Extend the domain of trigonometric functions using the unit circle
Analyze functions using different representations
Interpret functions that arise in applications in terms of the context
Model periodic phenomena with trigonometric functions
Prove and apply trigonometric identities
Summarize, represent, and interpret data on two categorical and quantitative variables
Build a function that models a relationship between two quantities
Build new functions from existing functions
Essential Questions What relationships between quantities can be modeled by functions? What does it mean to solve equations graphically? What are the similarities and differences between linear, quadratic, and exponential functions? How does the arithmetic of rational numbers relate to simplifying rational expressions? What does a graph of a function represent? How can you represent the zeroes of a function? How can you describe and show the ways you can find the zeroes (roots) of a function? How can the formula for the sum of a finite geometric series be derived and used to solve problems? How can you use the Binomial Theorem to expand powers of expressions? What is a function and how does it model a relationship between two quantities? How would you write a function that describes a relationship between two quantities? What are the differences and similarities between real and complex solutions of polynomial equations? Explain graphically or algebraically? How do you differentiate between an exponential and a logarithmic function? How and when do we use the laws of logarithms? How do you write the equation of a circle? What is the angle of rotation, how is it measured? How can you explain the unit circle? How can sine, cosine, and tangent functions be defined using the unit circle? What are periodic functions? Why is modeling them so important? Why is the Theorem of Pythagoras so essential?
Key: Green = Major Clusters; Blue = Supporting; Yellow = Additional Clusters
21st Century Skills Standard and Progress Indicators:
CRP4. Communicate clearly and effectively and with reason.CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.CRP11. Use technology to enhance productivity. CRP12. Work productively in teams while using cultural global competence.
A.SSE.A.2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
Pacing
3 days
ObjectivesSWBAT
Review how to find the zeros of polynomial functions and sketch the graph of the function while identifying the y-intercept
Identify ways to rewrite or factor expressions by using the difference of two squares and/or the diamond and box method
Write polynomial functions as a product of 2-4 factors or binomials over
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect:A-SSE.2 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 1 Topic A, Lessons 2-11Module 1 Topic B, Lessons 12, 13
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations –
The standards assessments below are in EdConnect. These are the quizzes/tests for that standard.
Algebra Touchpoint - A-SSE.2
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Shawn builds a rectangular sheep pen and then builds a feeding structure inside the pen.
Part A. Rectangular Sheep Pen. The area of the sheep
pen is modeled by the polynomial
square feet, where
Write an equivalent expression for the area that models the length and width of the pen. The expressions will be in terms of xand y.
Part B. Feeding Structure. Shawn builds a feeding structure inside the sheep pen. The area of sheep pen without including the area of the feeding
structure is
Write a polynomial expression that models the length and width of the area of the feeding structure. The expressions will be in terms of x and y. What shape is the feeding structure?
Use words, numbers, and/or pictures to show your work.
Write the dimensions of 2D/3D shapes given the area and volume as variable expressions and write an expression for the area of a shape given variable expressions for the dimensions
Use an appropriate factoring technique to rewrite quadratic equations in vertex form and determine the maximum height of the path of an object given a quadratic equation in a real world problem
Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Special Education Students Allow errors Rephrase questions,
Build on student’s motivations/future careers/aspirations
A.APR.B.2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
Pacing
3 days
ObjectivesSWBAT
Review factoring polynomials by Greatest Common Factor and by using special cases, such as difference of two squares, sum and difference of two cubes, perfect square
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect:A-APR.2 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 1, Topic B, Lessons 18, 19https://www.engageny.org/search-site?search=a-apr.2
Option 2– Slides review81-110, and Remainder Theorem 111-122
The standards assessments below are in EdConnect. These are the quizzes/tests for that standard.
Algebra Touchpoint - A-APR.2
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
A-APR.2 - Type 2-3 Question Bank
Part A. Write a cubic function that passes through the
points
Part B. Does your function also pass through Explain why or why not.
Part C. What is the remainder of your function when
you divide it by
Part D. Suppose the remainder of your function is 84
when you divide it by where p is a positive integer. What could be the value of p?
trinomials with leading coefficient of 1, trinomials with leading coefficient greater than 1 and by grouping
Understand the relationship between zeros and the factors of polynomials by knowing and applying the Remainder Theorem by using long division and synthetic division when possible
Find the value of functions given the polynomial expression as a factor of the function.
