Download Algebra 1: Unit 6 Systems of Equations and Inequalities.docx

Wentzville School District
Algebra 1: Unit 6
Stage 1 – Desired Results
Unit 6 Systems of Equations and Inequalities
Unit Title: Systems of Equations/Inequalities
Course: Algebra I
Brief Summary of Unit: Students will be able to solve systems of equations by graphing, substitution, and elimination.
Students will learn to interpret the point of intersection of two graphs as meaningful in a given real world situation.
Students will graph and solve systems of linear inequalities to represent real world situations.
Textbook Correlation: Glencoe Algebra I Chapter 6.1 - 6.6 (6.1 with technology)
Time Frame: 3 weeks
WSD Overarching Essential Question
Students will consider…
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How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
How do I effectively represent quantities and
relationships through mathematical notation?
WSD Overarching Enduring Understandings
Students will understand that…
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Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
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How accurate do I need to be?
When is estimating the best solution to a
problem?
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strategies.
Concrete understandings in math lead to more
abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
know that a system of equations or inequalities can be written to model a real world situation.
Meaning
Essential Questions
Understandings
Students will consider questions such as . . .
Students will understand that . . .
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How many solutions does a system of equation
have?
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Which method of solving a system of equations
(graphing, substitution or elimination) would be
most useful in different situations?
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What is the significance of the intersection point?
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In what real world situations is the intersection
point meaningful?
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When a system of equations does not have a
single solution, what does it mean?
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In a system of inequalities, what does the solution
mean?
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How can technology aide in finding the solution to
a system of equations?
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What is a viable solution to a system of
inequalities?
Acquisition
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The point of intersection or common solution is
where the functions share the same outcome. In
a real world situation this point of intersection is
meaningful.
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Systems of equations can be used to model real
world situations to determine real world
solutions.
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When two different functions can model the
same scenario, their point of intersection
describes where the models coincide.
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Systems of equations can be solved by graphing,
substitution and elimination. Each method has
benefits and drawbacks.
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The number of solutions of a system of equations
is dependent on the nature of the lines in the
system.
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There is an infinitely number of solutions to a
system of inequalities.
Acquisition
Key Knowledge
Key Skills
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System of Equations
Infinite number of solutions (same line,
coincident)
No solutions (parallel lines)
One Solutions (intersecting lines)
Substitution
Linear combination (elimination)
System of Inequalities
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Solve a system of equations using a graphing
utility to include graphing and viewing a table.
Determine the number of solutions of a system.
Write and solve a system of equations that
represents a real world situation.
Use substitution to solve a system.
Use elimination to solve a system.
Show that regardless the method of solution, the
result will be the same.
Solve a system of inequalities.
Apply system of linear inequalities in real world
situations.
Standards Alignment
MISSOURI LEARNING STANDARDS
A.REI.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.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear
equations in two variables.
A.CED 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.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.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.
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.
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.
SHOW-ME STANDARDS
Goals:
1.1, 1.4, 1.5, 1.6, 1.7, 1.8
2.2, 2.3, 2.7
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
4.1, 4.4, 4.5, 4.6
Performance:
Math 1, 4, 5