Download Alg I Unwrapped All Benchmarks SpecEd

“Unwrapping” Standard
Two-Column Template
Grade Level
9
Content Area Algebra 1
Standard(s) and/or Benchmark(s):
Standard 1: Read, write, compare, classify and represent real numbers, and use them to
solve problems in various contexts.
8.1.1.2 - Compare real numbers; locate real numbers on a number line. Identify the square root of
a positive integer as an integer, or if it is not an integer, locate it as a real number between two
consecutive positive integers.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Real numbers
- square root
- integer
Real number problems in various contexts
Square root
- integer square roots
- non integer square roots
- number line
Read
Write
Compare
Classify
Represent
Locate
Identify
Use
Solve
Read
Locate
Identify
Compare
Use
Solve
Represent
Overarching Questions:
1. How do we solve problems in various contexts?
Guiding Questions:
1. How are real numbers compared?
2. How are real numbers written in multiple forms?
3. How are square roots of positive integers calculated?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 1: Read, write, compare, classify and represent real numbers, and use them to
solve problems in various contexts.
8.1.1.4 – Know and apply the properties of positive and negative integer exponents to generate
equivalent numerical expressions.
Concepts
Real numbers
- positive integer exponents
- negative integer exponents
Properties of integer exponents
Equivalent numerical expressions
Integer exponent problems
-in various contexts
Skills
Read
Write
Compare
Classify
Represent
Know
Apply
Generate
Compare
Read
Write
Solve
Use
Understand
Overarching Questions:
1. How do we solve problems in various contexts?
Guiding Questions:
1. How can the properties of positive exponents be used to simplify expressions?
2. How can the properties of negative exponents be used to simplify expressions?
3. How can it be determined if two expressions are equivalent?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 2: Understand the concept of function in real-world and mathematical situations,
and distinguish between linear and non-linear functions.
8.2.1.2 - Use linear functions to represent relationships in which changing the input variable by
some amount leads to a change in the output variable that is a constant times that amount.
Concepts
Skills
Function
-linear
- input
- output
- variable
- constant
Understand
Use/Solve
Represent
Mathematical situations
- function
- relationships
- change
Understand
Distinguish
Represent
Linear functions
Non linear functions
Distinguish
Understand
Overarching Questions:
1. What is the difference between linear and non-linear functions?
Guiding Questions:
1. How does changing the input of a linear function affect the output?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 2: Understand the concept of function in real-world and mathematical situations,
and distinguish between linear and non-linear functions.
8.2.1.3 – Understand that a function is linear if it can be expressed in the form f(x) = mx + b or if
its graph is a straight line.
Concepts
Students need to know about:
Function
- Linear
f(x) = mx + b
Graph – straight line
Skills
Students need to be able to do:
Understand
Distinguish
Recognize
Manipulate
Overarching Questions:
1. What is the difference between linear and non-linear functions?
Guiding Questions:
1. How is a function recognized as linear?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s): Standard 3: Recognize, represent and solve linear
functions.
8.2.2.1 – Represent linear functions with tables, verbal descriptions, symbols, equations and
graphs; translate from one representation to another.
Concepts
-
Students need to know about:
Linear Functions
Tables
Symbols
Graphs
Verbal Descriptions
Equations
Skills
Students need to be able to do:
Recognize
Represent
Solve
Explain
Translate
Overarching Questions:
1. What are the different ways to represent linear functions?
Guiding Questions:
1.
2.
3.
4.
5.
How are functions represented with a graph?
How are functions represented with a table?
How are functions represented using language?
How are functions represented with an equation?
How are functions converted from one representation to another?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 3: Recognize, represent and solve linear functions.
8.2.2.2 – Identify graphical properties of linear functions including slopes and intercepts. Know
that the slope equals the rate of change, and that the y-intercept is zero when the function
represents a proportional relationship.