Write and graph the polynomial that passes through points on the x-axis (zeros).
Distinguish whether or not certain functions pass through the x-axis
Critique the
Option 4 – PearsonSee activities and resources
[Standard A.PR.2]Centers
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test/skills assessment data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Use words, numbers, and/or pictures to show your work.
F.IF.B.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.
Pacing
3 days
ObjectivesSWBAT
Given a factored function or a quadratic function, state the x and y intercepts and
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect:F-IF.4 - Type 2-3 Bank
Direct InstructionOption 1–Module 3 Topic C, Lessons 17-20, 21
Teacher Center – The teacher works in a small group with 1-4 students.
Algebra Touchpoint - F-IF.4
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Car Values
Kelly bought a new car 5 years ago. She paid $15,000 for the car. Each year, the car depreciated in value as shown in the table below.
Part A. What function could Kelly use to model the value of her car after 10 years? Explain how you built your function.
Part B. Graph your function. How do the key features of the graph relate to Kelly’s situation?
Part C. Kelly hopes to use the car for 10 years before selling it. What will the value of her car be in 10 years?
Part D. Kelly would prefer to sell her car forat least $4,000 so that she can have a down payment for her next car. How long can Kelly keep her car before she sells it, if she hopes to sell it for $4,000 or more?
Part E. Consider the data below on two other models of cars. Graph the functions that represent the values
state when the graph is increasing or decreasing (including identifying maximums, minimums, vertex, axis of symmetry and zeros)
Create a graph or a function from a real world problem and interpret the meaning of its intercepts, identify maximum height and distance traveled of an object and label the graph by choosing scales and units
Given a table of values of a quadratic function f(x), find the equation of the line of symmetry for the graph
graph the functions f(x) = log(x), g(x) = log2(x), and h(x) = ln(x) by hand and identify key
Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Classwork
Exit Ticket
Special Education Students Allow errors Rephrase questions,
directions and explanations
Allow extra time to
of these two models on the same coordinate grid as the function that represents the value of Kelly’s car. How do they compare to Kelly’s car? How will the values of the three cars compare over time? Explain your answer using evidence from the values listed below and your graph.
Model A. New price: $20,000. Annual depreciation: 2.3%
Model B. New price: $10,000. Annual depreciation: 1.7%
compare the graph of an exponential function to the graph of its corresponding logarithmic function and note the geometric relationship between the graph of an exponential function and the graph of its corresponding logarithmic function.
understand that the logarithm function base b and the exponential function base b are inverse functions.
Use properties of logarithms and exponents to produce equivalent forms of exponential and logarithmic
answer questions and allow students to draw as an explanation
Accept class participation at any level, including one word answers
Consult with Case Managers and follow IEP accommodations/modifications for students in need of them
Provide oral and written directions
English Language Learners
Allow errors in speaking
Assign a partner who speaks the same language or an English speaker
Rephrase questions, directions and explanations
Allow extra time to answer questions
Accept class participation at any level, including one word answers
Build on student’s motivations/future careers/aspirations
A.APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Pacing
3 days
Find solutions of polynomials by factoring, using the quadratic formula or completing the square and determine whether a quadratic expression has either no, one or two real roots
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect:A-APR.3 - Type 2-3 Question Bank
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Part A. Factor the
polynomial and use the factors to find the zeros of the function.
Part B. Sketch a graph of the function on the coordinate grid below. Make sure you use the key features of the graph including intervals where the function is increasing and decreasing, intervals where the function is positive and negative, and thex- and y-intercepts of the graph.
Factor certain forms of polynomial expressions by using the structure of the polynomials
Use the factored forms of polynomials to find zeros of a function and use the factored forms of polynomials to sketch the components of graphs between zeros
Graph polynomial functions, state x- and y- intercepts and describe end behavior based upon the degree of the polynomial
Fit polynomial functions to data values and model a cross-section of a riverbed with a polynomial function and estimate fluid flow with their algebraic model
See activities and resources[Standard A.APR.3]
CentersTeacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Use words, numbers, and/or pictures to show your work.
Build on student’s motivations/future careers/aspirations
N.RN.A.1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
Pacing
3 days
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect: N-RN.1- Type 2-3 Question Bank
Direct InstructionOption 1–Module 3 Topic A; Lesson 1, 3, and 4
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
A teacher asked her students to use the
expression to answer the questions below.
Part A. Given that what is the value
of Show your work and write your answer in radical form.
