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MIFFLIN COUNTY SCHOOL DISTRICT
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MCSD Mathematics Curriculum
Algebra I
Planned Instruction
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Title of Planned Instruction:
Algebra I |
| Subject Area: Mathematics Grade Level:
Grades 8-12 |
Prerequisites:
Eighth grade math with a grade of A or B (with teacher
recommendation)
Pre-algebra with a grade of A, B, or C
Seventh grade math with teacher recommendation
Course Description: This course builds the foundation for
all future math courses. It provides students with daily
opportunities to develop, experience, and apply algebraic concepts
and skills in order to become confident problem solvers in their
world. A strong mathematical background should be established
before taking this course.
Required Time: 180 days
Major Text(s) and Resources: |
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Merrill Algebra 1: Applications and
Connections,
Copyright 1995 by Glencoe/McGraw-Hill |
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Names of District Subject Area Curriculum Writing Committee: |
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- Diane K. Bray - Lewistown Middle School
- Lewis W. Brill - Strodes Mills Middle School
- Richard D. McCartney - Indian Valley Middle School
- Carl S. Sauer - Lewistown High School
- Matthew E. Shoemaker - Indian Valley High School
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Date of Board Approval: July 24, 2003 |
| Major Topics |
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- Operations
- Proportions and Algebra
- Linear equations
- Properties of linear functions
- Applications of Algebra
- Polynomials
- Graphing
- Problem solving
- Statistics
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| Course Objectives and Performance Indicators
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Strand: 2.1
Standard: Numbers, Number Systems and Number Relationships
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.1.11A |
Use operations. |
Add, subtract,
multiply, and divide integers. Add, subtract, multiply, and divide
rational numbers.
Solve open sentences that contain absolute value.
Evaluate expressions using order of operations.
Add, subtract, multiply, and divide polynomials.
Simplify rational expressions.
Simplify mixed expressions and complex fractions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.2
Standard: Computation and Estimation
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.2.11A |
Develop and use computation
concepts, operations and procedures with real numbers in problem-solving
situations. |
Write an equation that can
be used to find a solution to a problem situation. Solve one and two
step equations that contain real numbers. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11B |
Use estimation to solve
problems for which an exact answer is not needed. |
Determine if a problem
needs an exact or estimated answer. Using appropriate estimation skills,
find an estimated answer to a problem which does not need an exact answer. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11C |
Construct and apply
mathematical models (like lines) to estimate values of related quantities. |
Draw a linear graph using
given information like an equation, formula, table, or rule. Using the
student constructed graph of a linear function, find the answers to posed
questions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11D |
Describe and explain the
amount of error that may exist in a computation using estimates. |
Find the amount of error in
a computation by comparing an actual answer and an estimated answer.
Explain why the amount of error between estimated and actual answers in a
computation might change depending on the estimation technique that was
used.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11E |
Recognize that the degree
of precision needed in calculating a number depends on how the results
will be used and the instruments used to generate the measure. |
Knowing the problem
situation, correctly determine the number of decimal places in the answer
or the form of the answer (decimal, fraction, percent, etc.). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.211F |
Demonstrate skills for
using scientific and graphing calculators. |
Correctly use scientific
calculators when given the opportunity. Correctly use graphing
calculators to see linear graphs and find patterns. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.3
Standard: Measurement and Estimation
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.3.11A |
Select and use appropriate
units in particular measurement situations. |
Determine whether linear
units, square units, cubic units, or a combination of units are
appropriate in a given problem situation by listing them with the number
solution. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.4
Standard: Mathematical Reasoning and Connections
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.4.11A |
Use direct proofs or
proof by contradiction to validate conjectures. |
Identify properties of
equality that are used to solve an equation. Find a contradiction to
disprove a statement. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11B |
Construct valid arguments
from stated facts. |
Use the stated facts within
a problem and show the logical sequence of steps that lead to the
solution. Use the problem solving process: "facts, plan, solve, and
check."
Use properties (identity, distributive, commutative, and associative)
to simplify expressions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11C |
Determine the validity of
an argument. |
Determine whether a
conclusion drawn from a sequence of three or more statements is logically
valid. Check your solution(s) after solving an equation.
Check your solution(s) after solving a problem situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11E |
Demonstrate mathematical
solutions to problems. |
Use algebraic techniques to
solve problems involving real life situations. Use algebraic techniques
to solve problems involving ratio, proportion, and percent. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.5
Standard: Mathematical Problem Solving and Communication
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.5.11A |
Select and use appropriate
algebraic concepts and techniques and apply them to solving non-routine
and multi-step problems. |
Solve real life problems by
using appropriate algebraic concepts and techniques. Solve
interest, mixture, work, and uniform motion problems. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11B |
Use symbols, mathematical
terminology, standard notation, mathematical rules, graphing and other
types of mathematical representations to communicate observations,
concepts, procedures, generalizations, ideas and results. |
Communicate all of the
mathematical procedures concepts, conclusions, etc. necessary to the
solution of a problem situation using correct and appropriate mathematical
representations. Define variables and write equations from words. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11C |
Present mathematical
procedures and results clearly, systematically, succinctly and correctly |
Show all steps in the
process of solving various types of equations and inequalities. Clearly
label all results with the correct units. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11D |
Conclude a solution process
with a summary of results and evaluate the degree to which the results
obtained represent an acceptable response to the initial problem and why
the reasoning is valid. |
Explain how a problem was
solved and why the chosen procedures were used. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.6
Standard: Statistics and Data Analysis
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.6.11A |
Organize and represent
experimental results with graphs. |
Gather two types of related
data and represent their relationship in a graph. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11B |
Use appropriate technology
to organize and analyze data taken from the local community. |
Use graphing calculators to
enter data points and lists of information gathered from a local source.
