polynomials.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
Identifying Monomials
Classifying Polynomials
Writing Polynomials in Standard Form
Simplifying Polynomials
Evaluating Polynomials
Modeling Polynomial Addition Using Algebra Tiles
Adding Polynomials Using a Vertical Format
Adding Polynomials Using a Horizontal Format
Modeling with Polynomials
Modeling Polynomial Subtraction Using Algebra Tiles
Subtracting Polynomials Using a Vertical Format
Subtracting Polynomials Using a Horizontal Format
Modeling with Polynomials
Classify polynomials by
degree an terms.
Simplify polynomials.
1)
2)
3)
4)
Modeling Polynomial Multiplication
Multiplying Monomials
Multiplying a Polynomial by a Monomial
Multiplying a Polynomial by a Monomial to Solve a
Real-World Problem
Modeling Binomial Multiplication
Multiplying Binomials Using the Distributive Property
Multiplying Binomials Using FOIL
Multiplying Polynomials
Modeling with Polynomial Multiplication
Modeling Special Products
Multiplying (a + b)2
Multiplying (a - b)2
Multiplying (a + b) (a - b)
Modeling with Special Products
Multiply monomials,
Multiply binomials,
Multiply trinomials.
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
Find sum of polynomials.
Find difference of
polynomials.
Unit 7 Polynomial Operations
Module 17 Adding and
Subtracting Polynomials
Lesson 17.1 Understanding
Polynomial Expressions
Lesson 17.2 Adding Polynomial
Expressions
Lesson 17.3 Subtracting
Polynomial Expressions
Module 18 Multiplying and
Dividing Polynomials
Lesson 18.1 Multiplying
Polynomial Expressions by
Monomials
Lesson 18.2 Multiplying
Polynomial Expressions
Lesson 18.3 Special Products of
Binomials