Outcomes
Revisit the Principles to Actions book to deepen understanding of:
• Mathematical Representations
• Mathematical Discourse
Define Modeling in Mathematics
Investigate additional parent resources pertaining to the Common Core
AZCCRS Agenda
March 12, 2015
March 25, 2015
9:00 AM - 12:00 PM
1:00 – 4:00 PM
9:15
Getting started
Welcome, outcomes and agenda
Outcomes:
 Revisiting Principles to Actions for discourse and representations
 Defining Modeling in Mathematics
 Investigating Parent Resources
ppt
9:20
Principles to Action – Representations and Discourse
 Read pages 24 – 35 (20 minutes)
 Journal – What three points struck you most?
- What practices have you observed with your teachers?
 Whole group sharing (25 minutes)
Ppt
book
journal
10:05
Sorting Task – sort the cards based on how model is being used; sort
based on your interpretations of model. After completing the sort,
determine a meaning for model for each of the groups. Each table shares
at least one by reading a card from the pile and use the word in a
sentence. Discuss importance of understanding the intent of these terms
in the standards.
Discussion on sorting task
 Give examples of non-mathematical uses of model connecting to
examples given earlier.
 Mathematical uses of model – try to pull out models (noun) refer to
concrete objects while model/modeling (verb) refers to
mathematizing a situation- usually ending with symbolic
representations of the situation, an equation, a table, graph, function
 Share model as it relates to SMP4 and indirectly to SMP5.emphasizing its importance since it is a SMP; this verb model refers
to the students doing the modeling
Use of Model in the CCSS
Modeling in the LOI
Another aspect of modeling that is important in your work is in the LOI
element, Instructional Approach
 How is modeling used in the Instructional Approach Element of the
LOI?
 What is the meaning of and/or in that element?
set of cards/
1 set per
group
Examples of Instructional Approach
Ex. 1- http://mcesa.mediaspace.kaltura.com/media/Instructional+Approach+-
HO of
Instructional
Approach
page
+Level+3+-+3rd+Grade+Math/0_2homcqke/19475892
Reflect:
Comments on example 1: at some places this says level 5 and others it is
level3
Ex. 2 http://mcesa.mediaspace.kaltura.com/media/Instructional+Approach++Level+3+-+8th+Grade/0_vllxocpq/19475892pn
Journal
Handouts
Links
Reflect
Comments on ex. 2
Ex. 3- http://mcesa.mediaspace.kaltura.com/media/Instructional+Approach++Level+4+-+2nd+Grade+Math/0_g0y0b8d1/19475892
Reflect
Comments on ex 3
Consider ideas discussed today about model, models, and modeling,
what are the implications to your role as a school leader?
Modeling in Mathematics
 Write your definition of what this means. Share.
 Handouts: Posters / Illustrative Mathematics page
 Links: Articles in TMMS / Teaching Channel 3 Keys / PARCC task
 Review and revise definition of modeling
 Eighth grade – on a chart, on a table, in real life, on a graph
 Journaling – How does modeling relate to discourse and representations?
11:05
Break
11:15
Parent Resources
 Explore parent resources from handout given last time **MAPPS**
 Share discoveries
Handout from
last session
laptops
11:45
Revisit Outcomes for the day
Exit Ticket
Exit Ticket
Concrete representations of mathematical
quantities or situations
Serving as an example
An ideal
To display, especially by wearing
A mathematical representation or
simulation of a real world (empirical)
situation
A symbolic representation that matches an
observation.
