1. Go Deep - A Growth Mindset
UMathX Information
UMathX Training
Preliminaries – K to Alg1
Sample Lessons - CCLC Alabama Initiative
Differentiated Instruction - RTI
Assessments / Data Analysis
RNeufeld Senior Author
Toll Free:

2. CONTENTS The Learning Environment - Slides 3 to 20
Introductory Lesson For All – Slides 21 to 26
Sample Lessons – Slides 27 to 34
Lesson 2 - K.CC.01.03
Lesson 3 - K.CC.01.03
Lesson 4 – 1.OA.03.05
Lesson NBT.02.07
Lesson 6 – 3.OA.01.01
Lesson F.02.04
Differentiated Instruction – Slides 35 to 44
Examples – Gr 3, Gr 7, Gr 8, Algebra 1
Assessments / Data Analysis – Slides 45 to 47
Help & Thank You – Slide 48

3. Preliminaries to UMathX
In 1988, Rudy Neufeld attended a symposium by
Dr Seymour Papert at MIT.
Papert was a pioneer of Artificial Intelligence and of
Constructivist Learning, learning with active involvement.
He developed the LOGO programming language where a
small robot, a “turtle” is programmed.

4. Preliminaries to UMathX
Neufeld developed resources to use Robots and Logo in teaching teachers and students including those who were hearing impaired.
This led to ideas on teaching and learning mathematics.
It is with this mindset, that he, along with a dedicated group of programmers began to author “Understanding Math”, predecessor of UMathX , in the 1980s and 1990s.

5. UMathX – the 10th version is …
A browser-based, computer-assisted learning system that blends a variety of approaches to help students develop deeper understanding of mathematics concepts from K to Algebra 1.  
A full service learning environment, supporting a ‘growth mindset’ within a ‘learning pit’ encouraging students to ‘grapple’ with concepts through productive struggling, assessments, diagnostics and data analysis for a variety of mathematics curricula.
Please Visit
Play the Videos: UMathX – What is it? UMathX – Walk Through
UMathX – Navigation

6. Model of a Growth Mindset
UMathX
Grappling helps to create KNOWLEDGE
Please view the following 10 minute video.

7. Rich Learning Environment
UMathX
Software
Manipulatives
UMathX Frameworks
& Support Sheets

8. A Growth Mindset within UMathX
Introductory
Steps to
Scaffolded
UMathX Menu
(student use)
CCSS
Curriculum Menu
(teacher use)
(t(t
I Got It!!
Deeper
Understanding

9. Through UMathX, students are actively CONSTRUCTING UNDERSTANDING
LEARNING
occurs with
ACTIVE INVOLVMENT
Through UMathX, students are actively
CONSTRUCTING UNDERSTANDING
to build their KNOWLEDGE.
as opposed to being
PASSIVELY TOLD
what to learn.

10. Log into UMathX For the CCLC UMathX Alabama Initiative
One Can Access UMathX in one of 4 Ways:
Student, Teacher, Principal, Supervisor
Use any browser to key in the URL ..
Key in your USERNAME & PASSWORD

11. Example - Adding Numbers Vertically
The UMathX Menu
Example - Adding Numbers Vertically
The UMathX Menu allows student and teacher to follow a CONCEPTUAL PATH rather than an often disjointed GRADE focus.
It is flexible in that one can focus on concepts in a certain grade and conceptual scaffolding over a number of grade levels.
Scaffolded for easy
access to any concept.
For Student and Teacher
Across Grades (fill gaps)
( K to Algebra 1 )
TRY IT … In any browser, for example, “Google Chrome”,
USE THE URL …
Your Login … given to you
Your Password … given to you
If you have forgotten the login or password, contact us toll free at
or me personally at

12. The Example - Adding Numbers Vertically
The CCSS Curriculum Menu
The Example - Adding Numbers Vertically
Lessons from the UMathX Menu
that fit are copied into the CCSS menu.
CCSS Menu contains lessons & frameworks
written specifically for the teacher.
CCSS code for the above is … 2.OA.02.02
Grade - Domain – Cluster - Standard

13. The CCSS Curriculum Menu
2.OA.02.02
The Teacher chooses the lesson for … 2.OA.02.02
For Teacher to plan lesson and
framework .
2.OA.02.02

14. 2.OA.02.02 Go to www.umathx.com Play the video … “UMathX - Frameworks”
Frameworks – lessons to model implementation of UMathX
Go to Play the video … “UMathX - Frameworks”
2.OA.02.02
For the Teacher – choose lesson and framework.
2.OA.02.02
For Teacher to plan lesson and
framework .
2.OA.02.02

