2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Exponents
Time Allowed:
10 Days
Learning Goal: Students will be able to evaluate expressions containing exponents including scientific notation.
The below benchmark(s) is linked to the
Objectives:
CPALMS site that contains the Specifications
1. Analyze the meaning and value of exponents (both positive and negative)
to include the Content limits,
2. Convert numbers from standard form to Scientific Notation and vice versa
Attributes/Stimulus, and additional
3. Apply the laws of exponents to simplify expressions.
information.
4. Apply concepts of exponents to real world situations
MA.8.A.6.1: Use exponents and scientific
Common Core: (link to common core)
notation to write large and small numbers and
Linked Standards with Access Points:
vice versa and to solve problems.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
Date Range: Given during the instruction per
the outline in this section
Key Vocabulary:
Base, Exponent, Power, Scientific Notation
MA.8.A.6.1: Use exponents and scientific
notation to write large and small numbers
and vice versa and to solve problems.
MA.8.A.6.3: Simplify real number
expressions using the laws of exponents.
Essential Content & Understanding:
Essential Questions:
1.
How do exponents simplify multiplication?
Positive and negative exponents Pictorial
model
2. Demonstrate an understanding of a zero
value exponent
3. Demonstrate an understanding of
scientific notation, including positive and
negative exponents
4. Convert from standard notation to
scientific notation (single and multistep
problems)
5. Convert from scientific notation to
standard notation (single and multistep
problems)
6. Adds, subtracts, multiplies, and divides
with scientific notation
7. Multiply powers with the same base
8. Divide powers with the same base
9. Raise a power to a power
10. Identify, order, and compare the relative
size of numbers
11. Solve Real-World Problems
• Incorporate Reading Strategies
• Integer Exponents
• Laws of Exponents
• Scientific Notation
Can exponents be negative, and if so, what
does that mean?
Can we have a zero exponent?
How do the uses of exponents simplify writing
very large or very small numbers?
What are the properties / operations involving
exponents?
Resources/Links:
Supplemental Resources:
Writing Links:
Higher Order Questions:
Remediation/Enrichment:
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Square Roots
Time Allowed:
10 Days
Learning Goal: Students will be able to calculate the square root of a number, estimate square roots, and perform operations with
radicals.
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Estimate square roots on a number line
limits, Attributes/Stimulus, and
2. Graph irrational numbers
additional information.
3. Compare expressions using real numbers
4. Synthesize approximations to estimate answers to problems with square roots
MA.8.A.6.2: Make reasonable approximations
5. Simplify radicals
of square roots and mathematical expressions
that include square roots, and use them to
Common Core: (link to common core)
estimate solutions to problems and to
compare mathematical expressions involving
real numbers and radical expressions.
Linked Standards with Access Points:
MA.8.A.6.2: Make reasonable
approximations of square roots and
mathematical expressions that include
http://edusoft.com/login.jsp
square roots, and use them to estimate
solutions to problems and to compare
mathematical expressions involving real
Date Range: Given during the instruction
numbers and radical expressions.
per the outline in this section
EduSoft Mini-Assessment(s):
Key Vocabulary:
Square Root, Principal Square Root, Perfect
Square, Radical, Radicand, Irrational
Number, Real Number, Density Property
Essential Content & Understanding:
1.
2.
3.
4.
Demonstrate an understanding of
estimating the interval of a square root
on the number line
Locate rational and irrational numbers
on the number line
Simplify radicals
Identify, compare, and evaluate
mathematical expressions involving real
numbers and radical expressions
Essential Questions:
How is the area of a square related to the
length of its sides?
What does a square root tell us?
How do you solve equations with rational
numbers?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Pythagorean Theorem
Time Allowed:
5 days
Learning Goal: Students will be able to find the missing side of the triangle by applying the Pythagorean Theorem to the coordinate
plane and real-world applications.
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Prove the Pythagorean Theorem
limits, Attributes/Stimulus, and
2. Find the distance between two points on a coordinate plane
additional information.
