Download Big Idea - Southwest Washington Mathematics

Systems of Equations
Targets, Sub-Targets & BIG IDEAS
Practice 1. Make sense of problems and persevere in solving them.
Practice 3: Construct viable arguments and critique the reasoning of others.
Practice 4. Model with mathematics.
Practice 5: Use appropriate tools strategically.
Practice 6. Attend to precision.
Big Idea: Write and solve a system of equations with two variables.
Common Core Standards
Course Content
MAJOR CONTENT
A.CED I can create equations and inequalities that describe numbers or relationships.
 A-CED.2 Create equations in two or more variables to
 Create equations with two variables to represent relationships
represent relationships between quantities; graph equations on
between two quantities from a verbal description or tables.
coordinate axes with labels and scales.
 Graph equations on coordinate axes with labels and scales.
 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. 
 A-CED.4 Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations. 
Notes/Examples
“verbal description” is a word
problem.
 Interpret solutions in the context of the situation and determine
if they are reasonable.
Inequalities are in a separate unit.
 Rearrange an equation to solve for a variable
Use for the substitution method, or to
enter a function into technology that
needs to be entered as y =___.
A-REIa I can solve equations and inequalities.
 A-REI.1 Explain each step in solving a simple equation as following
from the equality of numbers asserted at the previous step, starting from
the assumption that the original equation has a solution. Construct a
viable argument to justify a solution method.
 Show the steps used for solving an equation.
 Use properties of numbers to justify each step of a
solution
o Properties: associative, commutative, distributive,
additive and multiplicative identity, additive and
multiplicative inverse and zero.
o Other justification: combine like terms
 A-REI.3 Solve linear equations and inequalities in one variable, including
 Solve linear equations in one variable.
equations with coefficients represented by letters.
Algebra 1 by Southwest Washington Common Core Mathematics Consortium is licensed
under a Creative Commons Attribution 4.0 International License 5/31/15
This applies when you combine two
equations with two variables to get
one equation with one variable.
The focus is on the conceptual
understanding.
The focus is procedural fluency.
o A-REI 1 and 3 are
connected.
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Systems of Equations
Targets, Sub-Targets & BIG IDEAS
Practice 1. Make sense of problems and persevere in solving them.
Practice 3: Construct viable arguments and critique the reasoning of others.
Practice 4. Model with mathematics.
Practice 5: Use appropriate tools strategically.
Practice 6. Attend to precision.
A-REIb I can solve a system of equations.
 A-REI.5 Prove that, given a system of two
 Produce equivalent equations by multiplying or
This standard is to provide justification and conceptual
equations and two variables, replacing one equation
dividing each equation by the same constant.
understanding for the combination method of solving
by the sum of that equation and a multiple of the
 Combining equivalent equations produces an
systems by transforming a given system of two equations
other produces a system with the same solutions.
equation that also passes through the solution of the into a equivalent system that has the same solutions as the
original system.
original.
* The Coin Combination Task
The focus is on the conceptual understanding.
Students can use www.geogebra.org or www.desmos.com.
 Explain and identify why some linear systems have
Use the combination and substitution methods (algebraically)
infinitely many solutions or no solution.
 Solve a system of linear equations to find an exact
Can use a graphing calculator to highlight the solutions with
solution.
the table function.
 Determine the approximate solution to a system by
graphing both equations and estimating the point of
The focus is on the procedural fluency.
intersection.
A-REIc I can represent and solve equations and inequalities graphically.
Can use technology to graph and
 A‐REI.10 Understand that the graph of an equation in two variables is the set  Understand that every point (x, y) on the line is a
solution to the equation.
trace lines to understand the
of all its solutions plotted in the coordinate plane, often forming a curve (which
 Verify that any point (x, y) on the line is a solution meaning of solutions.
could be a line).
to the equation.
 A-REI.11 Explain why the x coordinates of the points where the graphs of the  Set up a system of equations and use technology This is not referring to substitution.
to find or approximate a solution to a one variable 3(x + 1) = 2x + 5
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,
equation.
You can graph and find the
make tables of values, or find successive approximations. Include cases where
intersection of:
f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential and
y = 3(x + 1)
logarithmic functions.
y = 2x + 5
 A-REI.6 Solve systems of linear equations of two
variables exactly and approximately (e.g. with
graphs), focusing on pairs of linear equations in two
variables.
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Systems of Equations
Targets, Sub-Targets & BIG IDEAS
SUPPORTING CONTENT
Practice 1. Make sense of problems and persevere in solving them.
Practice 3: Construct viable arguments and critique the reasoning of others.
Practice 4. Model with mathematics.
Practice 5: Use appropriate tools strategically.
Practice 6. Attend to precision.
N-Q I can reason quantitatively and use units to solve problems.
 N-Q.1 Use units as a way to understand problems and to guide the solutions  Identify or choose the appropriate unit of
Units of measures may look like
of multi-step problems; choose and interpret units consistently in formulas;
measure according to the context.
“adult tickets” and “student tickets”.
choose and interpret the scale and the origin in graphs and data displays.
 Include units with answers.
 N-Q.2 – Define appropriate quantities for the purpose of descriptive
 Determine and interpret appropriate quantities
If the units are not provided in the
modeling.
when solving systems in context.
system, then students need to
determine which units are needed.
If one equation is measured in
minutes and another is measured in
hours, then students need to convert
to one unit.
 N-Q.3 – Choose a level of accuracy appropriate to limitations on
 Determine the accuracy of values based on their
For example, problems involving
measurement when reporting quantities.
limitations in the context of the situation.
money need to be rounded to 2
decimal places.
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