1. UMath X
Common Core Standards
Address PGCPS
Summer School

2. 4 Step Plan ●Digital Learning
Grounding Principles - UMath X - an example
●Model Blended Learning
3 part lessons - Build it, Draw it, Talk it, Write it … to OWN IT!
●Model RtI with a “smarter, not harder” Approach
Multi Sensory - Multi Entry - Tiered Approaches
●”Go Deep” - Unpack Content and Instruction
K to Algebra1 (10th grade)

3. PART 1: Digital Learning Environment
Diverse, Digital Learning
Browser Based
K to Alg 1 Curriculum
Understanding Math - 10th version

4. Digital Learning Principles
move from concrete to
pictorial to abstract
multiple representations
of concepts
interactivity
a mistake is an
opportunity to learn
pacing is controlled by
the learner
support scaffolded
learning
UMath X, the 10th version of Understanding Math, is a diverse, digital learning environment that includes browser based software and related resources to offer 100% coverage of curriculum.
Frameworks for Learning are 3 part content-driven lessons to model a wide variety of implementations of UMath X to create diverse learning environments.
Get Started
Work at It
Reflect and Connect
Frameworks for Learning
3 Part Lessons
Start - Work at it - Reflect

5. UMath X For a GLIMPSE, now LOG into Use any browser & Key in the URL …
Teacher Username Login is … lastname
Generic Password is … umathx
(lastname is lower case) example is .. jones
(corresponding student is .. example jones1
(password is lowercase and can be changed)

6. Note the Digital Learning Principles
Try this path.
Note the Digital Learning Principles

7. Try this path. Generic URL .. www.neufeldlearning.com/preview
Generic Login .. student
Generic Password .. studentpwd

8. Try this path. Generic URL .. www.neufeldlearning.com/preview
Generic Login .. student
Generic Password .. studentpwd

9. For each use 2 menus. .. UMath X & Common Core
The UMath X Menu
is converted into
the CCSS Menu.
Try this path…
Try one of these paths.
For each use 2 menus. .. UMath X & Common Core
3.NF Fractions – The Meaning of Fractions – Introduction .. Think, Write, Say – Circles
7.RP.01.02c Fractions – Ratio and Proportions – Ratio Table – Ex 4

10. PART 2: Blended Learning Environment
Frameworks for Learning
3 Part Lessons to offer many approaches
PART 1
PART 3
UMath X, the 10th version of Understanding Math, is a diverse, digital learning environment that includes browser based software and related resources to offer 100% coverage of curriculum.
Frameworks for Learning are 3 part content-driven lessons to model a wide variety of implementations of UMath X to create diverse learning environments.
Get Started
Work at It
Reflect and Connect
Audio - Click
under first letter
in sentence.
Frameworks for Learning
3 Part Lessons
Model Implementation of UMath X
PART 2

11. Try the path below .. 2 menus Also find the framework.
Frameworks on Paper Lessons on Computer ( (
Audio - Click
under first letter
in sentence.
Try the path below menus
Also find the framework.

12. Blended Learning Try the path below .. 2 menus Find Framework
Access to UMath X
Generic Login .. given …
Generic Password .. umathx (
Access to Frameworks (
Try the path below
.. 2 menus
Find Framework
Materials at each Carousel Station
7.RP.01.02c
Fractions – Ratio and Proportions – Ratio Table – Ex 4
(Framework: Ratio Tables – Pet Store)

13. PART 3: Model RtI withTiered Frameworks
(Modified to Accommodate Learning)
PART 3: Model RtI withTiered Frameworks
UMath X, the 10th version of Understanding Math, is a diverse, digital learning environment that includes browser based software and related resources to offer 100% coverage of curriculum.
Frameworks for Learning are 3 part content-driven lessons to model a wide variety of implementations of UMath X to create diverse learning environments.
Get Started
Work at It
Reflect and Connect
Example: Access CCSS Menu - 7.G (next slide)

14. Example: Access CCSS Menu - 7.G.02.06
..on computer
.. 3 part outlines
on 2 pages

15. Tiered Frameworks… online”

18. PART 4: “Go Deep”-Content / Instruction
Build it .. Draw it .. Talk it .. Write it .. then .. OWN IT!
Our 3 Part Presentation

19. Introduction to Fractions Multiplying Fractions
Differentiate Instruction
Introduction to Fractions
Multiplying Fractions
Decimals & Fractions
Find Frameworks at
for each of these 5 stations. Some frameworks are tiered.
Within your group:
work though tiered framework
discuss content
discuss instruction (
Adding Fractions
Equivalent Fractions (

