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DeBellis & Rosenstein: Discrete Mathematics for K-8 Teachers – Draft 11/4/04 – Classroom Guide Coloring Pictures and Maps Classroom Guide: Chapter One Topic A Coloring Pictures and Maps Figure 1 Figure 2 Figure 3 K-8 Topic Overview K - 2 3 – 5 6 - 8 identifies number of regions in a figure colors two regions with different colors if “they’re next to each other” articulates the number of colors needed to color a page in a coloring book decides if “corners count as a border or not” and colors pictures accordingly colors medium- difficulty pictures and maps identifies the least number of colors needed to properly color pictures & maps defines common border to exclude regions that meet only at a point identifies “problem spots” in simple figures that seem to require 3 or 4 colors begins to reason why a particular picture or map can’t be colored using fewer colors colors continental US Map as introductory activity and colors complex maps identifies “problem spots” in complex pictures or maps that seem to require 3 or 4 colors provides reasons why these figures can’t be colored using fewer colors designs maps that require four colors

Coloring Pictures and Maps -8 Top ic O v er debellis/ClassroomGuide.pdf · th t mee on y a po t • iden tifies “probl em spots” in simple figures that seem to require 3 or 4

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Page 1: Coloring Pictures and Maps -8 Top ic O v er debellis/ClassroomGuide.pdf · th t mee on y a po t • iden tifies “probl em spots” in simple figures that seem to require 3 or 4

DeBellis & Rosenstein: Discrete Mathematics for K-8 Teachers – Draft 11/4/04 – Classroom Guide

Coloring Pictures and Maps Classroom Guide: Chapter One Topic A

Coloring Pictures and Maps

Figure 1

Figure 2

Figure 3

K-8 Topic Overview

K - 2 3 – 5 6 - 8

• identifies

number of regions in a figure

• colors two

regions with different colors if “they’re next to each other”

• articulates the

number of colors needed to color a page in a coloring book

• decides if

“corners count as a border or not” and colors pictures accordingly

• colors medium-

difficulty pictures and maps

• identifies the

least number of colors needed to properly color pictures & maps

• defines common

border to exclude regions that meet only at a point

• identifies

“problem spots” in simple figures that seem to require 3 or 4 colors

• begins to reason

why a particular picture or map can’t be colored using fewer colors

• colors

continental US Map as introductory activity and colors complex maps

• identifies

“problem spots” in complex pictures or maps that seem to require 3 or 4 colors

• provides reasons

why these figures can’t be colored using fewer colors

• designs maps

that require four colors

Page 2: Coloring Pictures and Maps -8 Top ic O v er debellis/ClassroomGuide.pdf · th t mee on y a po t • iden tifies “probl em spots” in simple figures that seem to require 3 or 4

DeBellis & Rosenstein: Discrete Mathematics for K-8 Teachers – Draft 11/4/04 – Classroom Guide

Introduction to Vertex-Edge Graphs Classroom Guide: Chapter One Topic B Vertex-Edge Graphs

����� ���������� ���������������������������! #"�$ %'&�(')�(�*�+,(.- )�/0*�"1)�"2#3�465'798'3�:1;�<�=?>@;�:�A�7B<'CD5E;�F�3G�HJI�K�LMI�HNH#ODP'QSRUT K�V6I�WXO�Y,G.TZTG�LMI�HJP�G�WD[�Q�\�H�R9P�G�T]T \_^`O�a#Ib QcV6O�d6LMQ b QMIM^

Figure 5

Figure 6

K-8 Topic Overview

K - 2 3 – 5 6 - 8 • counts the

number of vertices and edges in simple graphs

• identifies all her

neighbors (while standing on a vertex in a floor graph)

• constructs

simple vertex-edge graphs from simple pictures or maps

• colors two

vertices with different colors if “they’re joined by an edge”

• articulates the

fewest number of colors needed to color a graph

• draws vertex-

edge graphs to represent concrete situations

• investigates

simple properties of graphs like degree

• colors medium-

difficulty graphs using fewest number of colors and finds the chromatic number

• constructs &

colors graphs that represent conflicts

• begins to look at

the structure of “problem spots” to explain why fewer colors can not be used

• begins to reason

why a particular graph can’t be colored using fewer colors

• represents

concrete & abstract situations using graphs

• articulates

reasons why maps & graphs can’t be colored using fewer colors

• designs maps

that require four colors

• shows the

relationship between coloring graphs & coloring maps

• understands &

demonstrates how to resolve conflicts using graph coloring

Page 3: Coloring Pictures and Maps -8 Top ic O v er debellis/ClassroomGuide.pdf · th t mee on y a po t • iden tifies “probl em spots” in simple figures that seem to require 3 or 4

DeBellis & Rosenstein: Discrete Mathematics for K-8 Teachers – Draft 11/4/04 – Classroom Guide

Coloring Mathematically Classroom Guide: Chapter One ����� ������2WKHU�. ���&RORULQJ�

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Page 4: Coloring Pictures and Maps -8 Top ic O v er debellis/ClassroomGuide.pdf · th t mee on y a po t • iden tifies “probl em spots” in simple figures that seem to require 3 or 4

DeBellis & Rosenstein: Discrete Mathematics for K-8 Teachers – Draft 11/4/04 – Classroom Guide

Coloring Mathematically Classroom Guide: Chapter One

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Page 5: Coloring Pictures and Maps -8 Top ic O v er debellis/ClassroomGuide.pdf · th t mee on y a po t • iden tifies “probl em spots” in simple figures that seem to require 3 or 4

DeBellis & Rosenstein: Discrete Mathematics for K-8 Teachers – Draft 11/4/04 – Classroom Guide

Coloring Mathematically Classroom Guide: Chapter One

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