Part B. Explain how the solution from part A would need to be manipulated using the properties of exponents in order to eliminate the radical
CentersTeacher Center – The teacher works in a small group with 1-4 students.
Standards Based Problems Center/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.
Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.
Manipulative Center –
expression.
Use words, numbers, and/or pictures to show your work.
Critique whether or not their partner's equation involving a rational exponent is correct or not and explain the reasoning behind it
Students work on solving problems using manipulatives.
Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach them the topic
Review Class work
Exit Ticket
Special Education Students Allow errors Rephrase questions,
directions and explanations
Allow extra time to answer questions and allow students to draw as an explanation
Accept class participation at any level, including one word answers
Consult with Case Managers and follow IEP accommodations/modifications for students in need of them
Model a real world scenario involving rational exponents, such as area and volume models in simplest radical form
Critique whether or not their partner's equation involving rational exponents and/or radicals is correct or not and explain the reasoning behind it
Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.
Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.
Manipulative Center – Students work on solving problems using manipulatives
Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach them
Review Class work
Exit Ticket
Special Education Students Allow errors Rephrase questions,
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Read "Kevin's Used Car" and answer the questions.
Part A
Kevin finds a car to purchase and needs to borrow $3,400. Calculate Kevin's monthly payment for a 4-year loan with a 4.75% annual percentage rate. Show your work.
Part B
How much more would Kevin's car payment be if he pays back the $3,400 in even payments over 3 years instead of 4 years at the same annual percentage rate? Show your work.
Part C
How much will Kevin save if he pays back the money over 3 years instead of 4 years?
Engage NYModule 3 Topic A, Lessons 1, 7Module 3 Topic D, Lesson 22Module 4. Topic A, Lesson 7
reveal the maximum or minimum value of the function it defines.
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression(including radioactive elements and population
Option 4 – PearsonSee activities and resources
[Standard A.SSE.3]Centers
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
participation at any level, including one word answers
Gifted and Talented Students
Provide enrichment/extension activities
Build on student’s motivations/future careers/aspirations
F.IF.B.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Pacing
3 days
ObjectivesSWBAT
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect:F-IF.6 - Type 2-3 Bank
Direct InstructionOption 1–Module 3 Topic A, Lessons 6Module 3 Topic D, Lessons 22-23, & 27
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
In 2007, Zack bought a new car for $17,500. The table below shows the value of the car between 2007 and 2012.
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Given a graph or real world problem, determine the average speed during a certain time frame
Students write an exponential function that represents the amount of water in a tank after t seconds if the height of the water doubles every 10 seconds.
Students discover Euler’s number e by numerically approaching the constant for which the height of water in a
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing
Part A. Calculate the average rate of change of the value of the car between 2007 and 2008. Explain what your answer means in terms of the car’s value over this interval.
Part B. Calculate the average rate of change of the value of the car between 2008 and 2012. Explain what your answer means in terms of the car’s value over this interval.
Part C. Compare the values from Part A and Part B. What can you conclude based on this comparison along with the data in the table in terms of the car’s value over the time period shown in the table?
Use words, numbers and/or pictures to show your work.
descriptions, and by comparing different data representations.
Rephrase questions, directions and explanations
Allow extra time to answer questions
Accept class participation at any level, including one word answers
Gifted and Talented Students
Provide enrichment/extension activities
Build on student’s motivations/future careers/aspirations
A.REI.A.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.
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect:A-REI.1 - Type 2-3 Question Bank
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
The speed of a boat, in still water is given
by the equation and the speed
of a river, is given by
Part A. Solve the equation to find the speed of
boat, Justify each step by writing the property or reason next to it.
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center –
Part B. Solve the equation to find the speed of the river, and justify each step by writing the property or reason next to it.
Part C. The time, taken by the boat traveling a distance of 45 miles upstream is given
by Solve this equation to find the
value of and justify each step by writing the property or reason next to it.
Part D. The time, taken by the boat traveling a distance of 45 miles downstream is given
by Solve this equation and justify each step by writing the property or reason next to it.
Use words, numbers, and/or pictures to show your work.
Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Special Education Students Allow errors Rephrase questions,
directions and explanations
Allow extra time to answer questions and allow students to draw as an explanation
Accept class participation at any level, including one word answers
Consult with Case Managers and follow IEP accommodations/modifications for students in need of them
Assign a partner who speaks the same language or an English speaker
Rephrase questions, directions and explanations
Allow extra time to answer questions
Accept class participation at any level, including one word answers
Gifted and Talented Students
Provide enrichment/extension activities
Build on student’s motivations/future careers/aspirations
A.REI.A.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect:A-REI.2 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 1 Topic C, Lessons
Algebra Touchpoint - A- REI.2
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.
Part A. Solve the equation for x, showing all steps and both resulting values of x.
Part B. Do both values of x represent solutions to the equation? Explain your answer. Use words, numbers, and/or pictures to show your work.
equation to represent real life problems, such as area and volume, solve it for certain values and justify each step by writing a property or reason
Create an equation in one variable that contains a square or a square root and has at least one extraneous solution.
Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Special Education Students Allow errors Rephrase questions,
directions and explanations
Allow extra time to answer questions and allow students to draw as an explanation
Accept class participation at any level, including one word answers
Consult with Case Managers and follow IEP accommodations/modifications for
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.*
Pacing
3 days
ObjectivesSWBAT
Apply properties of logarithms to solve exponential equations.
Relate solutions to f(x) = g(x) to the intersection point(s) on the graphs of y = f(x)
REI.11 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 3 Topic D, Lesson 24
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students
in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Who Will Catch Up When?
Three friends are packing gift boxes to be handed out at the high school dance. Each box has ten sections to be filled. They each pack the boxes at different rates.
Part A. The tables below show Kelsey’s and Andrew’s progress. The variable t stands for the time that has passed since their starting time at 10:00
a.m. Andrew had already packed 4 boxes the day before.
Fill in the tables, assuming that each person packs the boxes at a constant rate.
Part B. Let the number of boxes Kelsey packs be represented by k(t) and the number Andrew packs by a(t). Using the information from the tables, write
and y = g(x) in the case where f and g are constant or exponential functions.
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.
Given a table of
work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Special Education Students Allow errors Rephrase questions,
directions and explanations
Allow extra time to answer questions and allow students to draw as an explanation
Accept class participation at any level, including one word answers
the functions for k(t) and a(t). Interpret each function in terms of the context it represents.
Kelsey:
Andrew:
In terms of k(t) and a(t), what equation can be solved to find the time at which both Kelsey and Andrew have packed the same number of boxes? Explain.
Part C. Graph and label the functions k(t) and a(t) on the same coordinate grid below.
What is the solution of the equation that was written in part B that could be used to find the time at which Kelsey and Andrew have packed the same number of boxes? Explain how you can find the solution on the graph and then verify your answer by solving the equation algebraically.
Part D. The third friend, James, starts out packing the
values or a graph of two functions, such as f(x) and g(x), find the solutions of the equation f(x) = g(x)
Solve real world problems involving graphs of systems of equations by finding where the graphs intersect and solve real world questions by graphing linear inequalities
Consult with Case Managers and follow IEP accommodations/modifications for students in need of them
Provide oral and written directions
English Language Learners
Allow errors in speaking
Assign a partner who speaks the same language or an English speaker
Rephrase questions, directions and explanations
Allow extra time to answer questions
Accept class participation at any level, including one word answers
Gifted and Talented Students
Provide enrichment/extension activities
Build on student’s motivations/future careers/aspirations
boxes very quickly but then slows down. His approximate progress can be modeled by the square root equation below, where t stands for the time that has passed since their starting time at 10:00 a.m.
Fill in the table to show James’s progress. Round the values to the nearest 0.1 box.
Part E. Sketch a graph of the function j(t) on the coordinate grid above, where k(t) and a(t) are already graphed.
Write the equation that could be used to find the time at which Kelsey and James have packed the same number of boxes. Approximate the solution or solutions to this equation using the graph.
Write the equation that could be used to find the time at which Andrew and James have packed the same number of boxes. Approximate the solution or solutions to this equation using the graph.
F.BF.A.1. A) Determine an explicit expression, a recursive process, or steps for calculation from a context.B) Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
C) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect:F-BF.1 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 3 Topic A, Lesson 5Module 3 Topic B, Lesson 7Module 3 Topic C, Lesson 22Module 3 Topic D, Lessons 6, 26-28Module 3 Topic E, Lessons 30, 33
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Joe wants to sell his old car and an old set of furniture. He decides to assess their value by writing functions to represent their values after x years.
Part A. He bought the car for $10,000 and it has depreciated at a rate of 6% every year. Write an explicit function to determine the value of the car after x number of years.