The process of creating and using
mathematics to represent, analyze, and
understand empirical situations as well as
improve decisions about the situation
Using mathematics or statistics to describe a
real world situation and deduce additional
information about the situation by mathematical or statistical computation or analysis
Concrete pictures, physical scale
representations, or abstract
representations of relationships
Developing systems of equations to
behaviors of natural phenomena such as fluid
flow or the paths of ballistic missiles
A standard or example for imitation or
comparison
A representation, generally in miniature, to
show the construction or appearance of
something
A style or design of a particular product
To assume a typical appearance
Being a miniature version of something
To produce a design in plastic material
Writing an equation to predict an
outcome
to copy and cut out
Annotated cards
A mathematical representation of some
phenomenon that helps us better understand it
Concrete representations of mathematical
quantities or situations
Concrete model- noun
Serving as an example
A model home- adjective
An ideal
A model student, adjective
To display, especially by wearing
To model dresses- verb
A mathematical representation or
simulation of a real world (empirical)
situation
Numerical or symbolic representation–
noun
A symbolic representation that matches an
observation
A model of a real life situation - noun
The process of creating and using
mathematics to represent, analyze, and
understand empirical situations as well as
improve decisions about the situation
Modeling- verb
Using mathematics or statistics to describe a
real world situation and deduce additional
information about the situation by mathematical or statistical computation or analysis
Modeling symbolically – verb
Concrete pictures, physical scale
representations, or abstract
representations of relationships
Model- noun
Developing systems of equations to describe
behaviors of natural phenomena such as fluid
flow or the paths of ballistic missiles
Modeling symbolically – verb
A standard or example for imitation or
comparison
A representation, generally in miniature, to
show the construction or appearance of
something
Model to give an example- verb
A style or design of a particular product
To show how to do something
Model- verb
Last year’s model - noun
Being a miniature version of something
He had a model Corvette - Adjective
Writing an equation to predict an
outcome
Model a situation– verb
Use of models and modeling in the AZCCRS
To produce a design in plastic material
A mathematical representation of some
phenomenon that helps us better understand it
Mathematical Model- noun
1.
These tools include concrete models.
2.
Students use numbers …modeling simple joining and separating situations with objects
and eventually with equations..
3.
They use basic shapes and spatial reasoning to model objects in the environment … and
model shapes in the world…
4.
They use a variety of models, including discrete objects and length-based models…to
model add-to, take-from, …situations…
5.
Add within 100…using concrete models or drawings
6.
They solve problems… by applying their understanding of models for addition and
subtraction.
7.
…develop an understanding of the multiplication…involving…area models…
8.
…use fractions along with visual models to represent parts of a whole
9.
Explain … by using a visual fraction model
10. Use area models to represent the distributive property
11. They apply their understanding of models for multiplication…(…area models)… and
division, place value, properties of operations, and the relationship of division to
multiplication
12. …using a visual fraction model (in 8 fourth grade standards)
13. (operations with) decimals to hundredths using concrete models ……
14. using visual fraction models (in 7 fifth grade standards)
15. …compute quotients of fractions…using visual fraction models and equations
16. Develop a probability model…
17. Use the model to determine…Compare probabilities from a model…
18. …including modeling an association … with a linear equation
19. Use functions to model a linear relationship
20. Interpret the rate of change… in terms of the situation it models
21. Understand congruence and similarity using physical models…
22. Know that straight lines are widely used to model relationships…
23. …informally assess the model fit by…
24. Use the equation of a linear model to solve problems … (example: linear model for a
biology experiment)
Definitions of model Noun
1. a standard or example for imitation or comparison.
2.
a representation, generally in miniature, to show the construction orappearance of something.
3.
an image in clay, wax, or the like, to be reproduced in more durablematerial.
4.
a person or thing that serves as a subject for an artist, sculptor,writer, etc.
5.
a person whose profession is posing for artists or photographers.
6.
a person employed to wear clothing or pose with a product forpurposes of display and advertising.
7.a style or design of a particular product:
His car is last year's model.
adjective
12.
serving as an example or model:
a model home open to prospective buyers.
13.
worthy to serve as a model; exemplary:
a model student.
14.
being a small or miniature version of something:
He enjoyed building model ships.
verb (used with object), modeled, modeling or (especiallyBritish) modelled, modelling.
15.
to form or plan according to a model.
16.
to give shape or form to; fashion.
17.
to make a miniature model of.
18.
to fashion in clay, wax, or the like.
19.
to simulate (a process, concept, or the operation of a system),commonly with the aid of a computer.
20.
to display to other persons or to prospective customers, especially bywearing:
to model dresses.
21.
to use or include as an element in a larger construct:
verb (used without object), modeled, modeling or (especiallyBritish) modelled, modelling.
22.
to make models.
23.
to produce designs in some plastic material.
24.
to assume a typical or natural appearance, as the parts of a drawingin progress.
25.
to serve or be employed as a model.