Download SLV RT3 - Toe the Line - Integrated Math Unit 2

Curriculum Development Overview
Unit Planning for High School Mathematics
Unit Title
Toe the Line
Length of Unit
Focusing Lens(es)
Modeling
Equivalence
Inquiry Questions
(EngagingDebatable):
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Unit Strands
Number and Quantity: Quantities
Algebra: Creating Equations
Algebra: Reasoning with Equations and Inequalities
Functions: Interpreting Functions
Statistics and Probability: Interpreting Categorical and Quantitative Data
Concepts
Linear models, constant rate of change, slope, correlation, residual plots, predictions, data, equivalence, algebraic representations, y-intercept
Standards and Grade
Level Expectations
Addressed in this Unit
4 weeks
MA10-GR.HS-S.1-GLE.2
MA10-GR.HS-S.2-GLE.1
MA10-GR.HS-S.2-GLE.4
MA10-GR.HS-S.3-GLE.1
Why do adults over generalize the concept of linearity to all real world phenomena? Can you think of an example?
Generalizations
My students will Understand that…
Factual
Guiding Questions
Conceptual
Linear models describe situations with a constant rate of
change (slope). (MA10-GR.HS-S.3-GLE.1-EO.c.i)
What is slope?
How can I tell if a situation has a constant rate of
change?
Why can you only model situations with constant rates of
change with linear functions?
Correlation coefficients can determine the usefulness of
linear models for describing data and making predictions.
(MA10-GR.HS-S.3-GLE.1-EO.b.ii)
What is a correlation coefficient?
Where do I find correlation coefficient on the graphing
calculator?
How do I determine if I have a strong or weak linear
correlation?
Why is important to know the strength of a correlation
for a set of data?
Why does correlation not imply a causal relationship?
Why is a linear model not always the best choice for all
data sets?
Mathematicians focus on the slope and y-intercept of a
linear model when transforming representations and
interpreting situations. (MA10-GR.HS-S.3-GLE.1-EO.c.i)
What is a y-intercept?
What is a solution?
How do I transfer between algebraic and graphical
forms of a line?
How do I interpret the meaning of the y-intercept in
context?
What does it mean to be a solution of an equation or
inequality?
Why is it important to be able to represent a linear
function in multiple ways?
Authors of the Sample: Robin Gersten (Eagle County RE 50); Lori McMullen (Adams-Arapahoe 28J)
High School, Mathematics
Complete Sample Curriculum – Posted: February 15, 2013
Page 5 of 23
Curriculum Development Overview
Unit Planning for High School Mathematics
The points on the graph of an equation represent the set
of all solutions for a context often forming a curve (which
could be a line). (MA10-GR.HS-S.2-GLE.4-EO.e.i)
Key Knowledge and Skills:
My students will…
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How can you determine from a graph if an ordered is
part of the solution set of an equation?
Why is it important to coordinate and understand the
units of problem when determining solutions to the
problem?
What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics
samples what students should know and do are combined.