20. A Sample of FRACTION Lessons(
A Sample of FRACTION Lessons

21. PART 4: “Go Deep”-Content/Instruction
A Tangy Mix of
Amazing Proportions
6th grade to
Algebra 1

22. This session will model ... real world concept-driven tiered
… learning
to address ...
PROPORTIONALITY

23. Differentiate Instruction
Ratio Tables Introduction
Linear Relation Elastic /Walker
Proportions
Estimation
Graphs with/without
A Scale
Find Frameworks at
for each of these 6 stations. Some frameworks are tiered.
Within your group:
work though frameworks
discuss content
discuss instruction (
Proportion
Scale Drawing
Similar Triangles
Slope (

24. A Sample of Proportionality Lessons(

25. Randomized Tests Students need to see question and answer & learn
from them

26. Test for Understanding

37. Blended Learning involves all:
Teachers
School Leaders
Parents
Curriculum
Students
Activity … Ask group how they think these various components of the learning environment contribute to the math learning for a student. (5 min. – Add to Padlet and consolidate ideas quickly if .. the Padlet is available.)

38. ..to.. Change the Mindset Remember How Understand Why
The Emphasis is on:
•students doing mathematics.
•students demonstrating thinking and learning.
•students grapple with challenging tasks in a diverse learning environment
Remember How
..to..
Understand Why

39. Do More! Watch Less. Blended Learning Instructional Paradigm Shift

40. “Active learning practices have a more significant impact on student performance than any other variable.
Instructional Paradigm Shift
Dr. Brigid Barron and Dr. Linda Darling-Hammond, Stanford University
Teaching for Meaningful Learning: A Review of Research on Inquiry-Based and Cooperative Learning

41. … is what you do when you don’t know answers.
Good Mathematics ...
… is what you do when you don’t know answers.
more than “persevering”
more than “engaging”
is “productive” struggling
Too many feel that if we do not “get it” in the first few seconds that we will NEVER get it!
We need to be able to “grapple”.
“Grappling” is much more than “persevering” and “engaging”
In “grappling” one is in competition with him/her self.
… is … “GRAPPLING”
ie … in competition with oneself.

42. Productive Math Talk Moves
Revoicing
Show me another way?
Repeating
How are these same/different?
Reasoning
What would you do if…?
Adding On
What else could you have done?
Waiting
Why did you…?
Students:
Students articulate their own ideas and seriously consider their peers’ perspectives as a way to construct mathematical understandings.
Encourage students
to listen carefully to one another’s ideas
to disagree and question with respect … “ I beg to differ!”
… “ Excuse me. Can we talk about that?”
Use Effective Questions
Show me another way …
How are these the same / different …
What would you do if …
Why did you …
What else could you have done …
Use Productive Talk Moves
Revoicing - Repeating and asking for clarification
Repeating - Students restate someone else’s reasoning
Reasoning - Apply their reasoning to another’s reasoning
Adding on - Prompting for further participation
Waiting - “Take your time. We will wait.”
Effective Questions
Students articulate their own ideas and consider peer perspectives as a way to construct understandings.

43. is the KEY The Teacher Teach in New Ways Lead to Understand
Go Deep to Understand
Unpack the Math
Broad Ability Ranges
Differentiate
Parent Expectations
Challenge for teachers (juggling)
Broad ability ranges within a class
Need for differentiated instruction - RTI
Wide range of literacy skills
Diverse learning styles
Teachers are being asked to teach in ways that they were never taught.
Need to “go deep” and teach with understanding.
Unpack familiar math concepts to lead to understanding.
Require knowledge of an explanation of a concept.
Understand methods and solutions different from their own.

44. Blended Learning - Leadership
Support Teachers
Teach for Understanding
Answers are
Important
but
Not Sufficient
Communicate
with Parents
Teachers do
not provide
all answers.
Students are encouraged to
“Grapple”
convince teachers to teach for understanding.
prepare parents for the fact that teachers may not be providing all of the answers.
prepare parents that students will be grappling with challenging material.
note answers are important but not sufficient.

45. In Preparation for the First Class
Access to UMath X .. URL & login given to you or …
Go to
- see 2 videos .. Navigation / Frameworks
- then select tab “Training Documents” then select “Quickstart”
Professional Learning Options:
1 - 3 hour to 4 day handson session
2 - 1 hour personal Skype or Webinar
3 -
Contact R Neufeld - Sr Author/CEO … Neufeld Learning Sys
Call or