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# CPS Grade 4 Math Pacing Guide 2011-12

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• cours - matière potentielle : students
• cours - matière potentielle : grade
• cours - matière potentielle : year
• exposé
• leçon - matière potentielle : opportunities
• expression écrite
• cours - matière potentielle : page
• revision
• cours - matière potentielle : event
• cours - matière potentielle : years
Cambridge Public Schools Grade 4 Mathematics Pacing Guide 2011 – 2012 Cambridge Public Schools Page 1 2011-2012 The 2011-2012 school year will be the start of the district's transition to the new 2011 Massachusetts Mathematics Curriculum Framework for Grades 3 through 8. The pacing guides for these grades will incorporate new concepts that students need to be successful when the framework is fully implemented in the 2012-2013 school year. In addition, the 2012 MCAS will only test a subset of standards from the 2000/2004 framework, meaning standards not tested on the MCAS will receive less of a focus in this school year.
• unit pricing
• understanding of fraction equivalence
• subtraction of fractions
• problems
• angle
• standards
• data
• problem
• unit
• -1 unit

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 Publié par Nombre de lectures 13 Langue English

Conceptual Database Design Using the
Entity-Relationship (ER) Model
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 1
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Overview of Database Design
•Conceptual design: (ER Model is used for
this.)
– What are the entities and relationships we need?
•Logical design:
– Transform ER design to Relational Schema
• Schema Refinement: (Normalization)
– Check relational schema for redundancies and
We’ll do related anomalies.
this later …• Physical Database Design and Tuning:
– Consider typical workloads; (sometimes) modify the
database design; select file types and indexes.
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 2
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
1Entity-Relationship Model is a
different model than the Relational
Model
• Relation model has:
–tables (relations) with attributes, keys, foreign
keys, domain definitions for attributes
• Entity-Relationship model has:
with attributes, keys, – Entities and entity sets
and domain definitions for attributes
– relationships among entities and
relationship sets with cardinality constraints (in
the book they refer to key constraints and
participation constraints)
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 3
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Entity-Relationship Diagram (original
syntax)
code name
home
name lot
ssn
Department
managerEmployee
Legend:
number
assigned
start
dateRelationship set
end
Project date
Attribute name budget
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 4
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
2Definitions
• Entity: Real-world object distinguishable
from other objects.
– An entity is described using a set of attributes.
• Entity Set: A collection of similar entities.
E.g., all employees. (often referred to as just
entity)
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 5
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Definitions
• Relationship: Association among 2 or more
entities. E.g., Attishoo’s home department is
Pharmacy.
• Relationship Set: Collection of similar
relationships. E.g., Home. (often referred to
as just relationship).
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 6
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
3UML version of the same E-R Diagram
UML: Unified Modeling Language – for OO Design
Employee Departmenthomessn code
name namemanager
lot
Project
assigned number
name
end-date
budget
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 7
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Example
• Professors have a SSN, a name and an age and
their SSNs uniquely identify them.
• Professors teach courses. Each course is
supervised by one professor.
• Courses are uniquely identified by their
courseID, and they have a name.
•Draw the ERD.
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 8
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
4Practice
• Draw the UML version of the previous ERD.
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 9
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Equivalent Relational Schema
Employee (ssn, name, lot, home-dept)
Project-team(ssn, number)
Department (id, name, manager)
Project (number, name, start-date, end-date, budget, sponsor)
Employee Departmenthomessn code
name manager name
lot
Projectassigned
number
name
end-date
budget
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 10
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
5Equivalent Relational Schema - with
foreign keys shown
Employee (ssn, name, lot, home-dept)
Notice that the
many-to-many
Project-team(ssn, number) relationship set
must be represented
in a (new) table.
Department (id, name, manager)
Project (number, name, start-date, end-date,
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 11
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Many-to-many relationship sets
Employee DepartmenthomeERD ssn code
name manager name
lot
Projectassigned
number
start-date
end-date
budget
EmployeeRelational Departmenthome
ssn code
name manager nameDB Diagram
lot
assigned-projects Project
number
nameProj-Team team
end-date
PNumber
budget
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 12
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
6What data do we need to record a
relationship?
Employee Department
homessn code
name name
lot
we must indicate which employee and which department
we want to have connected (for each relationship).
we need the key value for an employee and the key value
for the department – stored together – to represent the
relationship.
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 13
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Cardinality Constraints on Relationship sets:
How many entities can participate?
Employee Department
homessn code
name namemanager
lot
Project
assigned number
name
end-date
budget
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 14
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
7Cardinality Constraints on Relationship sets
How many entities can participate?
Employee Department
0..* 0..1homessn code
name namemanager1..1 0..1
lot
1..1
0..*
Project
assigned 0..* number
0..*name
end-date
budget
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 15
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
An employee can have 0 or 1 home departments
Employee Department0..* 0..1homessn code
name name1..1 manager 0..1
lot
1..1
0..*
Project
assigned 0..* number
0..*
name
end-date
budget
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 16
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
8A department
can have
0 to any number
of employees
Employee Department
0..* 0..1homessn code
name namemanager1..1 0..1
lot
1..1
0..*
Project
assigned 0..* number
0..*name
end-date
budget
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 17
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Unified Modeling Language (UML):
Class Diagram
Employee Departments
homessn 1..1 0..* code
name name
lot
Employee Departments
ssn home0..* 0..1 code
name name
lot
Employee Departments
ssn home0..* 1..* code
name name
lot
Which one is right? We must discover the semantics of the application!
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 18
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
9Various notation for “one-to-many”
zero..one one..many
one many 0..1 1..*
1 m
1 * 0
0-1 1+
maximum cardinalities only minimum and maximum
cardinalities
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 19
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
Various notations for “many-to-many”
one..many one..many
many many 1..* 1..*
m n
1+ 1+
* *
maximum cardinalities only minimum and maximum
cardinalities
CS386/586 Introduction to Database Systems, © Lois Delcambre 1999-2005 Slide 20
Some slides adapted from R. Ramakrishnan, with permission Lecture 7
10