Math Performance Task Grade 9 FINAL. Algebra I. Modelling and Analysing Quadratic Equations. Scienti

downloaded from

Scholarfriends

https://scholarfriends.com Downloaded by: writerforacademic@gmail.com | https://scholarfriends.com/singlePaper/314808/math-performance-task-grade-9-final-algebrai-modelling-and-analysing-quadratic-equations-scienti Distribution of this document is illegal.

Math Performance Task Grade 9 MYP Subject Group: Mathematics Unit Title: Modelling and Analysing Quadratic Equations Key Concept: Form

Subject: Algebra I Related Concept: Equivalence, Patterns, Models Global Context: Scientific and technical innovation Exploration: Processes and solutions

SOI: Representing patterns through equivalent forms of models helps determine the appropriate process that leads to solutions.

Name:

MYP Year:

Common Formative Assessment Criteria Criterion B Your Level: Criterion C Criterion D

Your Level: Your Level:

Date:

_____/ 8 /8 /8

Goal: Your goal is to create a cost-efficient smart phone that will maximize your company’s profit Role: You are an entrepreneur of a mobile company Audience: Your audience is a group of executives of a mobile company Situation: To convince the executives of a mobile company to create a cost-efficient smart phone

1

Product: You will need to create an excel spreadsheet, brochure, or PowerPoint.

Standards: CCSS.MATH.CONTENT.HSA.SSE.B.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

CCSS.MATH.CONTENT.HSA.SSE.B.3.A

Factor any quadratic expression to reveal the zeros of the function defined by the expression.

CCSS.MATH.CONTENT.HSA.SSE.B.3.B

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function defined by the expression.

CCSS.MATH.CONTENT.HSA.REI.B.4

Solve quadratic equations in one variable.

CCSS.MATH.CONTENT.HSA.REI.B.4.A

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from ax2 + bx + c = 0.

CCSS.MATH.CONTENT.HSA.REI.B.4.B

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

CCSS.MATH.CONTENT.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

CCSS.MATH.CONTENT.HSF.IF.C.7.A

Graph linear and quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).

CCSS.MATH.CONTENT.HSF.IF.C.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

2

CCSS.MATH.CONTENT.HSF.IF.C.8.A

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. For example, compare and contrast quadratic functions in standard, vertex, and intercept forms.

CCSS.MATH.CONTENT.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one function and an algebraic expression for another, say which has the larger maximum.

Part I: You will compare profit functions for different companies from selling smart phones.

X-axis = Number of Smart Phones sold (in millions) = g (for galaxy phone) y-axis = Profit (in millions of dollars) = P(g)

Number of smart phones 3

The line above shows the profit from selling phones for the Samsung Galaxy Phone 1a. Label the line as “Samsung”, the x-axis and the y-axis. b. Describe the key features of the graph. Key features include concavity, x and y-intercepts and the vertex.

The parabola concaves upwards. vertex (1,2) X-intercepts=0, y-intercepts=3 c. Is the vertex a max. or min. point? Describe what the vertex means in terms of this problem.

Min point, Samsung started at 3 million, but the prophet dropped to 2 million after that it went up. d. Create an equation in completed the square form. Then translate this to standard form.

Completed the square form à f(x) = (x-1)^2=-2 Standard form à f(x) = x^2-2x+3

2. Apple is also analyzing their profit of the iPhones they sell.

Apple: Profit from iPhones Sold iPhones sold (in millions) i

Profit (in millions of dollars) P(i)

-1

0

2

-9

5

0

6

7

7

16

4

A. Based on the table, create an equation in factored form (hint: look for the x-intercepts of the function). Then translate the factored form into completed the square form and standard form.

Factored form à P(i) = (x+1) (x-5) Standard form à P(i) = x2-4x-5 Completed the square form à P(i) = (x-2)2=9 B. Sketch a graph of the function P(i) using information from the three forms of the equation you made in part b. Be sure to label the x and y axis.