3. Find distances in real-world applications
MA.8.G.2.4: Validate and apply Pythagorean Common Core: (link to common core)
Theorem to find distances in real world
situations or between points in the coordinate
plane.
Linked Standards with Access Points:
Essential Content & Understanding:
MA.8.G.2.4: Validate and apply Pythagorean
1) Validate the Pythagorean Theorem
Theorem to find distances in real world
EduSoft Mini-Assessment(s):
2) Use the Pythagorean Theorem to find
situations or between points in the
the distances between points
coordinate plane.
http://edusoft.com/login.jsp
a) Coordinate Plane
b) Graphs (2- and 3-D)
Date Range: Given during the instruction
c) Real World Problems
per the outline in this section
3) Applications of the Pythagorean
Theorem
a) Solve for Leg
Key Vocabulary:
b) Solve for Hypotenuse
c) Solve real world problems
Pythagorean Theorem, Leg, Hypotenuse
d) Solve problems on coordinate
plane
Essential Questions:
How does the area of a square relate to the
Pythagorean Theorem?
How can the Pythagorean Theorem be
applied to the coordinate place?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Similar Triangles
Time Allowed:
5 Days
Learning Goal: Students will be able to apply the concept of proportionality and similarity in triangles to calculate the length of a
missing side, or the measure of a missing angle.
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Apply concepts of similar triangle s to find an unknown measure
limits, Attributes/Stimulus, and
2. Synthesize concepts of similarity and transformations to solve problems
additional information.
Common Core: (link to common core)
MA.8.G.2.1: Use similar triangles to solve
problems that include height and distances.
EduSoft Mini-Assessment(s):
Linked Standards with Access Points:
Essential Content & Understanding:
Essential Questions:
MA.8.G.2.1: Use similar triangles to solve
problems that include height and distances.
1.
2.
What are he similarities in triangles, and in
what respect can we change/move them
without changing the integrity of the original
shape?
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Date Range: Given during the instruction
per the outline in this section
3.
Key Vocabulary:
Similar Triangle, Proportional, Indirect
Measurement
4.
Scale Factor
Corresponding Parts
• Corresponding Sides
• Corresponding Angles
Solve for unknown part using
proportions
• Toothpicks, popsicle sticks, or
Zomes
• Geometer’s Sketchpad
• Pictorial Model
• Shadow lab
Application incorporating height and
distance
• Mathematical
• Real-World
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Classifying and Solving Angles
Time Allowed:
8 Days
Learning Goal: Students will be able to classify various types of angles and understand their relationships, similarity, and
congruency. In addition, students will be able to apply these concepts to find complimentary and supplementary angle.
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Analyze angles created when parallel lines are cut by a transversal and determine their measures
limits, Attributes/Stimulus, and
2. Apply the concept of the Triangle Sum Theorem to derive the formula for the sum of interior angles in a triangle
additional information.
Common Core: (link to common core)
MA.8.G.2.2: Classify and determine the
measure of angles, including angles created
when parallel lines are cut by transversals.
Linked Standards with Access Points:
MA.8.G.2.3: Demonstrate that the sum of the
angles in a triangle is 180-degrees and apply MA.8.G.2.2: Classify and determine the
this fact to find unknown measure of angles measure of angles, including angles created
and the sum of angles in polygons.
when parallel lines are cut by transversals.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
Date Range: Given during the instruction
per the outline in this section
Essential Content & Understanding:
Essential Questions:
1.
What is the relationship between a triangle
and a straight line?
MA.8.G.2.3: Demonstrate that the sum of
the angles in a triangle is 180-degrees and
apply this fact to find unknown measure of
angles and the sum of angles in polygons.
Key Vocabulary:
Angle, Right, Acute, Obtuse, Straight,
Complementary, Supplementary, Adjacent
2.
Congruent, Vertical, Parallel Lines,
Perpendicular Lines, Transversal
Triangle Sum Theorem, Equilateral,
Isosceles, Scalene
Polygon, Regular, Trapezoid, Parallelogram,
rectangle, Square, Rhombus
3.
4.
5.