Part B: Write a recursive formula for the value of the car after x number of years. Make sure to define the variables used and the domain for the formula.
Part C. The value of the furniture over a period of 3 years is listed below.
location of the weather balloon as a function of time.
Pacing
3 days
ObjectivesSWBAT
Write a function that describes the relationship between two quantities (i.e. including height of a falling object and time)
Combine standard function types using arithmetic operations and function composition (including area of shapes/shaded regions with expressions as lengths)
Compose functions involving real world problems in order to answer questions and
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write
Write an explicit function for the value of the furniture for x number of years.
Part D. Write a recursive formula for the value of the furniture after x number of years. Make sure to define the variables used and the domain for the formula.
Use words, numbers, and/or pictures to show your work.
Write or create an explicit expression, a recursive process or steps for calculations from a context including word problems
Analyze data and real world situations and find a function to use as a model of it.
Create a function and answer questions using words, numbers and/or pictures given a word problem with a picture of a landscaping design with a walkway/pathway
their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Special Education Students Allow errors Rephrase questions,
directions and explanations
Allow extra time to answer questions and allow students to draw as an explanation
Accept class participation at any level, including one word answers
Consult with Case Managers and follow IEP accommodations/modifications for students in need of them
who speaks the same language or an English speaker
Rephrase questions, directions and explanations
Allow extra time to answer questions
Accept class participation at any level, including one word answers
Gifted and Talented Students
Provide enrichment/extension activities
Build on student’s motivations/future careers/aspirations
F.BF.A.2.Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect: F-BF.2 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 3 Topic D;
Algebra Touchpoint – F-BF.2
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
A scientist is studying the growth of a certain bacteria population in a dish. At 12:00 P.M., the scientist begins the study with 4 bacteria. After each hour of
[Standard F.BF.2 is not present in Pearson Algebra II
textbook}
CentersTeacher Center – The teacher works in a small group with 1-4 students.
Standards Based Problems Center – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.
Individual Center – Students work on the individual skill that they need based on
the study, the scientist records the time and the number of bacteria in the dish. The scientist’s records for the first few hours of the study are shown in the table below.
Part A. Write a recursive formula to represent the
bacteria growth in this study. Let represent the number of bacteria at the beginning of the study, and letn represent the number of hours that have passed since the study began.
Part B. Write an explicit formula to represent the
bacteria growth in this study. Again, let represent the number of bacteria at the beginning of the study, and let n represent the number of hours that have passed since the study began.
Part C. Using your recursive formula and assuming the bacteria population continues to grow at the same rate, determine the number of bacteria in the dish at 8:00 P.M. Show your work. Next, using your explicit formula and assuming the bacteria population continues to grow at the same rate, determine the number of bacteria in the dish at 8:00 P.M. Show your work.
Critique whether or not their partner's sequence is arithmetic or geometric and use their sequence to select the correct formula
their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.
Manipulative Center – Students work on solving problems using manipulatives.
Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach them the topic
Review Class work
Exit Ticket
Special Education Students Allow errors Rephrase questions,
directions and explanations
Allow extra time to answer questions and allow students to draw as an explanation
Accept class participation at any
Part D. Compare and contrast the methods you used when using the different formulas in part C. Which type of formula would you use if you had to determine the number of bacteria in the dish at 10:00 A.M. on the following day? Explain.
Use words, numbers, and/or pictures to show your work.
A.SSE.B.4. Derive and/or explain the derivation of the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
Pacing
3 days
ObjectivesSWBAT
Use the geometric formula to find the sum of the first nine terms of a geometric sequence
Determine which expression represents the sum of the first fourteen terms
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect: A-SSE.4 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 3 Topic E; Lesson 29, 30https://www.engageny.org/search-site?search=A.SSE.4
[Standard A.SSE.4 is not present in Pearson Algebra II
Algebra Touchpoint - A- SSE.4
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Yolanda is a medical student and is experimenting on a medicine that cures an infection. Each dosage contains 500 milligrams (mg) of an antibiotic, and about 15% of the mass of the antibiotic remains in the body at the time the next dose is taken.
Part A. Complete the table to determine the mass of the antibiotic in the body for 1 to 3 doses.
Part B. Yolanda wants to know the mass of the antibiotic in the body after 15 doses taken at equal intervals. Help Yolanda and show your work.
Part C. In one patient, Yolanda records that there is about 588.19 mg of the antibiotic present. How many doses of medicine would the person have taken?
