1. Project M3: Mentoring Mathematical Minds Richmond, Virginia
August 5, 2015
HCPS Gifted Programs

2. The Units

3. Materials Teacher Guide Student Journal Think Beyond/Hint Cards
Manipulative Kits
E-Book (

4. Curriculum Units Gifted and Talented Practices
Based on Exemplary
Gifted and Talented Practices
Focus on big ideas from the core curriculum
Add depth and complexity
Incorporate projects, investigations, and games
Engage students as practicing mathematicians
The units not only coincide with the NCTM content standards, but they are also based on what is considered exemplary gifted and talented practices
(Read Each)
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5. Teacher-Friendly Format
Unit Features
Teacher-Friendly Format
Connections to Standards
Suggested unit pacing
Materials list
Unit test and rubric
Check-ups
Resource section

6. In each unit, Students… Become Investigative Mathematicians
Think like a Mathematician
Ask Why? How? What if? What else?
Question the answers, don’t just answer the questions
Engage in written and verbal communication

7. The Lesson Format Planning Phase Teaching Phase Assessment Phase
Big Mathematical Ideas
Objectives
Materials
Mathematical Language
Teaching Phase
Initiate
Investigate
Mathematical Communication
A Quick Look
Assessment Phase
Check-Ups
Unit Test
Initiate: This is an introductory learning experience designed to engage students.
Investigate: Here is where students delve into the activity, exploring the concepts in interesting hands-on investigations.
Mathematical Communication: In this section, students reflect upon the mathematical concepts in the investigation using the think Deeply questions, discuss them with a partner, small group and/or the entire class, and write about them in their Student Mathematician’s Journal.
A Quick Look: A brief summary of the lesson outlining the sequence of instruciton ins

8. The Learning Format Create a spirit of inquiry Respect for each other
Classroom Discussions

10. Mathematical Communication
Verbal Communication
Suggested questions for discussion
Sample dialogues (M3)
Talk Moves
Written Communication
Two Think Deeply open-ended journal questions for every lesson
What to look for in responses
Possible difficulties
Scoring Rubrics

11. Mathematical Communication
Verbal
Goal 1: Help students clarify and share their own thoughts.
Goal 2: Help students orient toward the thinking of others.
Goal 3: Help students deepen their own reasoning.
Goal 4: Help students engage with the reasoning of others.
Written
Student Mathematician’s Journal
Think Deeply Questions

12. Talk Moves = Facilitate Thinking
Repeat and Check
Revoice
Add On
Agree/Disagree and Why
Think Time
Partner Talk
Towards this…
…rather than this.

13. Writing Goals 1. Break down and understand all questions
2. Clearly communicate their thoughts:
Write complete sentences
Organize their thoughts to flow together
Use mathematical language appropriately
3. Defend their ideas:
Provide important aspects of the solution, including the correct answer
If appropriate, provide suitable representations
(e.g., drawing, list, chart, table, diagram, examples)
Possibly provide different solutions and new questions to ponder

14. NCTM (2006) Math Takes Time
“To learn the mathematics required for today’s world, students need adequate time to study and learn mathematics in school…All students need to be engaged in learning challenging mathematics for at least one hour a day at the elementary, middle, and high school levels.”

15. Differentiating is not just deciding to enrich or accelerate.
Depth
Breadth Rate
Think Deeply Questions
Hint Cards
Think Beyond Cards

16. Hint Cards (Karen) [click so both cards show up]
Here is an example of a Hint Card
When you see groups having trouble, instead of you the teacher providing an answer, simply place a card on the table that is about the struggle they are having. They can then have an ah ha moment and remind themselves without being totally teacher dependent.
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17. Think Beyond Cards (Karen) [click so both cards show up]
Here is an example of Think Beyond Cards
The Think Beyond Cards are just what they imply, thinking beyond the current problem or activity and challenging the students with another similar activity.
There are 3-4 Hint cards and Think Beyond cards with each lesson in the Project M2 units. In addition there are other notes throughout the lessons about supporting and challenging students.
Being able to meet the needs of all students was important to the authors.
These cards are in the back of the teacher guide but are also available to be purchased in color cardstock.
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18. Word Wall

19. Flourish

20. At the Mall With Algebra

21. I’m Thinking of a Number
Lesson 1
I’m Thinking of a Number
Think of a number between 0 and 30.
Do not share your number with anyone else.
Follow these directions carefully:
-Take the number and multiply it by 3 to get a new
numbers.
-Add 4 to your new number.
-What is your answer?
Number multiplied by 3, plus 4, results in an answer of__
(Investigate 1 ½ days)

22. I’m Thinking of a Number (cont.)
Lesson 1
I’m Thinking of a Number (cont.)
Figure out what number student started with.
How did you figure it out? What strategy did you use?
The method of work backwards is the one you want to highlight in this lesson.
Have another student volunteer and answer and encourage students to figure out the starting number using the working-backwards strategy.

23. Lesson 1 I’m Thinking of a Number Introducing Symbolism
N X 3 N stands for the starting number
(N X 3) + 4
Number minus 5 N – 5
Twelve times a number 12 X N
Number times 2 plus 1 (N X 2) + 1

24. Lesson 1 I’m Thinking of a Number Introducing Symbolism
Expression – a statement involving numbers, operations and/or variables. Expressions do not use an equal sign. For example, 3 – 1 x
4 + 2 6

25. Lesson 1 I’m Thinking of a Number Introducing Symbolism
(N X 3) + 4 = 43
(N X 3) + 4 = 10
(N X 3) + 4 = 79
(N X 3) + 4 = 94
Equation – a statement that says the value of an expression is equal to the value of another expression.
7 = 7
8 = X
20 = 2a + 6

28. Lesson 1 – Hint Cards

29. Lesson 3 Variable Puzzles Objectives
Students will learn that the same variables have the same values in the same equation.
Students will replace variables with numbers to make true statements.
Students will make inferences and use a variety of strategies to solve problems.

30. Lesson 3
Variable Puzzles
Initiate (1 day)

31. Journal Scoring