Introduction to Math Unit 5

BY THE END OF THIS UNIT:

CORE CONTENT

Cluster Title: Creating Equations
Standard A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Concepts and Skills to Master
·  Write and graph an equation to represent a linear relationship
·  Model a data set using an equation
·  Write the equation of a line given two points or given the graph of a line in the coordinate plane.

SUPPORTS FOR TEACHERS

Critical Background Knowledge
Coordinates, plotting in the coordinate plane, interpreting tables of values, determining patterns
Academic Vocabulary
Linear relationship, slope, rate of change, variable, dependent and independent variable, domain, range, scale
Suggested Instructional Strategies
·  Use real-world application to generate a table of values. Use to table to construct a function that models a linear relationship.
·  Use technology to explore a variety of linear graphs / Resources
Sample Formative Assessment Tasks
Skill-based task
Write and graph an equation that models the cost of buying and running an air conditional with a purchase price of $250 which costs $0.38/hr to run. / Problem Task

CORE CONTENT

Cluster Title: Use functions to model relationships between quantities
Standard 8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Concepts and Skills to Master
·  Determine and interpret the rate of change given two points, a graph, a table of values, a geometric representation, or a story problem (verbal description) of a linear relationship.

SUPPORTS FOR TEACHERS

Critical Background Knowledge
Coordinates, plotting in the coordinate plane, interpreting tables of values, determining patterns
Academic Vocabulary
Linear relationship, slope, rate of change
Suggested Instructional Strategies
·  Use real-world application to generate a table of values. Use to table to construct a function that models a linear relationship.
·  Connect to other standards in the Expressions and Equations domain. / Resources
Sample Formative Assessment Tasks
Skill-based task
The student council is planning a trip to Carowinds. There is a $500 deposit for the trip and the tickets will cost $15 per student. Construct a function, build a table, and graph the data showing how much it will cost for the students’ trip. Determine the domain, range and rate of change for the function using the information provided in the table and graph. / Problem Task
Wally created the table below for a function he knows to be linear. He thinks something must be wrong with his table because he can’t find the original pattern from the table. Find the error and the original pattern. Explain your strategy for finding the error.
X / 3.2 / 6.4 / 9.6 / 12.8 / 16 / 19.2 / 22.4 / 25.6
Y / 17.8 / 30.6 / 43.4 / 56.2 / 66 / 81.8 / 94.6 / 107.4

CORE CONTENT

Cluster Title: Solve equations and inequalities in one variable
Standard A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Concepts and Skills to Master
·  Write inequalities in equivalent forms to solve problems.
·  Verify that a given number or variable is a solution to an inequality.
·  Use graphs, tables, and algebra to solve multi-step inequalities

SUPPORTS FOR TEACHERS

Critical Background Knowledge
Arithmetic fluency, solve multi-step equations
Academic Vocabulary
Inequality, inverse operation, <, >, ≥, ≤, interval notation
Suggested Instructional Strategies
·  Use applications from a variety of disciplines to motivate solving linear inequalities
·  Use TI84 calculator app to reinforce solving 1- and 2-step inequalities / Resources
·  Textbook Correlation: 2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8, 3-2, 3-3, 3-4, 3-5, 3-6
Sample Formative Assessment Tasks
Skill-based task
Solve for x: 3(x – 4) + 2x 7x – 5(2x – 8) / Problem Task
Solve 3(x – 4) + 2x 7x – 5(2x – 8) using a method of your choice (i.e. using tables, graphing, or algebraically). Explain why you chose your particular method.

CORE CONTENT

Cluster Title: Understand the concept of a function and use function notation
Standard F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Concepts and Skills to Master
·  Write equations using function notation
·  Use function notation to evaluate functions for given inputs in the domain
·  Interpret statements that use function notation in terms of the context in which they are used

SUPPORTS FOR TEACHERS

Critical Background Knowledge
·  Evaluate expressions
·  Familiarity with function notation
Academic Vocabulary
Function notation, evaluate, input, domain, output, range
Suggested Instructional Strategies / Resources
·  Explore a variety of types of situations modeled by functions.
·  Have students create contextual examples that can be modeled by linear or exponential functions / ·  Textbook Correlation: 4-6
·  Exponential Functions Lesson (contributed by S.Milton TI)
Sample Formative Assessment Tasks
Skill-based task
1.  Given f(x) = 3x find f(4)
2.  What does f(5) = 7 mean?
3.  Write an expression for the relationship depicted in the graph using function notation.
/ Problem Task
Find a function from science, economics, or sports; write it in function notation and explain its meaning at several points in its domain.