Apply the sum of a finite geometric series formula to a structured savings plan
Derive the formula for finding the sum of the first n terms in S of a geometric series
Critique whether statements or equations are correct involving finite geometric sequences given 2 terms in the middle of the sequence
Complete tables involving word problems involving geometric sequences and/or series
textbook}Centers
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Center – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as base ten blocks; etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach them
Review Class work
Exit Ticket
Special Education Students
Part D. What conclusion can Yolanda make about the increase in the mass of the antibiotic present in the body from the solutions in parts A, B, and C?
Use words, numbers, and/or pictures to show your work.
Build on student’s motivations/future careers/aspirations
F.BF.B.3.Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Pacing
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect: F-BF.3 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 3 Topic C; Lesson 20www.engageny.org/search-site?search=f-bf-3
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Slide, Stretch, and Squeeze
For this problem, you will take a basic exponential function and experiment with different ways to transform it. You may use a graphing calculator or graphing program and then sketch each graph on the grid provided.
Part A. Graph the function Describe the main features of the graph, including shape, quadrants, and key points.
CentersTeacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Center/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as base ten blocks; etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems
Part B. On the same grid, graph the
function identifying at least two key points. Describe how it differs from the graph
of
Part C. On the grid below, sketch again
and then sketch Describe how a
coefficient of on the term changes the graph of the function.
show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F.IF.C.7e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Pacing
3 days
Students formalize the periodicity, frequency, phase shift, midline, and amplitude of a general sinusoidal function by understanding how the parameters A, w, h, and k in the formula
(called number stories); Students listen to music/sing songs/create songs that teach them
Review Class work
Exit Ticket
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect: F-
Part D. On the grid below, sketch again
and then sketch Describe the new graph and how it compares with the original graph.
are used to transform the graph of the sine and cosine function, and how variations in these constants change the shape and position of the graph of the sine function.
Use reciprocal relationships to relate trigonometric functions and use these relationships to evaluate trigonometric functions for multiples of 30, 45 and 60 degrees on the unit circle
Sketch sine, cosine and tangent functions and analyze the shape of the curves and state amplitude, period, frequency, and midline by hand and with the graphing calculator
CentersTeacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Center/MATH STATIONS – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve
Part E. On the grid below, sketch again
and then sketch Describe the new graph and how it compares with the original graph.
Part F. Name two ways that you could transform the
function so that it passes through the
point Sketch the graphs of the functions you provide.
Recognize the relationship among the constant A, w, h, and k in the formula f(x) = Asin(w(x-h))+k and the properties of the sine or cosine graph.
For the sine and cosine functions, students sketch graphs showing key features, which include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maxima and minima; symmetries; end behavior; and periodicity.
Prove simple identities involving all six trigonometric functions
Derive proofs of sum and
the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as base ten blocks; etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach them
difference identities for sine and cosine functions
Algebra Touchpoint – F-BF.3
Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments above.
Collect data from everyday life to create a prediction equation
Compute the correlation coefficient using technology and investigate its meaning relevant to the data
Essential Questions What relationships between quantities can be modeled by functions? How can collecting and organizing data clarify what the data is revealing? When will you use the common measures of central tendency and spread and how will they help solve problems? What are the ways in which data can be organized into tables and/or graphs, and which are more useful in certain instances? How can I organize and interpret paired data to predict future events? How can you use technology to display data and interpret data?
New Jersey Student Learning Standards
Standards/Cumulative Progress Indicators (Taught and Assessed): S.IC.B.3S.IC.B.4S.IC.B.5S.IC.B.6
F.TF.A.1 F.TF.A.2F.TF.B.5 F.TF.C.8
Key: Green = Major Clusters; Blue = Supporting; Yellow = Additional Clusters
21st Century Skills Standard and Progress Indicators:
CRP4. Communicate clearly and effectively and with reason.CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.CRP11. Use technology to enhance productivity.
CRP12. Work productively in teams while using cultural global competence.
Instructional Plan Reflection
Unit 2 Pre-Test
SLO - SWBAT Student Strategies Formative Assessment Activities and Resources ReflectionS.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Pacing
7 days
ObjectivesSWBAT
State whether a given study represents an experiment, or an observational study and determine the study variables. Give examples of each.
Explain the importance of the role of
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect: S-IC.3 - Type 2-3 Question Bank
The standards assessments below are in EdConnect. These are the quizzes/tests for that standard.
