Planning for Student Engagement with Problem Solving

Nicole Beck

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.

Model the following division problem…

What does division mean?

1 2

What does division mean?

1 2

C

on

nect

ing

Learn

ing

DivisionHow many groups of

_ are in __?

236

2)3()6(

3

13

1

23

1

3

2

)3)(2(652 xxxx

1

1

12

2

2

Let’s think about fractions….

What do you NOT want to see

What do you want to see

1.

2.

3.

1.

2.

3.

C

on

nect

ing

Learn

ing

Addition __ + __

532

3

13

1

3

2

3

1

3

1

C

on

nect

ing

Learn

ing

Addition __ + __

532

5)3()2(

3

13

1

3

2

3

1

3

1

23)12()1( 22 xxxxx

Let’s think about fractions….

What do you NOT want to see

What do you want to see

1.

2.

3.

1.

2.

3.

A taste of newfangled word problemsNew 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. 5/8b. 3/8c. 1/4d. 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

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 ProblemUnderline the question.This problem is asking me to find whether Tito or Luis is correct on who ate more pizza.

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 FactsIdentify the facts.Eliminate the unnecessary facts.List the necessary facts.

Cheese Pepperoni Mushroom

Tito ate 1/4 ate 1/8 ate 1/2

Luis ate 3/8 ate 1/2

L Line Up a PlanWrite 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

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

Cheese Pepperoni Mushroom

Tito ate 1/4 ate 1/8 ate 1/2

Luis ate 3/8 ate 1/2

Tito

= 78

= 78

Luis

VVerify Your Plan with ActionEstimate your answer. Luis is correct because it looks like both boys ate the same amount

Carry out your plan.

2 1 48 8 8

Tito

Luis1 1 14 8 2

3 18 2

3 48 8

78

78

Luis is correct. Both boys ate the same amount.

E Examine Your ResultsDoes 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

Is your answer accurate? (check your work.)YesWrite your answer in a complete sentence.Luis is correct because they each ate the same; of a pizza.7

8

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

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.

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

ATLAS 2.0

Standard for Mathematical Practice #1

Standard for Mathematical Practice #1

Standard for Mathematical Practice #1

Standard for Mathematical Practice #1

Connections to ATLAS 2.0

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?

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.

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

How do we prepare teachers to become

highly effective?

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

Looking at Data

Nicole Beck VP of Growth & Developmentn.beck@ntnmath.com443.610.6039

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