Concepts
Skills
Students need to know about:
Students need to be able to do:
- Linear Functions
Tables
Symbols
Graphs
Verbal Descriptions
Equations
Graphical properties
- Slope/rate of change
- y-intercept
- Proportional relationship
-
Recognize
Represent
Solve
Explain
Know
Identify
Overarching Questions:
1. What are the different ways to represent linear functions?
Guiding Questions:
1. What are some ways to represent functions using slope and intercepts?
2. How are slope and rate of change related?
3. Why is a linear function a proportional relationship when the
y-intercept is
zero?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 3: Recognize, represent and solve linear functions.
8.2.2.3 – Identify how coefficient changes in the equation f(x)=mx+b affect the graphs of linear
functions. Know how to use graphing technology to examine these effects.
Concepts
Skills
Students need to know about:
Students need to be able to do:
- Linear Functions
Tables
Symbols
Graphs
Verbal Descriptions
Equations
Coefficient changes
- f(x)=mx+b
- graphs
Recognize
Represent
Solve
Explain
Identify
Graphing technology
Examine
Compare
Overarching Questions:
1. What are the different ways to represent linear functions?
Guiding Questions:
1. How do changes in m and b affect the graph of f(x) = mx + b?
2. How can graphing calculators be used to study how changes in m and b affect the
graph of f(x) = mx + b?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 4: Generate equivalent numerical and algebraic expressions and use algebraic
properties to evaluate expressions.
8.2.3.1 – Evaluate algebraic expressions, including expressions containing radicals and absolute
values, at specified values of their variables.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Expressions
- Numerical Expressions
- Algebraic Expressions
- Equivalent expressions
- Radicals
- Absolute Values
Generate
Use
Evaluate
Algebraic Properties
Use
Evaluate
Overarching Questions:
1. How are expressions simplified and evaluated?
Guiding Questions:
1. How are expressions containing radicals simplified and evaluated?
2. How are expressions containing absolute value simplified and evaluated?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 4: Generate equivalent numerical and algebraic expressions and use algebraic
properties to evaluate expressions.
8.2.3.2 – Justify steps in generating equivalent expressions by identifying the properties used,
including the properties of algebra. Properties include the associative, commutative and
distributive laws, and the order of operations, including grouping symbols.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Expressions
- Numerical Expressions
- Algebraic Expressions
- Equivalent expressions
Generate
Use
Evaluate
Algebraic Properties
- Associative
- Commutative
- Distributive
- Order of operations w/grouping
symbols
Use
Justify
Identify
Overarching Questions:
1. How are expressions simplified and evaluated?
Guiding Questions:
1. What steps are involved in generating equivalent expressions?
2. What properties are used in generating equivalent expressions?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 5: Represent real-world and mathematical situations using equations and
inequalities involving linear expressions. Solve equations and inequalities symbolically and
graphically. Interpret solutions in the original context.
8.2.4.2 – Solve multi-step equations in one variable. Solve for one variable in a multi-variable
equation in terms of the other variables. Justify the steps by identifying the properties of
equalities used.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Linear equations
- Multi step equations in one variable
- Multi variable equations
- Solutions
Solve
Justify
Represent situations
Interpret
Real world and mathematical situations
Represent
Interpret
Solve
Properties of equalities
Identify
Justify
Overarching Questions:
1. How are real-world situations represented using linear equations and inequalities?
Guiding Questions:
1. How are multi-step equations solved in one variable?
2. How are equations solved for a variable?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 5: Represent real-world and mathematical situations using equations and
inequalities involving linear expressions. Solve equations and inequalities symbolically and
graphically. Interpret solutions in the original context.
8.2.4.3 – Express linear equations in slope-intercept, point-slope and standard forms, and convert
between these forms. Given sufficient information, find an equation of a line.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Linear equations
- Slope-intercept
- Point-slope
- Standard form
Represent
Convert
Express
Interpret
Equation of a line
- Symbolically/graphically
- Real world and mathematical
Find
Interpret
Express
Solve
Overarching Questions:
1. How are real-world situations represented using linear equations and inequalities?
Guiding Questions:
1. How are linear equations represented using point-slope form, slope-intercept
form, and standard form?
