Overview and Background: Unit: Cookies

 

Marcia Uhls : Cheney USD 268

Mathematics. : Graphing equations : Interactive Mathematics

Cheney : Grades 10 - 10 : Aug. - Jun.

 

Title:

Cookies

Topics:

Solving Inequities, Linear Programming, Graphing

Time Frame:

 

Start Date:

-

Status:

Draft

Date Revised:

 

 

Other Designers:

 

Summary:
Students will develop a linear programming problem that involves two variables, has something that needs to be maximized or minimized and has three or four linear constraints. They will then solve it, and produce an oral and written presentation that explains the problem, provides a solution and proves that there is no better solution

 

Print Materials Needed:
IMP Math text
Graph paper

Resources:

 

Resource Attachments:

Internet Resource Links:

 

Notes:

 

 

Stage 1: Identify Desired Results

 

State:

KS      

Title:

Mathematics

Standard(s):

2.1.1.k
The student identifies and continues patterns presented in a variety of formats: numeric, algebraic, visual, oral, written, kinesthetic, pictorial, tabular, graphical, or listing.
2.2.1.k
The student explains or applies the concept of multiple variables.
2.2.2.k
The student knows and explains the use of variables as parameters for a specific variable situation such as the ma in b in y = mx + b or the h, k and r in (x-h)2 + (y-k)2 = r2.
2.2.3.k
The student sets up and solves equations and inequalities.
2.2.1.a
The student uses symbols, variables, expressions, inequalities, equations and simple systems of linear equations to represent problem situations which involve variable quantities.
2.2.2.a
The student formulates and solves problems involving symbols, percents, variables, expressions, inequalities, equations, and simple systems.
2.3.1.k
The student uses a variety of methods including mental mathematics, paper and pencil, concrete materials, and graphing utilities or other technological tools to evaluate and analyze functions.
2.3.1.a
The student moves between symbolic, numerical, and graphical representations of functions with fluency and accuracy.
2.3.5.a
The student interprets the meaning of points on a graph in the context of a real world situation.
2.4.1.k
The student uses mathematical models to represent and explain mathematical concepts and procedures.
2.4.2.k
The student creates mathematical models to show the relationship between two or more things.
2.4.1.a
The student uses the mathematical modeling process to make inferences about real world situations.
3.4.6.k
The student recognizes an equation of a line in any form and transforms the equation into slope intercept form in order to identify characteristics such as slope and the y-intercept and uses this form to graph the line.
3.4.8.k
The student explains the relationship between the solutions to systems of equations and/or inequalities in two unknowns and their graphs (linear programming).

 

Understandings:

user

Overarching
Analyzing relationships leads to predictions.
Unit
Analyzing relationships between two constraints leads to maximum or minimum when looking at profit.
Maximizing and minimizing profit or cost has business applications.

 

Essential Questions:

user

How do relationships allow us to make predictions?
How do you find maximum and minimum profit lines?
What intersection points of constraints help us?
How does a feasible region help you solve a business application?

 

Knowledge and Skills:

K
What an inequality is
Feasible region
Maximum
Minimum
Point of intersection

S
Use variables to represent problems.
Work with variables, equations, and inequalities.
Graph inequalities.
Draw feasible regions.
Reason based on graphs using parameters, find max and mins, to solve linear programming problems. Create word problems that can be solved by linear programming.

 

Stage 2: Determine Acceptable Evidence

 

Assessment Summary:
Students will develop a linear programming problem that involves two variables, has something that needs to be maximized or minimized and has three or four linear constraints. They will then solve it, and produce an oral and written presentation that explains the problem, provides a solution and proves that there is no better solution.

 

Task/Prompt: Cookies

 

Type:Performance Task

Topics: Solving Inequities, Linear programming, Graphing

 

Summary:
Students will develop a linear programming problem that involves two variables, has something that needs to be maximized or minimized and has three or four linear constraints. They will then solve it, and produce an oral and written presentation that explains the problem, provides a solution and proves that there is no better solution.

 

Print Materials Needed:

 

Resources:

 

Resource Attachments:

 

Internet Resource Links:
Link 1:
Link 2:
Link 3:
Link 4:
Link 5:

 

 

Notes:

 

Student Directions:



 

 

Other assessment evidence to be collected:

Process check

 

In class assessment
Take Home assessment
Portfolio for the unit
 

 

Stage 3: Plan Learning Experiences and Instruction

 

Learning Activities:

1. Hook - Abby and Bing Woo own a small bakery that specializes in cookies. They make only two kinds of cookies- plain and iced. They need to decide how many dozens of each kind of cookie to make for tomorrow. The Woos know that each dozen of their plain cookies requires 1 poind of cookie dough and no icing and each dozen of their iced cookies requires 0.7 poinds of cookie dough and 0.4 poinds of icing. The Woos also know that each dozen of the plain cookies requires about 0.14 hours of preparation time. Finally, they know that no matter how many of each kind they make, they will be able to well them. The Woos decision is limited by 3 factors. How many dozens of each kind of cookie should Abby and Bing make so that their profit is as high as possible?

2. Inequality stories- students are given several situations that need to be translated to algebraic inequalities.
3. Profitable Pictures- How does the graph of a feasible region help to maximize profit?
4. Changing What you eat- Can the same graphing process help to minimize nutritional fat or sugar?
5. Get the Point- How can we find the exact point of intersection on our graphs of feasible regions?
6. A Reflection of Money- How are our skills useful in the applications?
7. How Many of Each Kind Revisited- More Practice
8. Develop Linear program problems of your own.
9. Portfolio, Tests.
10. Performance Assessment