### M3 – Mathematical Practices PowerPoint

```Transition to PA Common Core
Mathematical Practices
1
PA
Common
Core
Local Curriculum
Toolbox
2
Following
• Connect to the Internet
• Navigate to: http://www.pdesas.org
– If a registered user, sign-in
• Place your name and school
3
PA Common Core Introduction
Essential Questions
• What are the Standards for Mathematical
Practices and how do they relate to the PA
Common Core?
• Can the characteristics of a student and
classroom that exemplify mathematical
practices be identified and implemented?
4
Math Class Makeover
Dan Meyer describes why we need
to makeover math classrooms.
5
Expected
Outcomes
Explore
the Standards for Mathematical Practice.
Identify
characteristics of a student and classroom
that exemplify mathematical practice.
6
Looks Like/Sounds Like
When all students are engaged in learning
mathematics, what does a classroom...
Look Like
Sound Like
7
Standards for
Mathematical Practice
The Standards for Mathematical Practice
describe varieties of expertise that
mathematics educators at all levels should seek
to develop in their students. These practices rest
‘processes and
proficiencies’ with longstanding
on important
importance in mathematics education.
(CCSS, 2010)
8
NCTM – Principles and Standards
for School Mathematics
o Problem solving
o Reasoning and proof
o Connections
o Communication
o Representation
9
Standards of Proficiency of
Mathematical Practice
Adding It Up: Helping Children Learn Mathematics
By Jeremy Kilpatrick,
Jane Swafford, & Bob Findell (Editors). (2001).
p. 117
10
Standards for
Mathematical Practice
1. Make sense of complex 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.
11
Grouping the Standards for
Mathematical Practice
(McCallum, 2011)
12
Standards for
Mathematical Practice
1. Make sense of complex 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 implications might the standards of
mathematical practice have on your classroom?
13
Rigor Is
o approaching mathematics with
a disposition to accept
challenge and apply effort;
o engaging in mathematical work
that promotes deep knowledge
of content, analytical
reasoning, and use of
appropriate tools; and
o emerging fluent in the
language of mathematics,
proficient with the tools of
mathematics, and being
empowered as mathematical
thinkers.
Rigor Is Not
o “difficult,” as in “AP calculus is
rigorous.”;
o enrichment activities for
o Problem Solving Friday
o Adding two word problems to the
end of a worksheet; and
o adding more numbers to a
problem.
14
Gita plays with her grandmother’s collection of black & white
buttons. She arranges them in patterns. Her first 3 patterns
are shown below.
Pattern #1
Pattern #2
Pattern #3
Pattern #4
1. Draw pattern 4 next to pattern 3.
2. How many white buttons does Gita need for Pattern 5 and
Pattern 6? Explain how you figured this out.
3. How many buttons in all does Gita need to make Pattern 11?
Explain how you figured this out.
4. Gita thinks she needs 69 buttons in all to make Pattern 24.
How do you know that she is not correct?
How many buttons does she need to make Pattern 24?
CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003
15
1. Individually complete parts 1 - 3.
2. Then work with a partner to compare your work and
complete part 4. Look for as many ways to solve parts
3 and 4 as possible.
3. Consider each of the following questions and be
prepared to share your thinking with the group:
a) What mathematics content is needed to complete the task?
b) Which mathematical practices are needed to complete the
National Council of Supervisors of Mathematics
CCSS Standards of Mathematical Practice: Reasoning and Explaining
CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003
16
www.Inside Mathematics.org
A reengagement
lesson using the
Francis Dickinson
San Carlos Elementary
•
17
Learner A
Pictorial Representation
What does Learner A see staying the same? What does Learner A see
changing? Draw a picture to show how Learner A sees this pattern
growing through the first 3 stages. Color coding and modeling with
square tiles may come in handy.
Verbal Representation
Describe in your own words how Learner A sees this pattern growing. Be
sure to mention what is staying the same and what is changing.
18
Learner B
Pictorial Representation
What does Learner B see staying the same? What does Learner B see
changing? Draw a picture to show how Learner B sees this pattern
growing through the first 3 stages. Color coding and modeling with
square tiles may come in handy.
Verbal Representation
Describe in your own words how Learner B sees this pattern growing. Be
sure to mention what is staying the same and what is changing.
19
Revisited
• Which of the Standards of Mathematical Practice did you see the
students working with? Cite explicit examples to support your
thinking.
• What value did Mr. Dickinson generate by using the same math
task two days in a row, rather than switching to a different
• How did the way the lesson was facilitated support the
development of the Standards of Mathematical Practice for
students?
• What classroom implications related to implementation of CCSS
resonate?
20
Standards for
Mathematical Practice
Standard 1: Make sense of problems and
persevere in solving them.
21
Standards for
Mathematical Practice
Standard 4: Model with mathematics.
22
Standards for Mathematical
Practice in a Classroom
Which fraction is closer to 1: 4/5 or 5/4?
Same problem integrating content and practice
standards
4/5 is closer to 1 than is 5/4.
Using a number line, explain why this is so.
(Daro, Feb 2011)
23
End of the Day
Reflections
1. Are there any aspects of your
own thinking and/or practice
that our work today has
caused you to consider or
reconsider? Explain.
2.
Are there any aspects of your
students’ mathematical
learning that our work today
has caused you to consider or
reconsider? Explain.
Slide 24
Reflection and Planning
• Does our list of words/phrases describe a
classroom where students are engaged in
mathematical practice?
• Use the reflection sheet to capture key
25
References
•
Jean Howard
Mathematics Curriculum Specialist
(406) 444-0706; [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */
•
Cynthia Green
ELA Curriculum Specialist
(406) 444-0729; [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */
•
Judy Snow
State Assessment Director
(406) 444-3656; [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */
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http://www.insidemathematics.org/index.php/class
•
http://insidemathematics.org/index.php/classroom
-video-visits/public-lesson-number-operations/182multiplication-a-divison-problem-4-part-c
•
http://www.insidemathematics.org/index.php/class
•
National Council of Supervisors of Mathematics
•
CCSS Standards of Mathematical Practice:
Reasoning and Explaining
•
•