Algebra - Touchpoint - S-IC.3
Teachers will agree on common class work problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments in column 5.
Women and Children
In the past 100 years, women’s decisions to have children have changed tremendously. Read the researcher’s descriptions of the studies below and consider how they are related and how they are different.
Study 1: This study examined what types of women have children and what types of women don’t have children. We were also interested in learning about the age when women decide to have children. We collected data from the Census Bureau about the demographic, marital status, and economic characteristics of women who had children and
randomization in sample surveys, experiments and in observational studies
Identify voluntary response samples and convenience samples
Determine the best way to select a random sample. Describe simple random samples, stratified random samples, and cluster samples.
Distinguish the difference between observational studies, experiments and sample surveys
Design and describe an experiment for given information to assess something, such as the impact of extra football practice has on the players during the playoffs, and explain all the factors you considered to determine the best design for the experiment.
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with
compared them to women who had not yet had children. We also looked at the age that women had their first child.
Study 2: This study looked at the kinds of communities women who have children live in. Are women with children more likely to live near parks, community centers, and schools? Are women with children more likely to live closer to other families? How much of their resources do these communities spend on education, social services, parks, and recreation? We considered Census data, but most of our research examined city government budgets, locations of nonprofit organizations, and community maps. We couldn’t do this in-depth analysis on all of the communities in the United States, so we chose a few representative communities.
Study 3: This study considered the reasons women have children or do not have children. We contacted 500 women and asked them questions about their reasons for having children, waiting to have children, or not having children. We asked them who influenced their decisions and what they thought about when they had their first child.
Study 4: This study focused on what young women think about having children, including teenagers and recent high school graduates. Some researchers visited high schools and colleges, while other researchers used random digit dialers and asked those who answered their phones about their age and their thoughts about having children.
Study 5: This study was designed to determine whether learning about the financial cost of raising children would impact teenager’s opinions about having children. In a selection of high schools, the freshman classes were split into two groups. One group participated in a home-finance curriculum, in
another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Special Education Students
Allow errors Rephrase
questions, directions and explanations
Allow extra time to answer questions and allow students to draw as an explanation
Accept class participation at any level, including one word answers
Consult with Case Managers and follow IEP accommodations/modifications for students in need of them
Provide oral
which the group members of the group managed monthly budgets as if they were parents. The second group participated in a selection of randomly assigned electives. Both groups of students then completed a survey about their opinions on having children. The researchers collected followup data five years later on whether these participants had children and the age at which they had children.
Part A. Which of these studies are observational studies? How do you know?
Part B. What is the role of randomization in the observational studies?
Part C. Which of these studies are sample surveys? How do you know?
Part D. What is the role of randomization in the sample surveys?
Part E. Which of these are experiments? How do you know?
Part F. What is the role of randomization in the experiments?
Part G. What are the purposes of observational studies, sample surveys, and experiments? How are they different?
Part H. Choose a question that interests you for which you could create an observational study, a sample survey, and an experiment. Describe how you would carry out these studies. How do each of these types of studies play a role in answering your question? How would you use randomization in each of your studies? Why?
S.IC.B.4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling
Pacing
7 days
ObjectivesSWBAT
Calculate the mean and standard deviation of data
Use data from a sample survey to estimate a population mean or proportion
Calculate and interpret a margin of error through the use of simulation models for random sampling and calculate the percent confidence interval from a population proportion
Understand that the
Journal WritingType 2-3 Problem of the Day –Taken from EdConnect: S-IC.4 - Type 2-3 Question Bank
Direct InstructionOption 1–Module 4 Topic C, Lessons 13-21
The standards assessments below are in EdConnect. These are the quizzes/tests for that standard.
Algebra - Touchpoint - S-IC.4
Teachers will agree on common class work problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments in column 5.
A group of high school students were asked about their favorite sports. The survey indicated that 37% of students, or 407 students, said baseball was their favorite sport.
Part A: What was the total number of students surveyed?
Part B: What is the margin of error of the survey for only the sample of students who said baseball was their favorite sport?
Part C: Write an interval that is likely to contain the exact percentage of all students who would say baseball is their favorite sport.
Use words, numbers, and/or pictures to show your work.
standard deviation of the sampling distribution of the sample proportion lets them know about the accuracy of the sample proportion as an estimate of the population
Know the relationship between sample size and margin of error in the context of estimating a population mean
Conduct simulations of random sampling to analyze and interpret data
CentersTeacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center –
Teachers will agree on common class work problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments in column 5.