2. How are linear equations converted between slope-intercept, point-slope, and
standard forms?
3. How is the equation of a line determined in multiple ways?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 5: Represent real-world and mathematical situations using equations and
inequalities involving linear expressions. Solve equations and inequalities symbolically and
graphically. Interpret solutions in the original context.
8.2.4.5 – Solve linear inequalities using properties of inequalities. Graph the solutions on a
number line.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Linear inequalities
- coordinate system
- solutions
- properties
Solve
Graph
Interpret
Apply
Real world and mathematical situations
Represent
Interpret
Graph
Overarching Questions:
1. How are real-world situations represented using linear equations and inequalities?
Guiding Questions:
1. How are linear inequalities solved?
2. How are solutions of linear inequalities represented graphically?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 5: Represent real-world and mathematical situations using equations and
inequalities involving linear expressions. Solve equations and inequalities symbolically and
graphically. Interpret solutions in the original context.
8.2.4.8 – Understand that a system of linear equations may have no solution, one solution, or an
infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting,
parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations
in two unknowns by substituting the numbers into both equations.
Concepts
Students need to know about:
Systems of linear equations
- one solution/intersecting
- no solution/parallel
- infinite/identical
Skills
Students need to be able to do:
Solve
Interpret graphs and solutions
Recognize
Relate
Understand
Check/substitute
Overarching Questions:
1. How are real-world situations represented using linear equations and inequalities?
Guiding Questions:
1. How are solutions to systems of linear equations determined?
2. How do solutions to a system of linear equations relate to the graph?
3. How can solutions to a system of linear equations be verified?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 6: Solve problems involving right triangles using the Pythagorean Theorem and
its converse.
8.3.1.1 – Use the Pythagorean Theorem to solve problems involving right triangles.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Pythagorean theorem
- converse
- right triangle
- problems
Recognize
Use
Solve
Overarching Questions:
1. How are problems involving right triangles solved?
Guiding Questions:
1. How is the Pythagorean Theorem used to solve problems involving right
triangles?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 8.3.2: Solve problems involving parallel and perpendicular lines on a coordinate
system.
8.3.2.3 – Given a line on a coordinate system and the coordinates of a point not on the line, find
lines through that point that are parallel and perpendicular to the given line, symbolically and
graphically.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Parallel and perpendicular lines in
coordinate system
- line through a given point
Find equation and graph
Overarching Questions:
1. How are problems that involve parallel and perpendicular lines solved?
Guiding Questions:
1. How are equations for parallel and perpendicular lines determined graphically?
2. How are equations for parallel and perpendicular lines determined symbolically?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.
Standard(s) and/or Benchmark(s):
Standard 8.4.1: Interpret data using scatterplots and approximate lines of best fit. Use
lines of best fit to draw conclusions about data.
8.4.1.1 – Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to
informally estimate a line of best fit and determine an equation for the line. Use appropriate
titles, labels and units. Know how to use graphing technology to display scatterplots and
corresponding lines of best fit.
Concepts
Skills
Students need to know about:
Students need to be able to do:
Scatterplot
- lines of best fit
- data
- shape
- title, labels, units
Interpret
Use
Conclude
Collect
Display
Graphing technology
Approximate/estimate
Lines of best fit
- equation of line
Determine
Interpret/conclude
Graphing technology
Overarching Questions:
1. How is data interpreted?
Guiding Questions:
1.
2.
3.
4.
How is data interpreted using scatter plots?
How is a line of best fit determined?
How can a scatter plot and line of best fit be displayed using technology?
How can technology help determine the equation for the line of best fit?
© 2006 by Elizabeth Menderhall, Brad Phelps, and Deanna York, Wayne Township Public Schools,
Indianapolis, IN
All rights reserved.