New York City Mathematics Project Tammy La Guarina, April 29, 2017 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 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

Here is a typical 7th grade problem. What is the first you notice Here is a typical 7th grade problem. What is the first you notice? All of the words…too many words.

What if we just presented the students with this diagram and asked them to talk about what they see or notice. Take 5 minutes to list as many things as you can that you notice using the notetaking sheet.

Include in packet

Here are some of the things that the students noticed.

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? Noticings and wonderings are closely linked. It is hard to notice things without asking questions. Here are some things the students might wonder. These wonderings might organically drift into the exact questions/concepts you want to cover.

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? Students are left to their own devices to figure out the question. Teacher as facilitator provides more information slowly and as needed. Now students have access to the problem, have ownership of the information because for the most part they have generated it and have developed an interest in pursuing the solution.

These activities are designed to support students to: Connects their own thinking to the math they are to do Attend to details within math problems Provides a safe, welcoming opening for students who don’t often feel like they have anything to say in math class Slow down and think about the problem before rushing to calculate Generate engaging math questions that they are interested in solving Identify what is confusing or unclear about the problem Conjecture about possible paths for solving the problem Find as much math as they can in a scenario, mot just the path to an answer Keeps speedy students engaged in creative brainstorming rather than closed-ended problem solving.

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.

Good ways to use noticing and wondering to get unstuck: Make a public record of noticings and wonderings and keep them on display throughout the problem solving process. Use noticing and wondering as a way to step back when you’re stuck. 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…”

Resources http://ntimages.weebly.com/

What do you NOTICE? What are you WONDERING?

More Resources… http://mathforum.org Powerful Problem Solving, by Max Ray- http://mathforum.org Powerful Problem Solving, by Max Ray- Riek

How can we adapt textbook math problems to make Notice and Wonder routine a daily practice?

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?

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? How many quarters, dimes and nickels 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 can you use NW within your textbooks (if you have to use your textbooks?) Look at the examples taken from a generic textbook. How are they altered to allow students a deeper experience and conceptual understanding?

Mr. Gavin has a ladder that is 100 centimeters tall. Ms 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.

Tammy La Guarina Bronx Field Support Center Mathematics Instructional Lead Talessa@schools.nyc.gov