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Planning for Student Engagement with Problem Solving Nicole Beck

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Let’s Do Some Math! Stephanie was away for two weeks. While she was away, her three neighbors alternated taking care of her mail, plants, and fish. To thank them, she is baking each of them a pound cake. Each cake calls for ¼ cup of whipping cream. Stephanie has ½ cup of whipping cream. Does Stephanie have enough whipping cream to make 3 pound cakes? Why or why not? Show a model to justify your answer.

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Model the following division problem…

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What does division mean? 1 2

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1 2

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Connecting Learning Division How many groups of _ are in __? 1 1 1 2 2 2

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Let’s think about fractions…. What do you NOT want to see What do you want to see 1. 2. 3. 1. 2. 3.

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Grade 3 The Meaning of Fractions The Number Line and Number Line Diagrams Equivlent Fractions Comparing Fractions Grade 4 Equivalent Fractions Comparing Fractions Adding and Subtracting Fractions- Like Denominators Multiplication of a Fraction by a Whole Number Grade 5 Adding and Subtractracting Fractions- Unlike Denominators Multiplying Fractions Multiplication as Scaling Dividing Fractions- Whole Number by a Fraction and Fraction by a Whole Number

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Connecting Learning Addition __ + __

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Connecting Learning Addition __ + __

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Let’s think about fractions…. What do you NOT want to see What do you want to see 1. 2. 3. 1. 2. 3.

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A taste of newfangled word problems New Common Core standards are due to roll out in 46 states by 2014. They're designed to get students ready for college and careers by requiring them to think, write and explain their reasoning. They also de-emphasize multiple-choice test questions in favor of written responses. Here's an example for New York City fifth- graders: Old question: Randa ate 3/8 of a pizza, and Marvin ate 1/8 of the same pizza. What fraction of the pizza did Randa and Marvin eat? a. 5/8 b. 3/8 c. 1/4 d. 1/2 New question: Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate one-eighth of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Luis ate three-eighths of a cheese pizza. Luis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more pizza than Luis because Luis did not eat any pepperoni pizza. Luis says they each ate the same amount of pizza. Who is correct? Show all your mathematical thinking. Source: New York City Department of Education

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New Problem: Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate one-eighth of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Luis ate three-eighths of a cheese pizza. Luis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more pizza than Luis because Luis did not eat any pepperoni pizza. Luis says they each ate the same amount of pizza. Who is correct? Show all your mathematical thinking. S Study the Problem Underline the question. This problem is asking me to find whether Tito or Luis is correct on who ate more pizza.

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Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate one-eighth of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Luis ate three-eights of a cheese pizza. Luis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more pizza than Luis because Luis did not eat any pepperoni pizza. Luis says they each ate the same amount of pizza. Who is correct? Show all your mathematical thinking. O: Organize the Facts Identify the facts. Eliminate the unnecessary facts. List the necessary facts. CheesePepperoniMushroom Titoate 1/4ate 1/8ate 1/2 Luisate 3/8 ate 1/2

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LLine Up a Plan Write in words what your plan of action will be. Add all of the pizza Tito ate to get a total. Add all of the pizza Luis ate to get a total. Compare the totals to see who is correct. Choose an operation or operations. Addition and Comparing

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VVerify Your Plan with Action Estimate your answer. Luis is correct because it looks like both boys ate the same amount Carry out your plan.

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__ 4 1 4 1 4 1 4 1 _ 8 1 1 Whole __ 2 1 2 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1

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CheesePepperoniMushroom Titoate 1/4ate 1/8ate 1/2 Luisate 3/8 ate 1/2 Tito __ 4 1 _ 8 1 2 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 = 2 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 _ 8 1 = Luis

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VVerify Your Plan with Action Estimate your answer. Luis is correct because it looks like both boys ate the same amount Carry out your plan. Tito Luis Luis is correct. Both boys ate the same amount.

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EExamine Your Results Does your answer make sense? (Compare your answer to question.) Yes, because we are looking for whether Tito or Luis are correct on who ate more pizza. Is your answer reasonable? (Compare your answer to the estimate.) Yes, because it is close to my estimate that both boys ate equal amounts

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Is your answer accurate? (check your work.) Yes Write your answer in a complete sentence. Luis is correct because they each ate the same; of a pizza.

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Methodology Creating opportunities for students to build conceptual understanding of, and experience success with fundamental skills building connections to higher levels of understanding.

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Domain 3: Instruction In the classrooms of accomplished teachers, all students are highly engaged in learning. They make significant contributions to the success of the class through participation in high-level discussions and active involvement in their learning and the learning of others. As a result, students understand their progress in learning the content and can explain the learning goals and what they need to do in order to improve. Effective teachers recognize their responsibility for student learning and make adjustments, as needed, to ensure student success.

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How would the teacher measure for each of the following components: 3a: Communicating with Students 3b: Using Questions and Discussion Techniques 3c: Engaging Students in Learning 3d: Using Assessment in Instruction 3e: Demonstrating Flexibility and Responsiveness

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ATLAS 2.0

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Standard for Mathematical Practice #1

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Connections to ATLAS 2.0

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Speculate... What do you think this teacher’s lesson plan looked like? What do you believe needs to be included in an effective lesson plan?

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Domain 3: Instruction In the classrooms of accomplished teachers, all students are highly engaged in learning. They make significant contributions to the success of the class through participation in high-level discussions and active involvement in their learning and the learning of others. As a result, students understand their progress in learning the content and can explain the learning goals and what they need to do in order to improve. Effective teachers recognize their responsibility for student learning and make adjustments, as needed, to ensure student success.

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How would the teacher measure for each of the following components: 3a: Communicating with Students 3b: Using Questions and Discussion Techniques 3c: Engaging Students in Learning 3d: Using Assessment in Instruction 3e: Demonstrating Flexibility and Responsiveness

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How do we prepare teachers to become highly effective?

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Seven Levels of Staff Development Staff development is viewed as a process, not as an event. National Training Network’s “Seven Levels of Staff Development” create an essential link between classroom instruction and higher student achievement. Level 1: Intensive Professional Development Level 2: Comprehensive Lessons Level 3: Coaching Level 4: Assisting Through Looking at Students (ATLAS) Level 5: Professional Learning Communities Level 6: Technology Level 7: Leadership Academy

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Looking at Data

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Nicole Beck VP of Growth & Development n.beck@ntnmath.com 443.610.6039 The Key Elements to Fraction Success One Day Workshop You can register now at: register.ntnmath.comregister.ntnmath.com

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www.NTNMath.com 1.800.686.1001

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LEARNING RESEARCH AND DEVELOPMENT CENTER © 2012 UNIVERSITY OF PITTSBURGH Supporting Rigorous Mathematics Teaching and Learning Using Assessing and Advancing.

LEARNING RESEARCH AND DEVELOPMENT CENTER © 2012 UNIVERSITY OF PITTSBURGH Supporting Rigorous Mathematics Teaching and Learning Using Assessing and Advancing.

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