Identify angles created by parallel lines
cut by a transversal using manipulatives
(straws) spaghetti, etc.)
• Vertical
• Corresponding
• Same-Side Interior
• Same-Side Exterior
• Alternate Interior
• Alternate Exterior
• Complementary
• Supplementary
Determine the measures of angles that
are created by parallel lines cut by a
transversal
• Protractor
• Geometer’s Sketchpad or
Geogebra
• Mathematically
Solve for Angles inside polygons
• Triangles
• Polygons up to 8 sides
Sum of Angles in a polygon
Apply learning to real world context
How are geometric figures and properties of
parallel lines used to solve problems
involving logical reasoning?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Converting Units of Measure
Time Allowed:
10 Days
Learning Goal: Students will be able to convert units of measure within and across systems of measurement using dimensional
analysis, and apply to dimensions of area/volume and mass.
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Apply concepts of dimensional analysis to compare, contrast, and convert units of capacity, mass, length, and temperature
limits, Attributes/Stimulus, and
between customary and metric measurement systems
additional information.
2. Convert derived units
3. Convert between dimensions, including area and volume
MA.8.G.5.1: Compare, contrast, and convert
units of measure between different
Common Core: (link to common core)
measurement systems (US customary or
metric (SI)) and dimensions including
temperature, area, volume, and derived units
Linked Standards with Access Points:
Essential Content & Understanding:
Essential Questions:
to solve problems.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
Date Range: Given during the instruction
per the outline in this section
MA.8.G.5.1: Compare, contrast, and convert 1.
units of measure between different
2.
measurement systems (US customary or
3.
metric (SI)) and dimensions including
temperature, area, volume, and derived units
to solve problems.
4.
Key Vocabulary:
Conversion Factor, Customary, Metric,
Dimensional Analysis, Bracket Method,
Derive
Scale, Capacity, Area, Volume
5.
6.
7.
8.
Define dimensional analysis
Convert rates using dimensional analysis
Compare and contrast customary and
metric measurement systems
• Qualities of customary
measurement system
• Qualities of metric
measurement system
Convert units between systems using
dimensional analysis and vice versa
• Length
• Volume
• Mass
• Temperature
Justify and apply conversions of units
between systems
• Using virtual manipulatives
Define derived units
Convert between derived units
Move from one dimension to two
dimension to three dimension
• Convert unit of area
• Convert units of mass
How are conversions made within the same
system of measurement?
How are conversions made across systems of
measurement?
Why are there different units for length,
capacity, and mass, and how are they related
within and across systems of measurements?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Display/Interpret/Change Data
Time Allowed:
13 Days
Learning Goal: Students will be able to organize, display, and interpret data, determine its measures of central tendency, and
determine how changes applied to the data affect its outcomes and displays.
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Create box and whisker plots, scatter plots, and lines of best fit
limits, Attributes/Stimulus, and
2. Hypothesize relationships on graphs
additional information.
3. Interpret changes in data and its overall affect on the measures of central tendency
MA.8.S.3.1: Select, organize and construct
appropriate data displays, including box and
whisker plots, scatter plots, and lines of best
fit to convey information and make
conjectures about possible relationships.
MA.8.S.3.2: Determine and describe how
changes in data values impact measures of
central tendency.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
Common Core: (link to common core)
Linked Standards with Access Points:
Essential Content & Understanding:
MA.8.S.3.1: Select, organize and construct
1.
appropriate data displays, including box and
whisker plots, scatter plots, and lines of best
fit to convey information and make
conjectures about possible relationships.
MA.8.S.3.2: Determine and describe how
changes in data values impact measures of
Date Range: Given during the instruction
central tendency.
per the outline in this section
2.
Key Vocabulary:
Line Plot, Stem-and-Leaf Plot, Back-to-Back
Stem-and-Leaf Plot, Venn Diagram, Bar
Graph, Double Bar Graph, Frequency Table,
Histogram, Line Graph, Pie Chart
Mean, Median, Mode, Range, Outlier,
Variability, Box-and-Whisker Plot, First
Quartile, Third Quartile, Inner-quartile
Range, Omit/Omission
Scatter Plot, Correlation, Line of Best Fit,
Misleading Graph
3.