Wilson owns a bike store. He is trying to decide between ordering bike tires from Brand A or Brand B. To do so, he orders bike tires from Brand A and B and conducts an experiment to compare the efficiency of the tires regarding the stop time. In order to test the brands, he asks a customer to participate in his experiment consisting of 10 trials. Within each trial, the road and weather conditions and speed of the bike remain constant. However, from trial to trial, the conditions are altered. For example, in Trial 1 the bike speed may be different than in Trial 2.
During each trial, the customer rides a bike that has Brand A tires and Wilson measures the time the bike takes to stop after the brakes are applied. Then the customer rides an identical bike under the same conditions, but using Brand B tires. The table below lists the times he records for the 10 trials.
difference in the two groups’ means can be described in terms of shape, center, and spread.
Students understand that when one group is randomly divided into two groups, the two groups’ means will differ just by chance (a consequence of the random division).
Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Special Education Students
Allow errors Rephrase
questions, directions and explanations
Allow extra
Part A. Wilson reasons that if the difference between the mean times for the two brands is 200 milliseconds or less, the brands do NOT have an impact on the time taken to stop the bike. What should Wilson conclude using these data?
Part B. Construct a box plot to represent the differences in the brake times of each trial. To find the difference in brake times subtract the Brand A time from the Brand B time.
Part C. Wilson uses the following criteria to decide whether the difference in brake times in any of the trials is an outlier: An outlier is any value that lies more than one and a half times the length of the box from either end of the box-and-whisker plot. Using this criteria, is there any time difference that should be deemed an outlier? If
The standards assessments below are in EdConnect. These are the quizzes/tests for that standard.
Algebra - Touchpoint - S-IC.6
Teachers will agree on common class work problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments in column 5.
Using Data to Evaluate Claims about the Effectiveness of a Treatment
The long-term symptoms of a particular viral infection include a fever and intermittent tremors.
Construct scatter diagrams from data and estimate a line of best fit on a graph using technology
Read and explain, in the context of the situation, data from outside reports – discussing experimental study design, drawing conclusions from graphical and numerical summaries, and identifying characteristics of the experimental design.
Students interpret margin of error from reports that appear in newspapers and other media.
Students critique and evaluate statements in published reports that involve estimating a population proportion or a population mean.
Teacher Center – The teacher works in a small group with 1-4 students.Standards Based Problems Centers/Math Stations – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard.Individual Center – Students work on the individual skill that they need based on their pre-test data. Achieve the Core Coherence Map should be used to guide remediation.Manipulative Center – Students work on solving problems using manipulative, such as
There is no known cure for the infection, but researchers believe that regular doses of a new drug may make the tremors less frequent. The figure below shows the results of the first phase of an experimental treatment: for 25 subjects, the daily dosage of the drug is plotted against the number of tremors the subject experienced during the second month of treatment.
During the treatment, some subjects complained of weight gain. The table below records the drug dosage for each subject and the weight that subject gained during the first two months of treatment.
Students critique and evaluate statements in published reports that involve determining if there is a significant difference between two treatments in a statistical experiment.
algebra tiles, candy, etc.Interdisciplinary Center – Students work on math problems that interconnect with another subject. [Examples – Students write their own word problems (called number stories); Students listen to music/sing songs/create songs that teach]
Review Class work
Exit Ticket
Special Education Students
Allow errors Rephrase
questions, directions and explanations
Allow extra time to answer questions and allow students to draw as an explanation
Accept class participation at any level, including one word answers
accommodations/modifications for students in need of them
Provide oral and written directions
English Language Learners
Allow errors in speaking
Assign a partner who speaks the same language or an English speaker
Rephrase questions, directions and explanations
Allow extra time to answer questions
Accept class participation at any level, including one word answers
Gifted and Talented Students
Provide enrichment/extension activities
Part B
When the researchers publish these preliminary results on their website, several people reply to the news, making claims in their comments. For each of the following claims, determine whether the experimental data:
prove the claim to be true, suggest that the claim is likely, but do not
provide proof, neither support nor cast doubt on the claim, cast doubt on the claim, but do not prove it
false, or prove the claim to be false.
Claims
1. "A dosage of at least 10,000 mg would eliminate the tremors entirely."