5

3. Blackberry is also in the business of selling phones. The data for the profit that Blackberry makes on selling phones is represented by the following equation with profit being P(b) and b being number of blackberry phones sold (both variables in millions):

P(b) = -x2 + 8x – 8 a. Use the quadratic formula to solve the equation. What do these points tell us about the graph?

X=2+or- 2√2 b. Complete the following table. Based on the table, estimate the vertex for the function. Is the vertex a max. or a min. point?

Blackberry: Profit from Smart Phones Sold Smart Phones sold (in millions) b

Profit (in millions of dollars) P(b)

-1

-17

0

-8

2

4

3

7

4

8

5

7

6

4

c. Sketch a graph for Blackberry. Label the x and y axis (for b and P(b))

6

Y=-8 Axis of symmetry=-4 Vertex= 4,8 d. Tell me how you sketched the graph (what information did you use?)

I used the formulas to identify the vertex and the axis of symmetry and the y intercepts then I graph them.

Part II: Report on Tablet Profit In complete sentences and 1-2 complete paragraphs, please write a report on the three companies selling phones. In the report please include the following: a. What is the same about the three data sets/lines?

Notes/Ideas:

Well, Samsung and apple has a minimum point in the parabola, both companies have an increase in profits if the number of mobiles are sold is increasing.

7

b. What is different about the three data sets/lines?

Notes/Ideas:

The three companies have different vertex and profits, blackberry has the least, apple has the second and Samsung has the highest.

c. Describe the long-term trend for each company. In other words, for each company, write at least one sentence that describes if each company will make money as they sell more phones, lose money or come out even.

Notes/Ideas: Samsung: Samsung started dropping, in the first 1 million phones Samsung profit went down, but when Samsung sold 2 million phones, the profit of it went up and kept increasing. Samsung profit will keep increasing if they sell more phones.

Apple: apple had a large drop in the first 2 million phones, when apple sold 5 million phones, they had an even profit, but when apple sold 6 million phones, they had an increase in profit. And when apple sold 7 million phones, they had a large increase and if they continue in selling more phones their profit will increase.

Blackberry: blackberry started with an increase in profit and continued in increase until it had a large drop when they sold 6 million phones, I think that blackberry will continue dropping if they sell more phones. d. Recommend one company to invest in based on the graph – what company would you want to be a part of and why?

Notes/Ideas: Apple, because it has a great raise in the profit which makes the company stable which is very good for the employees. e. Reflection – write at least one sentence describing how you felt about this assignment – which representation (graph, table or equation) is easiest for you to work with and why. my feeling about this assignment is that this assignment was little hard but it will affect us in real life, the easiest representation is the table because to find the y you should solve the equation only.

8

Write down one task or problem from this assignment that you think you need more review/work on. the thing that I need review on is how do we find the vertex because for some equations it is very hard.

How to start the writing assignment.

It is highly recommended that you jot down notes for each part and then complete an Idea Organizer to help organize and clarify your thoughts.

Criterion B: Investigating Patters Achievement Level 0 1-2

3-4

5-6

7-8

Level Descriptor You do not reach a standard described by any of the descriptors below.

You are able to: i. apply, with teacher support, mathematical problem-solving techniques to discover simple patterns, ii. state predictions consistent with patterns.

You are able to: i. apply mathematical problem-solving techniques to discover simple patterns, ii. suggest general rules consistent with findings.

You are able to: i. select and apply mathematical problem-solving techniques to discover complex patterns, ii. describe patterns as general rules consistent with findings, iii. verify the validity of these general rules.

You are able to: i. select and apply mathematical problem-solving techniques to discover

Task specific descriptor

You can  apply algebraic concepts to process the data collected using a step-by-step guide  state the possible pattern of data based on the curve of the graph You can  apply algebraic concepts to process the data collected  suggest a pattern in the data based on the curve of the graph You can  select and apply algebraic concepts to process the data collected  describe the pattern based on the curve of the graph  verify your findings but evaluating the data using tabular or graphical means You can  select and apply algebraic concepts to process the data

9

complex patterns, ii. describe patterns as general rules consistent with correct findings, iii. prove, or verify and justify, these general rules.