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the
scale and origin in graphs and data displays. (MA10-GR.HS-S.1-GLE.2-EO.a.i.1,2)
Interpret the scale and origin in a graph
o Explain how changing the scale and origin affects the presentation of the data
Choose an appropriate scale and origin for a graph or data display
o Use appropriate units and select appropriate spacing for tic marks on the x and y axis
Choose an appropriate origin
Define appropriate quantities for the purpose of descriptive modeling. (MA10-GR.HS-S.1-GLE.2-EO.a.ii)
Create appropriate descriptive models to represent real-world math scenarios
o Identify and select variables in a real-world situation that represent essential features of the situation
o Develop a model (graph, table, diagram, algebraic equation or other descriptive representation) that describes the relationship between the
variables
Differentiate between descriptive and analytical models
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. (MA10-GR.HS-S.1-GLE.2-EO.a.iii)
Create appropriate descriptive models to represent real-world math scenarios
o Identify and select variables in a real-world situation that represent essential features of the situation
o Develop a model (graph, table, diagram, algebraic equation or other descriptive representation) that describes the relationship between the
variables
Differentiate between descriptive and analytical models
Graph linear functions and show intercepts. (MA10-GR.HS-S.2-GLE.1-EO.c.ii)
Graph linear functions and determine x and y intercepts
Graph exponential functions
o Identify the y intercept
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (MA10-GR.HS-S.2-GLE.4-EO.a.iv)
Rearrange formulas to highlight a quantity of interest (limit to formulas with a linear focus)
Use principles of operations to isolate variables and to solve equations
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (MA10-GR.HS-S.2-GLE.4-EO.c.i)
Understand the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). (MA10Authors of the Sample: Robin Gersten (Eagle County RE 50); Lori McMullen (Adams-Arapahoe 28J)
High School, Mathematics
Complete Sample Curriculum – Posted: February 15, 2013
Page 6 of 23
Curriculum Development Overview
Unit Planning for High School Mathematics
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GR.HS-S.2-GLE.4-EO.e.i)
Solve linear equations in one variable
Solve linear inequalities in one variable
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (MA10-GR.HS-S.3-GLE.1-EO.b.ii)
Represent data on a scatter plot
Construct a line of best fit and describe the function for data on two quantitative variables
Use scatter plots to determine the strength of the relationship between two data sets
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Fit a function to the data; use functions fitted to data to solve problems in the context of the data. (MA10-GR.HS-S.3-GLE.1-EO.b.ii.1)
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Identify and interpret x and y intercepts in the context of a problem
Interpret the slope and intercept of a linear model
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Fit a linear function for a scatter plot that suggests a linear association
Fit a linear function for a scatter plot that suggests a linear association. (MA10-GR.HS-S.3-GLE.1-EO.b.ii.3)
Fit a linear function for a scatter plot that suggests a linear association
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (MA10-GR.HS-S.3-GLE.1-EO.c.i)
Compute (using technology) and interpret the correlation coefficient of a linear fit. (MA10-GR.HS-S.3-GLE.1-EO.c.ii)
Explain the concept of correlation
Given a correlation coefficient, assess the strength of the correlation between two variables
Using technology, compute and interpret the correlation coefficient of a linear fit
Distinguish between correlation and causation. (MA10-GR.HS-S.3-GLE.1-EO.c.iii)
Distinguish between correlation and causation
Describe the factors affecting take-home pay and calculate the impact. (MA10-GR.HS-S.1-GLE.2-EO.a.iv) *
Distinguish between gross pay, net pay, and take-home pay
Calculate the impact of the monthly cost of health insurance and income tax on take-home pay
Calculate the change in take home pay when there is a specific increase in income tax
Calculate the decrease in take home pay if the cost of health insurance changes due to the addition of a new family member
Design and use the budget, including income (i.e., net take-home pay) and expenses to demonstrate how living within your means is essential for a secure financial future.
(MA10-GR.HS-S.1-GLE.2-EO.a.v) *
Categorize monthly expense into wants and needs
Given a specific take-home pay amount, design a budget that is within one’s means
Contrast the monthly budget of two different income levels with two different life styles
Critical Language: includes the Academic and Technical vocabulary, semantics, and discourse which are particular to and necessary for accessing a given discipline.
EXAMPLE: A student in Language Arts can demonstrate the ability to apply and comprehend critical language through the following statement: “Mark Twain exposes the
hypocrisy of slavery through the use of satire.”
Authors of the Sample: Robin Gersten (Eagle County RE 50); Lori McMullen (Adams-Arapahoe 28J)
High School, Mathematics
Complete Sample Curriculum – Posted: February 15, 2013
Page 7 of 23
Curriculum Development Overview
Unit Planning for High School Mathematics
A student in ______________ can demonstrate the
ability to apply and comprehend critical language
through the following statement(s):
I can use linear models to describe situations with a constant rate of change (slope).
Academic Vocabulary:
Solve, identify, compare, analyze, develop, definition, interpret, association, recognize, predictions, data,
Technical Vocabulary:
Slope, y-intercept, x-intercept, scatterplot, correlation, correlation coefficient, residuals, literal equation, inequality, solution, linear models, constant
rate of change, equivalence
* Denotes a connection to Personal Financial Literacy (PFL)
Authors of the Sample: Robin Gersten (Eagle County RE 50); Lori McMullen (Adams-Arapahoe 28J)
High School, Mathematics
Complete Sample Curriculum – Posted: February 15, 2013
Page 8 of 23