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

The Units

Materials Teacher Guide Student Journal Think Beyond/Hint Cards Manipulative Kits E-Book (www.flourishkh.com)

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) NEXT SLIDE

Teacher-Friendly Format Unit Features Teacher-Friendly Format Connections to Standards Suggested unit pacing Materials list Unit test and rubric Check-ups Resource section

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

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

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

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

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

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

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

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.”

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

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. NEXT SLIDE

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. NEXT SLIDE

Word Wall

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At the Mall With Algebra

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)

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.

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

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

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

Lesson 1 – Hint Cards

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.

Lesson 3 Variable Puzzles Initiate (1 day)

Journal Scoring