2. I will now present three versions of the same problem. They are presented to help you think about the problem and how it might be applied to a middle school classroom. The actual problem I want you to solve is found below. Middle school version of the problem: You are cutting a pizza using straight cuts. After 6 cuts, how many pieces can the pizza be divided into? Mathematical version of the problem: What is the maximum number of regions into which 6 lines can divide a plane? Scaffolded version of the problem: A line divides the plane into two pieces (regions). Draw another line. The plane is now divided into three or four regions. It is three regions if the lines are parallel and four if they intersect. In this problem, we want the greatest number of regions. So, two lines yield four regions. A third line divides the plane into seven regions (See the diagram). The results so far: lines regions 7 2 3 1 6 S 1 2 2 4 3 7 Into how many regions would 4 lines divide the plane? Into how many regions would 5 lines divide the plane? Into how many regions would 6 lines divide the plane? The question I'd like you to answer: What is the maximum number of regions into which 12 lines can divide a plane? or What is the maximum number of regions into which 12 straight slices can divide a pizza? (HINT: Rather than draw the picture, start with simpler cases and apply generalized reasoning).
2. I will now present three versions of the same problem. They are presented to help you think about the problem and how it might be applied to a middle school classroom. The actual problem I want you to solve is found below. Middle school version of the problem: You are cutting a pizza using straight cuts. After 6 cuts, how many pieces can the pizza be divided into? Mathematical version of the problem: What is the maximum number of regions into which 6 lines can divide a plane? Scaffolded version of the problem: A line divides the plane into two pieces (regions). Draw another line. The plane is now divided into three or four regions. It is three regions if the lines are parallel and four if they intersect. In this problem, we want the greatest number of regions. So, two lines yield four regions. A third line divides the plane into seven regions (See the diagram). The results so far: lines regions 7 2 3 1 6 S 1 2 2 4 3 7 Into how many regions would 4 lines divide the plane? Into how many regions would 5 lines divide the plane? Into how many regions would 6 lines divide the plane? The question I'd like you to answer: What is the maximum number of regions into which 12 lines can divide a plane? or What is the maximum number of regions into which 12 straight slices can divide a pizza? (HINT: Rather than draw the picture, start with simpler cases and apply generalized reasoning).
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Transcribed Image Text:2. I will now present three versions of the same problem. They are presented to help
you think about the problem and how it might be applied to a middle school
classroom. The actual problem I want you to solve is found below.
Middle school version of the problem: You are cutting a pizza using straight cuts.
After 6 cuts, how many pieces can the pizza be divided into?
Mathematical version of the problem: What is the maximum number of regions
into which 6 lines can divide a plane?
Scaffolded version of the problem: A line divides the
plane into two pieces (regions). Draw another line. The
plane is now divided into three or four regions. It is
three regions if the lines are parallel and four if they
intersect. In this problem, we want the greatest number
of regions. So, two lines yield four regions. A third line
divides the plane into seven regions (See the diagram).
The results so far:
lines regions
7
2
3
1
6
S
1
2
2
4
3
7
Into how many regions would 4 lines divide the plane?
Into how many regions would 5 lines divide the plane?
Into how many regions would 6 lines divide the plane?
The question I'd like you to answer:
What is the maximum number of regions into which 12 lines can divide
a plane? or
What is the maximum number of regions into which 12 straight slices
can divide a pizza?
(HINT: Rather than draw the picture, start with simpler cases and apply
generalized reasoning).
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