More Possible Mathematical Models 2F I can apply the concept of minimum and maximum to applied problems (box, garden, fence problems) that involve quadratic and cubic functions and use domain to determine if my solution is viable. 2G I can determine when equations, inequalities, systems of equations and/or inequalities (mixture/projectile) should represent a problem and its constraints. 2H I can create direct, inverse, and joint variation equations (physics) in two or more variables to represent relationships between quantities.

Observe the materials What properties do both have? Describe all of the information you know about each

PROBLEM Approach Independently Create 1 Plan independently that might work Compare plans by communicating with partner Draft a proposal Approach Create Plans How can you minimize the cost and maximize the height for building a structure using spaghetti and marshmallows that will support a tennis ball. Write a proposal that will convince the manufacturing company to accept your plan

Task Approach Independently Create 1 Plan independently that might work Compare plans by communicating with partner Draft a proposal Approach Create Plans What’s the biggest open box that you can make with the given piece of paper?

II. More Mathematical Models A.Mathematical models, key features and parent functions are used to analyze data in real-world situations. What models do we already know?

B2. Visual for Mixture Models Credit: Linear

B3. Visual for Projectile Motion Credit: Quadratic

B1. Visuals for Box, Garden & Fence Quadratic/Polynomi al

B3. Visual for Variation y = kx xy=k y = kx xy=k

C. Process What are the two ways we can approach answering the question? Are there any constraints on the domain and range? Are the x-intercepts needed to answer this question? Do I need to know the max/min? What are the two ways we can approach answering the question? Are there any constraints on the domain and range? Are the x-intercepts needed to answer this question? Do I need to know the max/min? The profit P (in millions of dollars) for a T-shirt manufacturer can be modeled by P = -x 3 +4x 2 +x where x is the number of T-shirts produced (in millions). Currently the company produces 4 million T-shirts and makes a profit of $4,000,000. What lesser number of T-shirts could the company produce and still make the same profit?

D. Purpose Predict revenue, profit and demand Percent mixture for products Projectile Motion Minimizing materials and maximizing costs

Active Sense-Making LT 2FGH Recall & Reproduction Whiteboard Wall Routine At your desk Non-Routine See Mr. Wong

Practice Insights Given the context what restrictions are there on the domain? (ALL) Given the context, what values of x are viable solutions? (R&R #1,3, Routine #4,6) Are the solutions always roots? (R&R #1,3, Routine #4,6) Given two of the roots how can you find the missing root(s)? (R&R Box Problem) For a quadratic model, what is the value of a when the height is given in feet? Meters? (Non- Routine)

Active Sense-Making LT 2FGH Recall & Reproduction Whiteboard Wall Routine At your desk Non-Routine See Mr. Wong

Practice Insights Given the context what restrictions are there on the domain? (ALL) Given the context, what values of x are viable solutions? (R&R #1,3, Routine #4,6) Are the solutions always roots? (R&R #1,3, Routine #4,6) Given two of the roots how can you find the missing root(s)? (R&R Box Problem) For a quadratic model, what is the value of a when the height is given in feet? Meters? (Non- Routine)

Active Practice Part 3: What questions did you star? What practice problems will you go back and re-do outside of class with a peer or Mrs. Ramirez? When will you practice the problems you selected? Set date and time and write in notebook next to questions/practice problems

Goal Problems: LT FGH  You will need:  Pen/Pencil  Calculator  Notes  You have 10 minutes to work on the Goal Problems (ALONE)

Goal Problems LT 2FGH Recall & Reproduction Write Algebraic models for the following: "F varies as x“ "F varies jointly as x and y“ "F varies as x + y“ "F varies inversely as x“ You Decide: Which 5 problems from the Learning Targets from this category do you choose? What 1 problem from previous concept category do you choose? Routine A park contains a flower bed 50 m long and 30 m wide with a path of uniform width around it having an area of 600m 2. Determine the width of the path. Non-Routine To contain radiation, a closed rectangular safe is to be made of lead of uniform thickness on the top, bottom and sides. The inside dimensions are 4ft x 4ft x 6ft and 450ft 3 of lead is to be used. Find the thickness of the sides.

Error Analysis 1.) Where are you? 2.) What are you missing? 3.) What did you learn? Use your solution pathway on your Quick Check to find the answers to the questions found on the key. Identify and copy the questions your solution pathway did not answer. Use your solution pathway on your Quick Check to find the answers to the questions found on the key. Identify and copy the questions your solution pathway did not answer.

Error Analysis 1.) Where are you? 2.) What are you missing? 3.) What did you learn? 1.Use Notes and/or Concept Map to answer the questions that you identified 2.For any remaining questions ask a peer and analyze the Answer key to find the answers to the rest of your questions 3.Still stuck????? Write down your point of confusion and ask me 1.Use Notes and/or Concept Map to answer the questions that you identified 2.For any remaining questions ask a peer and analyze the Answer key to find the answers to the rest of your questions 3.Still stuck????? Write down your point of confusion and ask me

Error Analysis 1.) Where are you? 2.) What are you missing? 3.) What did you learn? For every answer to your questions, add the information you learned in the appropriate place in your notes and note on the Goal Problems the date of notes where information is found If answer was already in your notes highlight and/or add reminders so you don’t forget next time. For every answer to your questions, add the information you learned in the appropriate place in your notes and note on the Goal Problems the date of notes where information is found If answer was already in your notes highlight and/or add reminders so you don’t forget next time.

Analyze Goal Problem Results: What are areas of strength? Where do you need more targeted practice? Based on the questions that you have from the goal problems, choose 5 problems from the current practice

Concept Connections 1.Strengthen Notes(LT 2FGH): Math Models Types of models: Linear, Quadratic, Polynomial, Variation Relevant key features based on model Notes, Learning Targets, Goal Problems, Quick Checks