15. The Framework – 3 Parts
If you wish, check the last 5 slides by logging into with your login and password.

16. Example - Multiplying Fractions
The UMathX Menu
Example - Multiplying Fractions
Ex here is Mu
The UMathX Menu allows student and teacher to follow a CONCEPTUAL PATH rather than an often disjointed GRADE focus.
It is flexible in that one can focus on concepts in a certain grade and conceptual scaffolding over a number of grade levels.
Scaffolded for easy
access to any concept.
For Student and Teacher
Across Grades (fill gaps)

17. Example - Multiplying Fractions
The CCSS Curriculum Menu
Example - Multiplying Fractions
If you wish, click on
and log in with login and password that you were given.
Now as a teacher, access … 5.NF.02.04a in CCSS.
Find the appropriate lesson and framework.
Lessons from the UMathX Menu
that fit are copied into the CCSS menu.
CCSS Menu contains lessons & frameworks
written specifically for the teacher.
CCSS code for the above is 5.NF.02.04a
Grade – Domain – Cluster - Standard

18. Design Principles of UMathX
UMathX presents a
variety of approaches
to meet learning needs
.. concrete (with blocks) to
abstract (without blocks)
UMathX features Instructional Scaffolding
This allows student & teacher to follow a CONCEPTUAL PATH
rather than a disjointed GRADE focus.
It is flexible. One can focus on concepts in a certain grade
and conceptual scaffolding over a number of grade levels.

19. Built-in Differentiation – Tiered lessons
UMathX
Encourages Grappling
“Grappling” is:
-more than “persevering”
-is “productive” struggling
Interactions present hints.
A mistake is an opportunity to learn.
Teachers, please do not tell. Encourage grappling.
“ask three before you ask me”
Built-in Differentiation – Tiered lessons

20. Classroom Learning Environments for UMathX…

21. In Preparation for UMathX Lesson 1 for All
Log into with the secure password and login given to you. From the UMathX Menu, follow the path below and work through Hexagon1 and on .. Fractions>Equivalent Fractions>Pattern Blocks>Hexagon 1 and on .. From the CCSS Menu, select 3.NF.01.03b. Click <Lessons> Select Hexagon1 . Work through a few screens. Click on Click on <Frameworks> and select <Equivalent Fractions -1> Go to and select Training Select UMathX-TreasureHunt–CCSS–Kto5 or 6toAlg1 Work through the Treasure Hunt. Select a few of the examples that fit your grade level. Work through them.

22. Lesson 1 for All
Step 1 We suggest a teacher directed whole class lesson here for all
students. Make sure that your interactive board or projector and
computer are ready. The computer has a mouse. In K to 1 or 2,
we suggest that students sit on your learning carpet in front of the
screen or interactive board. In all classes, we suggest that you
choose a student to be the computer pilot as you direct.
Step 2 Go through relevant previous screens 6 to 20 of this powerpoint.
Discuss the contents of the slides with them.
Step 3 Keep the information in this lesson simple and short.
Go to any browser. Reinforce where that is.
Show them their URL
This is the name of their virtual UMathX school.
Step 2 Review
Visit and play 3 videos: UMathX – What is it? – The Learning Pit
UMathX – Navigation
UMathX – Frameworks for Learning
Step 3 Log into with secure password and login given to you.
From the UMathX Menu, follow the path below and work through Hexagon1 and on ..
Fractions>Equivalent Fractions>Pattern Blocks>Hexagon 1 and on ..
From the CCSS Menu, select 3.NF.01.03b. Click <Lessons> Select Hexagon1.
Go to and select Training
Select UMathX-TreasureHunt–CCSS–Kto5 or 6toAlg1 and work through the Treasure Hunt.
Select one of the examples that is a fit for your grade level and work through it.

23. Step 4 You login with your login and password
Step 4 You login with your login and password. They receive theirs later. Step 5 Click on “Enter the Program”. Maximize the screen. Direct your student navigator to the UMathX menu on the left. Navigate to Fractions and just hover over the word. Then navigate to the right - hover over Equivalent Fractions Then navigate to the right and hover over Pattern Blocks Then navigate the mouse to the right and click on Hexagon 1. Step 6 Note functionality of the <proceed> button and of the <enter> key. This gives the operator time to think. When the <proceed> button is not shown, then there is another instruction on the screen which one should look for. Step 7 Note when any sentence is double clicked, the line is read and it is highlighted to help with reading and word recognition.

24. Step 8 Emphasize that a mistake is an opportunity to learn
Step 8 Emphasize that a mistake is an opportunity to learn. If there is a flashing cursor in a text field, enter a number or letters depending on what is asked for. Then press the <enter> button. When you press the <enter> button, you are commanding, DO IT! Step 9 After you have worked through some of this lesson, clear the screen by clicking on the HOME icon at the top. Click on the logout button to the far right. Have another student, key in a login and password. Repeat previous steps to review them by choosing another topic. Repeat this process with a number of students. Step 10 Note the correct way to login and logout. When one clicks on the X on the far top right on screen, one is thrown out of the program. For security reasons another person cannot login for 2 minutes.