CORE CONTENT

Cluster Title: Interpret functions that arise in applications in terms of a context.
Standard F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end-behavior; and periodicity.
Concepts and Skills to Master
·  Given a graph, identify key features such as x-and y-intercepts and intervals where the function is increasing or decreasing
·  Given a table of values, identify key features such as x- and y-intercepts and intervals where the function is increasing or decreasing
·  Find key features of a function and use them to graph the function
·  Given a table of values for an exponential function, write a next-now equation and determine the growth factor
·  Given a table of values for a linear function, write a next-now equation, determine the slope and write an equation

SUPPORTS FOR TEACHERS

Critical Background Knowledge
·  Ability to graph a linear or exponential function from a table or equation
Academic Vocabulary
Increasing, decreasing, intercepts
Suggested Instructional Strategies / Resources
·  Use graphing technology to explore and identify key features of a function.
·  Use key features of a function to graph functions by hand / ·  Textbook Correlation: 4-2, 4-3, 5-3, 5-4, 5-5, 7-6, 7-7, 9-1, 9-2, 9-7, 11-7
Sample Formative Assessment Tasks
Skill-based task
Identify the intervals where the function is increasing and decreasing.
/ Problem Task
Create a story that would generate a linear or exponential function and describe the meaning of key features of the graph as they relate to the story.

CORE CONTENT

Cluster Title: Explain volume formulas and use them to solve problems.
Standard G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Concepts and Skills to Master
·  Find the volume of cylinders, pyramids, cones, and spheres in contextual problems.

SUPPORTS FOR TEACHERS

Critical Background Knowledge
·  Formula for the volume of cones, cylinders, and spheres (8.G.9)
Academic Vocabulary
Pyramid, cylinder, cone, sphere, volume, length, width, height, base, radius, π
Suggested Instructional Strategies / Resources
·  Have students bring household objects with the given characteristics. Provide opportunities for students to measure with rulers or tape measures to gather needed information. Compute the volume of the objects.
·  Make connections between metric measurements. For example, using rice to fill a cylinder compares the liquid volume in liters and the geometric volume in cubic meters. / ·  Textbook Correlation: check Pearson website – geometry book.
Sample Formative Assessment Tasks
Skill-based task
Find the volume of a cylindrical oatmeal box. / Problem Task
Given a three-dimensional object, compute the effect on volume of doubling or tripling one or more dimensions (for example, how is the volume of a cone affected by doubling the height?)

CORE CONTENT

Cluster Title: Reason quantitatively and use units to solve problems
Standard N.Q.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities
Concepts and Skills to Master
·  Determine whether whole numbers, fractions, or decimals are most appropriate
·  Determine the appropriate power of ten to reasonably measure a quantity
·  Determine the resulting accuracy in calculations
·  Determine what level of rounding should be used in a problem situation

SUPPORTS FOR TEACHERS

Critical Background Knowledge
·  Understand basic units of measurements and their relationship to one another (e.g. a foot is smaller than a yard)
·  Understand how to properly round and estimate
Academic Vocabulary
Precision, accuracy
Suggested Instructional Strategies / Resources
·  Discuss misconceptions in resulting calculations involving measurement, e.g. you cannot increase accuracy through calculation, only through more accurate measurement
·  Compare the difference between rounding at different places in a calculation and discuss which yields the best result
·  Discuss how mathematicians maintain precision through the representations that they use.
Sample Formative Assessment Tasks
Skill-based task / Problem Task

Standards are listed in alphabetical /numerical order not suggested teaching order.

PLC’s must order the standards to form a reasonable unit for instructional purposes.

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