1. Go Deep - A Growth Mindset
UMathX – First Steps
CCSS Curricula – K to Alg1
Training#1
RNeufeld Senior Author
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2. CONTENTS – UMathX Training#1 Focus – First Steps (K to Alg1)
The Learning Environment - Slides 3 to 15
Preparation for Lesson 1 for All - Slide 16
Lesson 1 for All – Slides 17 to 21
Sample Lessons - Kindergarten
Lesson 2 – Kindergarten – Slides 22, 23
Lesson 3 – Kindergarten – Slides 24, 25
Lesson 4 – Kindergarten – Slides 26
Lesson 5 – Kindergarten – Slide 27
Sample Lesson – Grade 1 – Slide 28
Sample Lesson – Grade 2 – Slide 29
Sample Lesson – Grade 3 – Slide 30
Sample Lesson – Grade 4 – Slide 31
Sample Lesson – Grade 7 – Slide 32
Training#1 – Final Notes – Slide 33
Training#2 – Focus on Testing

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

4. 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

5. 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.

6. Model of a Growth Mindset
UMathX
Grappling helps to create KNOWLEDGE

7. Design Principles of UMathX
UMathX presents a
variety of approaches
to meet learning needs
(often concrete to abstract).
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.

8. 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

9. Classroom Learning Environments for UMathX…

10. Making It Work In Your School
Single Classroom
Computer / Workstation
School ‘Lab’
Classroom ‘Cluster’
of 4 or 5 computers

11. The UMathX Menu
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)

12. The UMathX Menu Scaffolded for easy access to any concept.
For Student and Teacher
Across Grades (fill gaps)

13. The CCSS Curriculum Menu
UMathX lessons are placed
into CCSS menu.
For Teacher – lesson and framework.
Domain – Cluster – Standard
2.OA.02.02

14. The CCSS Curriculum Menu
2.OA.02.02
For Teacher – choose lesson and framework.
2.OA.02.02
For Teacher to plan lesson and
framework .
2.OA.02.02

15. The UMathX Framework
Frameworks – 3 part lessons to model implementation of UMathX
If you wish, check the last 5 slides by logging into with your login and password.

16. In Preparation for UMathX Lesson 1 for All
Step 1 Review. Do a quick check of the following.
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 the secure password and login given to you.
Click on “Enter the Program” .. Always maximize the screen.
From the UMathX Menu, follow the path below.
Fractions>Equivalent Fractions>Pattern Blocks>Hexagon 1 and on ..
From the CCSS Menu, select 3.NF.01.03b.
Click on <Lessons> Select Hexagon1 and work through a few screens.
Click on <Frameworks> Select Equivalent Fractions- 1 and check it.
Go to and select Training
Select UMathX-TreasureHunt–CCSS–Kto5 or 6toAlg1 . Select one or two examples from
the Treasure Hunt that are a good fit for your grade level. Work through it.  `

17. 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 3 to 15 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 the 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.

18. 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.

19. 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! Usually up to 3 hints are given. Step 9 After you have worked through some of this lesson, go ahead and 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 far top right on screen, one is thrown out of the program . For security reasons another person cannot login for 2 minutes.

20. Step 11 Discuss with 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 them 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 me if you have discussed it with your partner(s). The teacher is not a “teller”.

21. Step 14 Everyone helps each other to learn
Step 14 Everyone helps each other to learn. 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 for 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

22. Sample Lesson 2 … K.CC.01.03 UMathX
Student’s Turn:
1. Follows Instructions
on Framework
2. Work with UMathX on
Computer (UMathX Menu)
& Framework (Paper)
& get base 10 ..blocks
3. Hands in Framework
for evaluation.
Teacher’s Turn:
1. Reflects & Connects.
“how did you learn best?”
2. Evaluates Student
Performance
Teacher’s Turn:
1. CCSS Menu K.
2. Domain CC
3. Cluster 01
4. Standard 03
5. Lesson: Keep Track by Marking
6. Framework:.. Note 3 parts ..
1 to 1 : Keep Track by Marking
Print one per group

23. Kindergarten Sample Lesson 2 Comments
The 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.
Note that they are learning concepts in many ways.
Note the “Reflect and Connect” section. Find out how they learn.
If you wish, log into again. Navigate to
K.CC Review the 3 steps from the previous screen again.