 

collected describe the pattern based on the curve of the graph verify your findings but evaluating the data using tabular and graphical means

Criterion C: Communication Achievemen t Level 0 1-2

3-4

5-6

Level Descriptor

Task specific descriptor

You do not reach a standard described by any of the descriptors below.

You are able to: i. use limited mathematical language, ii. use limited forms of mathematical representation to present information, iii. communicate through lines of reasoning that are difficult to interpret.

You can  use limited math terms correctly in explaining the details of your solution.  communicate your solution with word difficult to understand

You are able to: i. use some appropriate mathematical language, ii. use appropriate forms of mathematical representation to present information adequately, iii. communicate through lines of reasoning that are complete, iv. adequately organize information using a logical structure.

You are able to: i. usually use appropriate mathematical language, ii. usually use appropriate forms of mathematical representation to present information correctly, iii. usually move between different forms of

You can  usually use math terms correctly in explaining the details of your solution.  communicate your solution with complete explanation  present your work in a logical manner You can  usually use math terms correctly in explaining the details of your solution.  usually use either algebraic or graphical method to represent your

10

7-8

mathematical representation, iv. communicate through lines of reasoning that are complete and coherent, v. present work that is usually organized using a logical structure.

You are able to: i. consistently use appropriate mathematical language, ii. use appropriate forms of mathematical representation to consistently present information correctly, iii. move effectively between different forms of mathematical representation, iv. communicate through lines of reasoning that are complete, coherent and concise, v. present work that is consistently organized using a logical structure.

 

solutions communicate your solution using complete and coherent explanation present your work in an organized and logical manner

You can  consistently use math terms correctly in explaining the details of your solution.  consistently and effectively use both algebraic and graphical method to represent your solutions  communicate your solution using complete, coherent, and concise explanation  present your work in a consistently organize and logical manner

Criterion D: Applying Mathematics in real-life context Achievemen t Level 0

1–2

3–4

5–6

Level Descriptor You do not reach a standard described by any of the descriptors below.

You are able to: i. identify some of the elements of the authentic real-life situation ii. apply mathematical strategies to find a solution to the authentic real-life situation, with limited success.

You are able to: i. identify the relevant elements of the authentic real-life situation, ii. select, with some success, adequate mathematical strategies to model the authentic real-life situation, iii. apply mathematical strategies to reach a solution to the authentic real-life situation, iv. discuss whether the solution makes sense in the context of the authentic real-life situation.

You are able to: i. identify the relevant elements of the authentic real-life situation ii. select adequate mathematical strategies to solve the authentic real-life situation

Task specific descriptor

You can  identify some information on different brands by collecting data  apply the method to determine which brand would yield best profit You can  identify relevant questions to collect data  select any method to determine best profit  apply the method to find out the brand that yields best profit  discuss your findings using factual information You can  identify relevant questions to collect data  select either method to determine best profit

11

7–8

iii. apply the selected mathematical strategies to reach a valid solution to the authentic real-life situation iv. describe the degree of accuracy of the solution You are able to: i. identify the relevant elements of the authentic real-life situation, ii. select appropriate mathematical strategies to model the authentic real-life situation, iii. apply the selected mathematical strategies to reach a correct solution to the authentic real-life situation, iv. justify the degree of accuracy of the solution, v. justify whether the solution makes sense in the context of the authentic real-life situation.

 

apply the method to validate solution on which brand would yield best profit describe the accuracy of your findings using factual information

You can  identify relevant questions to collect data  select either method to determine best profit  apply the method to validate solution on which brand would yield best profit  justify the accuracy of your findings using factual information  justify how the solution makes sense in the context of brands making profit

12