Standards for Mathematical Practice

Standards for Mathematical Practice Triangle High Five Middle School Summit August 8, 2013 Ashton Megson North Carolina Department of Public Instruc...
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Standards for Mathematical Practice Triangle High Five Middle School Summit

August 8, 2013 Ashton Megson

North Carolina Department of Public Instruction

Welcome “Who’s in the Room”

Norms • Listen as an Ally • Value Differences • Maintain Professionalism • Participate Actively

DPI Updates

4

http://maccss.ncdpi.wikispaces.net/

Announcements Page

Building the Language of Mathematics for Students

Notification of a slight change in the Numbering System of CCSS for Mathematics

K-8 Lessons for Learning

K-12 AIG Lessons released mid-August

Testing EOG/EOC assessments for the 2013-2014 school year There are no plans to change the format of these assessments for 2013-2014. The number of questions, the balance between calculator active, calculator inactive, and grid-ins won't change. For the following year, 2014-2015, the plan is for North Carolina to use the Smarter Balanced assessments. Smarter Balanced practice assessments are on the wiki. . Michael P. Gallagher, Ph.D. [email protected] Mathematics Test Development Accountability Services, Test Development Section North Carolina Department of Public Education 919.807.3777

• •

Learning Opportunities Resources

Sample Mathematics Resources Who Wants Pizza? A Fun Way to Learn About Fractions Summary: This site comprises six lesson activities including the definition of a fraction, equivalent fractions, addition of fractions, and multiplication of fractions. Students may respond online to get immediate feedback, or they can work the examples on grid paper. Standards: • CCSS.Math.Content.3.NF.A.3a • CCSS.Math.Content.3.NF.A.3b • CCSS.Math.Content.4.NF.B.3a • CCSS.Math.Content.5.NF.A.1 • CCSS.Math.Content.5.NF.A.2 • CCSS.Math.Content.5.NF.B.4a

Exploring Linear Data Summary: Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit. Standards: • CCSS.Math.Content.8.SP.A.1 • CCSS.Math.Content.8.SP.A.2 • CCSS.Math.Content.8.SP.A.3 • CCSS.Math.Content.HSS-ID.B.6c

Why is change necessary?

8+4=[ ]+5 Turn and Talk

8+4=[ ]+5 Percent Responding with Answers Grade

7

12

17

12 & 17

1st - 2nd 3rd - 4th

5th - 6th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

8+4=[ ]+5 Percent Responding with Answers Grade

7

12

17

12 & 17

1st - 2nd

5

58

13

8

3rd - 4th

5th - 6th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

8+4=[ ]+5 Percent Responding with Answers Grade

7

12

17

12 & 17

1st - 2nd

5

58

13

8

3rd - 4th

9

49

25

10

5th - 6th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

8+4=[ ]+5 Percent Responding with Answers Grade

7

12

17

12 & 17

1st - 2nd

5

58

13

8

3rd - 4th

9

49

25

10

5th - 6th

2

76

21

2

Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

Estimate the answer to (12/13) + (7/8)

A. B. C. D.

1 2 19 21

Only 24% of 13 year olds answered correctly. Equal numbers of students chose the other answers. NAEP

Students were given this problem:

 168 20 4th grade students in reform math classes solved it with no problem. Sixth graders in traditional classes responded that they hadn’t been taught that yet.



Dr. Ben Klein, Mathematics Professor Davidson College

Butterfly method

More research - It gets worse! A number contains 18 tens, 2 hundreds, and 4 ones.

What is that number?

1824

2824

218.4

384 Grayson Wheatly

Lesson Comparison United States and Japan The emphasis on skill acquisition is The emphasis on understanding is evident in the steps most common in U.S. evident in the steps of a typical Japanese classrooms lesson •Teacher instructs students in concept or skill

•Teacher poses a thought provoking problem

•Teacher solves example problems with class

•Students and teachers explore the problem

•Students practice on their own while teacher assists individual students

•Various students present ideas or solutions to the class •Teacher summarizes the class solutions

•Students solve similar problems

We know “What” Students Need… 21st Century Skills, critical thinking and problem solving, collaboration and leadership, agility and adaptability, oral and written communication, accessing and analyzing information. Tony Wagner, Rigor Redefined

Teaching for the 21st Century Video

Teacher Evaluation

WIDA

Universal Design for Learning A universally designed curriculum is developed from the start to be accessible as well as challenging, for ALL students.

We Know the “What” But Not “How” to Meet Their Needs

Common Core Standards for Mathematical Practice

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

What should it look like in our classrooms?

Implementing Standards for Mathematical Practices ( Handout) • Read one of the mathematical practices and the information that describes it. • Answer the following questions about the practice. – Why is this practice important? – What does this practice look like when students are doing it? – How can a teacher model this practice? – What could a teacher do within a lesson to encourage students in this practice? Turn and talk with your neighbor about the practice you read.

Standards for Mathematical Practice “What task can I give that will build student understanding?” rather than

“How can I explain clearly so they will understand?” Grayson Wheatley, NCCTM,2002

Let’s Do Some Math using Standards for Mathematical Practice

The Famous Horse Problem

A farmer buys a horse for $60. Later he sells it for $70. He buys it back for $80. Finally, he sells it for $90. How much money did the farmer make or lose?

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

What do you see?

40

4

10 30

2 4

44

Predict some additional data.

40

4

10 30

2 4

45

How close were you?

40

4

10 30 20

2 4 3

46

All the numbers – so?

45 25

4 3

15 40 10 30 20

2 4 2 4 3

47

Where are you?

Roller Coaster Ferris Wheel

45 25

4 3

Bumper Cars Rocket Ride Merry-go-Round Water Slide Fun House

15 40 10 30 20

2 4 2 4 3

48

Fill in the blanks. Ride

???

???

Roller Coaster Ferris Wheel

45 25

4 3

Bumper Cars Rocket Ride Merry-go-Round Water Slide Fun House

15 40 10 30 20

2 4 2 4 3

49

The Amusement Park Ride

Time Tickets

Roller Coaster Ferris Wheel

45 25

4 3

Bumper Cars Rocket Ride Merry-go-Round Water Slide Fun House

15 40 10 30 20

2 4 2 4 3

50

The Amusement Park The 4th and 2nd graders in your school are going on a trip to the Amusement Park. Each 4th grader is going to be a buddy to a 2nd grader.

Your buddy for the trip has never been to an amusement park before. Your buddy wants to go on as many different rides as possible. However, there may not be enough time to go on every ride and you may not have enough tickets to go on every ride. 51

The Amusement Park The bus will drop you off at 10:00 a.m. and pick you up at 1:00 p.m. Each student will get 20 tickets for rides. Use the information in the chart to write a letter to your buddy and create a plan for a fun day at the amusement park for you and your buddy.

52

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Contact Information Ashton Megson

Secondary Mathematics Consultant [email protected]

For all you do for our students!

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