24. Sample Lesson 3 K.OA.01.05 UMathX
Student’s Turn:
1. Follows Instructions
on Framework
2. Work with UMathX on
Computer (UMathX Menu)
& Framework (Paper)
& get base 10 ..blocks
3. Hands in Framework
for evaluation.
Teacher’s Turn:
CCSS Menu
K.OA.01.05
2. Lesson:
Ways to Make 5
3. Framework:..
Addition Facts – Ways to Make 5
Print one per group
Teacher’s Turn:
1. Reflects & Connects.
“how did you learn best?”
2. Evaluates Student
Performance

25. Kindergarten Sample Lesson 3 .. COMMENTS
Be consistent. Be strong. Maintain your learning environment. They talk quietly to each other. They fulfill their roles. “Ask 3 before you ask me”. They record on the framework. The teacher uses the CCSS menu to find possible lessons and frameworks. Print the framework. (can be b&w on 1 page) Teachers use the CCSS and UMathX menus. Students use the UMathX menu. It is easy to follow. Because of scaffolding, the UMathX menu is used to fill gaps. If you wish, log into again with your login and password. Navigate to K.OA Review the 3 steps from the previous screen.

26. Sample Lesson 4 K.NBT.01.01 UMathX
Student’s Turn:
1. Follows Instructions
on Framework
2. Work with UMathX on
Computer (UMathX Menu)
& Framework (Paper)
& get base 10 ..blocks
3. Hand in Framework
“evaluation”.
Teacher’s Turn:
CCSS Menu
K.NBT.01.01
2. Lesson:
Ones and Groups of 10
3. Framework:..
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.

27. Sample Lesson 5 .. K.CC.01.03 UMathX
Student’s Turn:
1. Follows Instructions
on Framework
2. Work with UMathX on
Computer (UMathX Menu)
& Framework (Paper)
& get base 10 ..blocks
3. Hand in Framework
“evaluation”.
Teacher’s Turn:
CCSS Menu
K.CC.01.03
2. Lesson:
Counting Solids #1
3. Framework:..
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.

28. Grade 1 Sample Lesson 1 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.

29. Grade 2 Sample Lesson 1 2.NBT.02.05 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:
1. Discuss the lesson.
Discuss the framework.
Reflect & Connect.
“how did you learn best?”
2. Collect Frameworks.
3. Self Evaluate.
Teacher’s Turn:
CCSS Menu
2.NBT.02.05
2. Lesson:
Subtraction Without
Regrouping .. concretely
3. Framework:..
Subtract 2 Digit Numbers without
Regrouping
Print one per group
If you wish, check this lesson by logging into with your login and password.

30. Grade 3 Sample Lesson 1 .. 3.OA.01.01 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:
1. Discuss the lesson.
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.

31. Grade 4 Sample Lesson 1 .. 4.NF.01.01 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:
1. Discuss the lesson.
Discuss the framework.
Reflect & Connect.
“how did you learn best?”
2. Collect Frameworks.
3. Self Evaluate.
Teacher’s Turn:
CCSS Menu
4.NF.01.01
2. Lesson:
Hexagon 1, Hexagon 2 etc
3. Framework:..
Equivalent Fractions -1
Print one per group
If you wish, check this lesson by logging into with your login and password.

32. Grade 7 Sample Lesson 1 .. 7.RP.01.02c
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:
1. Discuss the lesson.
Discuss the framework.
Reflect & Connect.
“how did you learn best?”
2. Collect Frameworks.
3. Self Evaluate.
Teacher’s Turn:
CCSS Menu
7.RP.01.02c
2. Lesson:
Introduction 1, Introduction 2
3. Framework:..
Ratio Tables – Introduction - 2
Print one per group
If you wish, check this lesson by logging into with your login and password.

33. Final Notes from Training#1
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 more UMathX features at this time.
Training#2 Objectives - Testing/Evaluation/Analysis
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)