Find the measure of central tendency
from a chart, table, graph, or plot when
there is a change in data sets
• Mean
• Median
• Mode
• Range
Determine change in measures of central
tendency by data manipulation for data
presented in a chart, table, graph, scatter
plot, line plot, or box and whisker plot
• Given all data but one point
• Include additional data
• Exclude data including outliers
Draw graphs and make conjectures
including trends and misleading data
about possible relationships
• Scatter plots with positive,
negative, and no correlation
• Lines of best fit
• Box and whisker plots (including
human box and whisker plot
activity)
Essential Questions:
What are the types of data displays and
how/when do we use them?
How do changes in the data set
(addition/omission) affect the overall
measures of central tendency?
(How does taking more tests affect your
grade?) --- not essential, but relevant 
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Solve Literal Equations
Time Allowed:
5 days
Learning Goal: Students will be able to solve formulas for a given variable, and apply literal equations to solve real-world problems.
The below benchmark(s) is linked to the Objectives:
CPALMS site that contains the
1. Analyze and select effective strategies to manipulate literal equations
Specifications to include the Content
2. Solve literal equations for a specified variable
limits, Attributes/Stimulus, and
additional information.
Common Core: (link to common core)
MA.8.A.4.1: Solve literal equations for a
specified variable.
EduSoft Mini-Assessment(s):
Linked Standards with Access Points:
Essential Content & Understanding:
Essential Questions:
MA.8.A.4.1: Solve literal equations for a
specified variable.
1.
2.
If all of the information is given (to solve an
equation) except for one variable, how do we
solve for that variable?
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Date Range: Given during the instruction
per the outline in this section
Key Vocabulary:
One-Step Equation, Two-Step Equation,
Inverse Operation
Terms, Like Terms, Equivalent Expressions,
Simplify
Linear Equation
Remember Key Properties/Identities:
• Additive Inverse
• Multiplicative Inverse
• Multiplicative Identity
• Zero Property
3.
Solve formulas for a given variable
Solve equations for given variables
• Manipulatives (pattern blocks
and snap cubes)
• Pictorial model
Use literal equations to solve real-world
problems
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Inequalities
Time Allowed:
5 Days
Learning Goal: Students will be able to solve one- and two-step equalities and graph their results.
The below benchmark(s) is linked to the Objectives:
CPALMS site that contains the
1. Apply concepts to solve one- and two-step equalities
Specifications to include the Content
2. Design graphs for solutions of inequalities
limits, Attributes/Stimulus, and
3. Use inequalities in real-world problems
additional information.
Common Core: (link to common core)
MA.8.A.4.2: Solve and graph one- and twostep inequalities in one variable.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
Linked Standards with Access Points:
Essential Content & Understanding:
Essential Questions:
MA.8.A.4.2: Solve and graph one- and twostep inequalities in one variable.
1.
How is the process of solving one- and twostep equations similar to solving one- and
two-step equalities?
Date Range: Given during the instruction
per the outline in this section
Key Vocabulary:
Inequality, Algebraic Inequality, Solution
Set
2.
3.
Solve simple on- and two-step
inequalities form math problems, graphic
models, number lines, and real-world
problems
• Rule for multiplying and dividing
by -1
• Compound inequalities on one
line (using “and”, “or”
Write inequalities from verbal
descriptions, tables, or graphs
• Incorporate reading strategies
Graph inequalities in one variable
• Greater than, less than
• Greater than or equal to, less
than or equal to
How does a negative coefficient in front of a
variable affect the problem solving process?
How do you graph an inequality?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Grade:
8
Course: MJ3
Linear Equations and Functions
Time Allowed:
10 Days
Instructional Focus Benchmarks
Learning Goal: Students will be able to locate points on a coordinate plane, graph them, interpret graphs of functions, determine
variable dependence, understand the relationship of domain and range of a function, apply tests for functions, and use equations and
The below benchmark(s) is linked to the tables to create graphs and vice versa.