Use graphing calculators to plot points and linear lines of regression
from a local source. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11C |
Determine the linear
regression equation of best fit. |
Using a graphing
calculator, find the linear regression equation of best fit. After
making a scatter plot on graph paper, draw a linear regression line of
best fit and find the equation for that line. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11D |
Make predictions from
graphs. |
Draw conclusions and make
predictions from linear graphs. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11E |
Determine the validity of
the sampling method described in a given study. |
Interpret the results of a
sampling method as valid or invalid. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11F |
Determine the degree of
dependence of two quantities specified by a two-way table. |
Use graphs to determine
whether there is a relationship between two quantities (e.g. high
positive, low positive, high negative, low negative, no relationship). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11G |
Describe questions of
experimental design. |
Write questions that can be
used to sample a population. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11H |
Use sampling techniques to
draw inferences about large populations. |
Use samples to determine
relationships between populations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.8
Standard: Algebra and Functions
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.8.11A |
Represent a linear pattern
algebraically and graphically. |
Make a graph and an
equation from a given list of data points. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11B |
Give examples of patterns
that occur in data from other disciplines. |
Find examples of patterns
that occur in data from related subjects. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response=
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| 2.8.11C |
Use patterns, sequences and
series to solve routine and non-routine problems. |
Determine and extend the
patterns of given sequences. Find a missing term in a pattern, given an
explicit rule or table.
Determine the rule of a given sequence. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11D |
Formulate expressions,
equations, and inequalities to model routine and non-routine problem
situations. |
Formulate expressions,
equations, and inequalities to represent routine and non-routine problem
situations. Write algebraic expressions from word expressions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11E |
Use equations to represent
lines. |
Given a line on a graph,
find the equation for that line. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11J |
Demonstrate the connection
between algebraic equations and inequalities and the geometry of relations
in the coordinate plane. |
Graph an equation or
inequality on the coordinate plane. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11K |
Select, justify and apply
an appropriate technique to graph a linear function in two variables,
including slope-intercept, x- and y- intercepts, and the use of a graphing
calculator. |
Graph linear functions by
correctly choosing the algebraic technique that applies to the situation.
Correctly use all of the algebraic techniques to graph linear functions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11L |
Write the equation of a
line when given the graph of the line, two points on the line, or the
slope of the line and a point on the line. |
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Write an equation of a line when given one of the following:
- the graph,
- two points on the line,
- the slope and a point on the line.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11M |
Given a set of data points,
write an equation for a line of best fit. |
Make a scatter plot, and
then find an equation that describes the data. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11N |
Solve equations and
inequalities both symbolically and graphically. |
Solve one step and
multi-step equations using symbol manipulation and by graphing the related
function. Solve rational equations.
Solve literal equations.
Solve inequalities using algebra and graph the solutions.
Solve compound inequalities. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11O |
Determine the domain and
range of a relation, given a graph or set of ordered pairs. |
Given the graph of a
relation, determine the domain and range. Given a set of ordered pairs,
determine the domain and range. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11P |
Analyze a relation to
determine whether a direct or inverse variation exists and represent it
algebraically and graphically. |
Determine whether a
relation varies directly or inversely. Represent direct and inverse
variations algebraically and graphically.
Determine whether the graph of a linear equation varies directly or
inversely. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11Q |
Represent all linear
functions in tables and graphs. |
Represent linear functions
in tables. Represent linear functions graphically. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11R |
Create and interpret
functional models. |
Use the distance formula to
create and interpret real life data. Use the interest formula to create
and interpret real life data.
Use real life information to create algebraic models that can be used
to interpret the situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11S |
Analyze properties and
relationships of linear and polynomial relations or functions. |
Analyze a linear function
for its slope, x-intercept(s), y-intercept, and other pertinent
information. Compare linear functions with respect to their slopes,
x-intercepts, and y-intercepts.
Identify polynomials (monomials, binomials, difference of two squares,
perfect square trinomials, etc).
Use FOIL to multiply binomials.
Completely factor polynomials. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11T |
Analyze and categorize
linear functions by their characteristics. |
Analyze functions, graphs,
tables, and ordered pairs to determine if they are linear. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.9
Standard: Geometry
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.9.11I |
Model situations
geometrically to formulate and solve problems. |
Use geometry formulas to
solve problem situations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.11
Standard: Concepts of Calculus
Course: Algebra I |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.11.11B |
Interpret maximum and
minimum values in problem situations. |
Answer questions that
involve maximum and minimum values contained in a problem situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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District Recommended Instructional Approaches For
the Course
To Drive Teacher’s Instructional Activities |
- Whole group instruction
- Small group instruction
- Projects
- Class discussion
- Peer evaluation
- Teacher and peer conferencing
- Oral presentations
- Individual instruction
- Research
- Dramatization
- Role playing
- Independent reading
- Read aloud
- Directed reading-thinking activities
- Modeling process
- Games
- Self-reflection
- Self-evaluation
- Independent study
- Guest speaker
- Guest reading
- Writing activities
- Thematic units
- Notebooks
- Study guides
- Computer technology
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