25. Step 11 Inform the class on how you plan to use UMathX – alone on one computer, small group or pair and whole group. In group work each student will have a role. Step 12 Discuss “grappling” and the “learning pit” with your students. Students formulate their ideas and knowledge in many different ways. When in pairs or small groups, we want students to discuss. The teacher will rarely give answers during the lesson. Try to work towards this situation. Step 13 If one answers incorrectly, the computer will give up to 3 hints. One cannot continue until one has entered the correct answer. IDEA: Tell them .. “If you have a question for the teacher, turn the empty cup on your desk UP. Only ask the teacher if you have discussed it with your partner(s). The teacher is not a “teller”.

26. Step 14 Everyone is a partner in learning
Step 14 Everyone is a partner in learning. Everyone is important along with UMathX, the paper, the manipulatives, the teacher. Step 15 When they walk in tomorrow, there will be 1 page on their desk. (a framework) It will tell them what to do. If they are working in pairs, they share the one page. They bring a pencil. The teacher will help with reading the framework if needed. Step 16 The student will follow instructions on the page. When the instruction is to go to the UMathX menu, only then do they proceed to a computer station and login to UMathX. Stress the importance of learning with a variety of approaches. The framework will lead the student through 3 steps. Step 17 Inform students that they may access UMathX from home. If you wish to review the above, log into with your login and password. Navigate to 3.NF.01.03b

27. Sample Lesson 2 … K.CC.01.03 UMathX
Teacher’s Turn:
1. Reflects & Connects.
“how did you learn best?”
2. Evaluates Student
Performance
Student’s Turn:
1. Follows Instructions
on Framework
2. Work with UMathX on
Computer (UMathX Menu)
& Framework (Paper)
& base 10 ..blocks
3. Hands in Framework
for evaluation.
Teacher’s Turn:
CCSS Menu
K.CC.01.03
2. Lesson:
Keep Track by Marking
3. Framework:.. Note 3 parts ..
1 to 1 : Keep Track by Marking
Print one per group

28. Sample Lesson 2 - Comments
The first lesson sets the tone. Please be well prepared.
Consider using base 10 blocks and frameworks.
Discuss the learning environment with your class. Be tough, be
consistent. It will make future life easier for you. Note frameworks –
3 part lessons. Adapt them. They will give you ideas.
Possibly use groups of 2 - a Pilot and a CoPilot.
One person is on computer and the other uses paper and pencil.
They are learning concepts in many ways.
Note the “Reflect and Connect” section. Discuss with them.
Find out how they learn best
If you wish, log into again. Navigate to
K.CC Review the 3 steps from the previous screen again.

29. Sample Lesson 3 .. K.CC.01.03 UMathX
Student’s Turn:
1. Follows Instructions
on Framework
2. Work with UMathX on
Computer
(UMathX Menu)
3. Discuss the lesson as
instructed by teacher.
Teacher’s Turn:
1. CCSS Menu
K.CC.01.03
2. Lesson:
Counting Solids #1
3. A Framework has not been
written for this lesson. You
might look at ways to implement
this lesson or do the entire lesson
within UMathX on computer.
Teacher’s Turn:
1. Discuss the lesson. .
Reflect & Connect.
“how did you learn best?”
2. The teacher
self evaluates.
If you wish, check this lesson by logging into with your login and password.

30. Grade 1 Sample Lesson 1.OA.03.05 UMathX
Student’s Turn:
1. Follows Instructions
on Framework
2. Work with UMathX on
Computer (UMathX Menu)
& Framework (Paper)
3. Hand in Framework
“evaluation”.
Teacher’s Turn:
CCSS Menu
1.OA.03.05
2. Lesson:
Adding Along the Numberline
3. Framework:..
Addition Facts- Adding Along The
Numberline.
Print one per group
Teacher’s Turn:
1. Discuss the lesson.
Discuss the framework.
Reflect & Connect.
“how did you learn best?”
2. Collect Frameworks.
3. Self Evaluate.
If you wish, check this lesson by logging into with your login and password.

31. Grade 2 Sample Lesson 2.NBT.02.07 UMathX
Teacher’s Turn:
1. Discuss the lesson.
Discuss the framework.
Reflect & Connect.
“how did you learn best?”
2. Collect Frameworks.
3. Self Evaluate.
Student’s Turn:
1. Follows Instructions
on Framework
2. Work with UMathX on
Computer (UMathX Menu)
& Framework (Paper)
3. Hand in Framework
“evaluation”.
Teacher’s Turn:
CCSS Menu
2.NBT.02.07
2. Lesson:
Subtraction With Regrouping#3
3 Digit Numbers, Concretely D
3. Framework:..
Subtract 3 Digit Numbers
with Regrouping #3
(note-base 10 blocks-real/draw)
Print one per group
If you wish, check this lesson by logging into with your login and password.