CPALMS site that contains the
Specifications to include the Content
Objectives:
limits, Attributes/Stimulus, and
1. Create and use tables, graphs, and models of linear equations
additional information.
2. Analyze domain, range, discrete data, and continuous data
3. Identify various representatives of linear functions
MA.8.A.1.1: Create and interpret tables,
graphs, and models to represent, analyze, and Common Core: (link to common core)
solve problems related to linear equations,
including analysis of domain, range, and the
difference between discrete and continuous Linked Standards with Access Points:
Essential Content & Understanding:
Essential Questions:
data.
MA.8.A.1.1: Create and interpret tables,
MA.8.A.1.5: Translate among verbal, tabular, graphs, and models to represent, analyze,
graphical, and algebraic representations of
and solve problems related to linear
linear functions.
equations, including analysis of domain,
range, and the difference between discrete
and continuous data.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
1.
2.
MA.8.A.1.5: Translate among verbal, tabular, 3.
graphical, and algebraic representations of
Date Range: Given during the instruction
linear functions.
per the outline in this section
4.
Key Vocabulary:
Equation, Table, Graph, Coordinate Plane,
Continuous, Discreet, Increase, Decrease,
Constant
Function, Domain, Range, Independent
Variable, Dependent Variable, Vertical Line
Test
Find solutions for linear equation
problem by creating and interpreting:
• Tables
• Graphs
• Models
Determine variable dependence
• Continuous data/graphs
• Discrete data/graphs
Determine the parts of a relation
• Domain
• Range
Identify another representation of the
function
• Rule
• Table
• Graph
• Other symbolic representation
How do we plot an equation on a graph?
How do we interpret real-world data to
create graphs?
What is the difference between continuous
and discrete data?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Linear and Nonlinear Functions
Time Allowed:
3 Days
Learning Goal: Students will be able to graph linear functions and compare them with non-linear functions
The below benchmark(s) is linked to the Objectives:
CPALMS site that contains the
1. Compare and contrast the graphs of linear and nonlinear functions for real world situations
Specifications to include the Content
limits, Attributes/Stimulus, and
Common Core: (link to common core)
additional information.
MA.8.A.1.6: Compare the graphs of linear and
Linked Standards with Access Points:
non-linear functions for real-world situations.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
Date Range: Given during the instruction
per the outline in this section
Key Vocabulary:
Linear Equation, Rate of Change
MA.8.A.1.6: Compare the graphs of linear
and non-linear functions for real-world
situations.
Essential Content & Understanding:
Essential Questions:
1.
How do we recognize linear functions?
Compare linear to nonlinear graphs
• Given a real-world scenario
identify the representative
linear or nonlinear graph
• Given a linear or linear graph,
identify the representative realworld scenario
What is an example of a non-linear function?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Slope and Intercepts of Linear Equations
Time Allowed:
15 Days
Learning Goal: Students will be able to calculate the slope of a linear function, and determine where the line crosses the x and y axes
in real-world problems
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Interpret the slope of a linear equation in real-world problems
limits, Attributes/Stimulus, and
2. Analyze the x- and y-intercepts of a linear equation in real-world problems
additional information.
Common Core: (link to common core)
MA.8.A.1.2: Interpret the slope and the xand y-intercepts when graphing a linear
equation for a real-world problem.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
Linked Standards with Access Points:
Essential Content & Understanding:
Essential Questions:
MA.8.A.1.2: Interpret the slope and the xand y-intercepts when graphing a linear
equation for a real-world problem.
1.
When graphing real world data, what do the
slope and intercepts tell us?
Date Range: Given during the instruction
per the outline in this section
Key Vocabulary:
Slope, Rise, Run, Change in Y, Change in X,
Positive Slope, Negative Slope, Zero Slope,
Undefined Slope, Horizontal, Vertical
Intercept, X-intercept, Y-intercept, SlopeIntercept Form
2.
3.
4.
5.
