As of 5 27 15 I Notice I Wonder How

As of 5/27/15 I Notice, I Wonder: How to Get Students to Think New York City Mathematics Project Tammy La Guarina, April 29, 2017 Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 1

AGENDA Welcome & Introductions Ever Wonder What They’d Notice? Teresa’s Tiles Standards of Mathematical Practice #1: Make Sense of Problems and Persevere in Solving Them Resources for Notice and Wonder How to Adapt Typical Textbook Problems Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 2

Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education

Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 4

Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 5

Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education

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What Might the Students Wonder? How many inches long is the sink? How do you know how many tiles it would take to cover the room? How many tiles would it take to cover the whole room? Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 8

After Students Notice and Wonder…. Teacher can ask if anyone needs anything clarified to make sure everyone has participated and understands the scenario thoroughly. Then teacher adds more information and/or reveals a question that he/she would like the students to work on (if the question hasn’t been generated already). For example, Teresa is going to put down new tiles on her bathroom floor. These tiles are 4 inches by 4 inches. (Draw a label a 4 inch tile). Now what do we wonder? Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 9

These activities are designed to support students to: q Connects their own thinking to the math they are to do q Attend to details within math problems q Provides a safe, welcoming opening for students who don’t often feel like they have anything to say in math class q Slow down and think about the problem before rushing to calculate q Generate engaging math questions that they are interested in solving q Identify what is confusing or unclear about the problem q Conjecture about possible paths for solving the problem q Find as much math as they can in a scenario, mot just the path to an answer q Keeps speedy students engaged in creative brainstorming rather than closed-ended problem solving. Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 10

CCLS Mathematical Practice 1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education

Good ways to use noticing and wondering to get unstuck: v Make a public record of noticings and wonderings and keep them on display throughout the problem solving process. v Use noticing and wondering as a way to step back when you’re stuck. v Use wondering as a way to see things that are in the back of your mind. Try to wonder things like: “I wonder what would happen if…” “I wonder if it would help to…” Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education

Resources • http: //ntimages. weebly. com/ Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 13

Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 14

What do you NOTICE? What are you WONDERING? Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education

More Resources… • http: //mathforum. org • Powerful Problem Solving, by Max Ray- Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 16

How can we adapt textbook math problems to make Notice and Wonder routine a daily practice? Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 17

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I Notice I Wonder There are two lines. What is the trend shown here? One line says male, the other says female. How many female doctors will there be in the year 2020? The male line is going down as the years get higher. When will the lines meet? Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 19

Notice and Wonder with your Textbooks Apple juice costs 50¢. The juice machine accepts quarters, dimes and nickels. • If you only have dimes, how many would you need to buy one apple juice? Mr. Gavin has a ladder that is 100 centimeters tall. Ms. Cornell has a ladder that is 2 meters tall. • How many quarters, dimes and nickels would you need to buy one apple juice? Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 20

Mr. Gavin has a ladder that is 100 centimeters tall. Ms. Cornell has a ladder that is 2 meters tall. Mike had 3 puzzles. Now he has 5 puzzles. Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 21

Tammy La Guarina Bronx Field Support Center Mathematics Instructional Lead Talessa@schools. nyc. gov Confidential and Proprietary Distribution of this document is not authorized without the express written consent of New York City Department of Education 22