32. Grade 3 Sample Lesson 3.OA.01.01 UMathX
Student’s Turn:
Follows Instructions
Framework “Get Started”
- in UMathX on Computer.
2. Follow Framework
- “Working In It”
3. Follow Framework
- “Reflect & Connect”
Teacher’s Turn:
1. Facilitate discussion
2. Reflect & Connect.
Discuss the framework.
Reflect & Connect.
“how did you learn best?”
2. Collect Frameworks.
3. Self Evaluate.
Teacher’s Turn:
CCSS Menu
3.OA.01.01
2. Lesson:
Eggs in Bowl…Introduce X
3. Framework:..
Multiplication – Introduction – 2 –
Eggs in Bowls
Print one per group
If you wish, check this lesson by logging into with your login and password.

33. Grade 8 Sample Lesson 8.F.02.04 UMathX
Student’s Turn:
Follows Instructions
Framework “Get Started”
- in UMathX on Computer.
2. Follow Framework
- “Working In It”
3. Follow Framework
- “Reflect & Connect”
Teacher’s Turn:
1. Facilitate discussion
2. Reflect & Connect.
Discuss the framework.
Reflect & Connect.
“how did you learn best?”
2. Collect Frameworks.
3. Self Evaluate.
Teacher’s Turn:
1. CCSS Menu
8.F.02.04
2. Lesson: Setup Equations
Linear Relations
-- The Elastic Example
3. Framework:..
Linear Relations – Elastic- 1
(STEM Activity)
Print one per group
If you wish, check this lesson by logging into with your login and password.

34. Summary 1. Teachers plan within the CCSS menu.
First select and preview the lesson
Then select and preview the framework (if exists)
2. Students work in UMathX Menu .. scaffolded.
A lesson leads to the next lesson. (fill gaps)
Develop a concept by working down the UMathX menu (challenges increase)
3. The start is critical. Keep it simple.
Set up and model the learning environment. (begin with whole class lessons)
Don’t confuse them with too many UMathX features at this time.
If you wish, check any items in this training by logging into with your login and password.
If you need help, me at
or call (toll free)

35. Differentiated Instruction RTI with Tiered Frameworks
(modified to accommodate learning)

36. Access the CCSS Menu for 3.NF.01.01

37. The Common Core
selection
offers 2 options.

38. Frameworks (3 Part Lessons for Blended Learning – TIER 1

39. If you wish to check any items here, log into www. umathx
If you wish to check any items here, log into with your login and password.

40. .. 3 part outlines
on 2 pages

41. Slope & Line – Walk in Real World - tier 1, tier 2, tier 3 8.EE.02.06

42. If you wish to check any items here, log into www. umathx
If you wish to check any items here, log into with your login and password.

44. If you wish to check any items here, log into www. umathx
If you wish to check any items here, log into with your login and password.

45. Assessments / Analysis
Visit
Play the Videos:
UMathX – Assessments
UMath – Data Analysis
One can access UMathX in 4 ways: Student
Teacher
Principal
District Lead
We will enter as a Teacher.
We use neufeld as teacher.
Click Profile then select Classes to form a class.
Profile
We will form Neufeld Class 1.
We will select 4 students with data. (from Student List)
They are .. Student1, Student2, Student3, Student4
You may want to follow along with your own login at

46. Click on the Tests Icon.
UMathX has 4 Types of Assessments.
Now return to the Home Screen.
Tests
Now click on the Data Module Icon.
A teacher can click on 2 of the 4 choices which appear as below.
Data Module
You may want to follow along with your own login at
Click on this option.

47. Now, back in Teacher Summary, select Student1.
Click on “View a Report “.
Double Click on Advanced Report -“Results Over Time”
Double Click on .. CCSS
Double Click on .. Common Core 5th Grade … Numbers and Operations – Fractions.
Pick a start date of Feb 1.
Pick an end date after the present date.
Click on <Done>.
Double Click the line giving information on results of Common Core – Grade 5 test done on Aug 26..
Double Click on Student1.
Double Click on line for Question 11 to see how the student answered and the solution.
You may now want to go back 3 slides and review the steps with your own login and password in the URL:

48. Thank You for Participating in this Introduction to UMathX
If you are a member of the CCLC UMathX Alabama Initiative but do not have usernames and passwords for yourself and/or your students:
Contact: or or
call toll free
Contact me directly for a personal session, a webinar, for permanent access or if you have any difficulties at:
R Neufeld (CEO/Sr Author)
Neufeld Learning Systems Inc.
toll free in North America