Interpret the slope for real-world
problems using mathematical
terminology
• Positive slope
• Negative slope
• Undefined
• Zero
Determine x- and y- intercepts
• Graphs (Geoboards, white
boards, graphing calculator or
Geogebra)
• Tables of values
Given a graph interpret x- and yintercepts for real-world problems
including appropriate labels
Given a table of ordered pairs find the
slope of the line
• Slope formula
• Interpret the slope in terms of
the table
Graph a linear equation given:
• Table of values
• Two ordered pairs
• Slope-intercept form for
equation of a line
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Systems of Equations
Time Allowed:
7 Days
Learning Goal: Students will be able to solve systems of equations in real-world problems to determine a common solution (point of
equilibrium).
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Use systems of equations to solve real world problems by determining the solution set (equilibrium point)
limits, Attributes/Stimulus, and
2. Understand the relationship slope has to the solutions set
additional information.
Common Core: (link to common core)
MA.8.A.1.3: Use tables, graphs, and models
to represent, analyze, and solve real-world
problems related to systems of linear
Linked Standards with Access Points:
Essential Content & Understanding:
Essential Questions:
equations.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
MA.8.A.1.3: Use tables, graphs, and models
to represent, analyze, and solve real-world
problems related to systems of linear
equations.
1.
Date Range: Given during the instruction
MA.8.A.1.4: Identify the solution to a system
per the outline in this section
of linear equations using graphs.
Key Vocabulary:
System of Equations, Solution of a System of
Equation, Equilibrium Point, Intersecting
Lines, Parallel Lines, Same Lines
2.
3.
Solutions for systems of equations:
• One solution/ordered
pair/independent and
consistent
• No solution/empty
set/inconsistent
• All numbers/dependent and
consistent
Solve systems of equations using:
• Graphs (white boards,
Geogebra, graphing calculator)
• Models (Geoboards)
• Tables
• Simple Substitution
Solve real-world problems using
systems of equations
• Graphs
• Tables
• Simple Substitution
How are linear equations used to solve realworld problems?
What is the equilibrium point of two
equations?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities
2012-2013 Instructional Curriculum Plan
Topic/Idea:
Instructional Focus Benchmarks
Grade:
8
Course: MJ3
Percents and Rational Number Applications
Time Allowed:
5 Days
Learning Goal: Students will be able to apply rules for percentages to real-world applications including percent change, taxes, and
simple interest.
The below benchmark(s) is linked to the
CPALMS site that contains the
Objectives:
Specifications to include the Content
1. Calculate percents of change (discounts, mark-ups)
limits, Attributes/Stimulus, and
2. Apply percents to real world scenarios (commissions, tax)
additional information.
3. Solve the simple interest equation (for all variables) in real-world applications
MA.8.A.6.4: Perform operations on real
Common Core: (link to common core)
numbers (including integer exponents,
radicals, percents, scientific notation, absolute
value, rational numbers, and irrational
numbers) using multi-step and real world
Linked Standards with Access Points:
problems.
EduSoft Mini-Assessment(s):
http://edusoft.com/login.jsp
Date Range: Given during the instruction
per the outline in this section
Key Vocabulary:
Percent of Change, Percent of Increase,
Percent of Decrease, Mark-up, Discount
Commission, Commission Rate
Interest, Simple Interest, Principal, Rate of
Interest, Time
Key Concept**
Total = Principal + Interest
Essential Content & Understanding:
MA.8.A.6.4: Perform operations on real
1.
numbers (including integer exponents,
radicals, percents, scientific notation,
absolute value, rational numbers, and
irrational numbers) using multi-step and real 2.
world problems.
3.
Solve real-world problems with the
following:
• Percents
• Rational Numbers
Solve for change in percent
Solve for all variables in the simple
interest equation
Essential Questions:
If the price of an item goes up or down, how
do we determine the amount of change as a
percent?
How do we calculate tax?
If we take out a loan, how much do we have
to pay back?
Resources/Links:
In not included in the Essential Content area,
links should include if available:
1. Remediation Links
2. Writing Links
3. Higher Order Questions
4. Enrichment Opportunities