1. District Learning Day Southwind High School August 5, 2015
Utilizing Tasks to Engage Students in the Mathematics Content Standards
District Learning Day
Southwind High School
August 5, 2015
Introduction Slide
Materials Needed:
Do Now Handout
Task Handout
Chart paper
Markers
Post-it pads

2. Do Now
Task
Angel and Jayden were at track practice. The track is 25 kilometers around.
Angel ran 1 lap in 2 minutes.
Jayden ran 3 laps in 5 minutes.
a. How many minutes does it take Angel to run one kilometer? What about Jayden?
b. How far does Angel run in one minute? What about Jayden?
c. Who is running faster? Explain your reasoning.
( standards/7/RP/A/1/tasks/82)
Allow 5 minutes
Solution (see solution handout)
Say:
We can create a table that shows how far each person runs for a certain number of laps:
Number of lapsNumber of km
We can see from the table that 1 km is exactly half way between 2 and 3 laps. So it will take 2.5 laps to run 1 km.
Since it takes Angel 2 minutes to run 1 lap, she will take
2.5 laps1 km⋅2 minutes1 lap=5 minutes1 km.
So it takes Angel 5 minutes to run 1 km. Since it takes Jayden 5 minutes to runs 3 laps, she runs 1 lap in 53 minutes. Thus, it takes Jayden
2.5 laps1 km⋅5 minutes3 laps=52⋅53 minutes/km=256 minutes/km=416 minutes/km.
So it takes Jayden 416 minutes to run 1 km.
Angel runs 1 lap in 2 minutes so she runs 12 lap in 1 minute. Since 1 lap is 25 km, 12 lap is 15 km. So she also runs 15 km in one minute.
Since Jayden runs 1 lap in 53 minutes, she will run 35 laps in 1 minute. Since Jayden runs 1 km in 256 minutes, she will run 625 km in 1 minute.
Jayden runs the same distance in less time than Angel (alternatively, Jayden runs farther in the same time than Angel), so Jayden is running faster than Angel.

3. Norms Be present and engaged.
Be respectful of differences in perspective while challenging each other productively and respectively.
Monitor “air time.”
Make the most of the time we have.
Stay focused on students.
Allow 1 minute
Say: We will adhere to the following norms.

4. Objectives
Know:
how to provide engaging mathematics with rigorous content
how to support and encourage critical thinking and problem solving
Understand:
the importance of developing and using higher-level tasks that build conceptual understanding and mathematical success
the importance of using the resources provided in the instructional map
Do:
integrate literacy strategies in solving mathematical tasks to facilitate communication, problem-solving, and conceptual understanding
develop and plan lessons that will engage students in cognitively demanding tasks
Allow 5 minutes
Please select volunteers to read the objectives for today’s session.

5. What are Standards?
Standards define what students should understand and be able to do in their study of mathematics. But asking a student to understand something also means asking a teacher to assess whether the student has understood it.
Standards do not tell teachers what to do at the classroom level or how to begin making essential changes to implement them.
Allow 2 minutes
Say: Read these two points silently.
Say: Before we engage students in work with the math standards, we must understand the actual meaning and purpose of standards. Standards define what students should understand and be able to do. But they do not lend any information on how to get the students to that point.
Emphasize “Standards do not tell teachers what to do at the classroom level or how to begin making essential changes to implement them”.
Say: It is left up to the professionalism of the teacher to plan lessons and activities that will engage students with the content in order to ensure understanding.

6. Brief History of Mathematics Standards:
In 1989 the National Council of Teachers of Mathematics (NCTM) launched the standards-based education movement in North America with the release of Curriculum and Evaluation Standards for School Mathematics, an unprecedented initiative to promote systemic improvement in mathematics education.
Allow 2 minutes
Say: Let’s begin this session with a brief history of how the math standards were launched. In 1989 the National Council of Teachers of Mathematics (NCTM) launched the standards-based education movement in North America with the release of Curriculum and Evaluation Standards for School Mathematics, an unprecedented initiative to promote systemic improvement in mathematics education.

7. Brief History of Mathematics Standards:
Now, twenty-five years later, the widespread adoption of college- and career-readiness standards, including adoption in the United States of the Common Core State Standards for Mathematics (CCSSM) in some states, provides an opportunity to reenergize and focus our commitment to significant improvement in mathematics education.
Allow 2 minutes
Say: Now 25 years later, we have the Common Core State Standards for Math which “provides an opportunity to reenergize and focus our commitment to significant improvement in mathematics education”.

8. Principles to Actions: Ensuring Mathematical Success for All
The primary purpose of PtA is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards.
Allow 2 minutes
Say: In response to the inception of CCSS for math and the College and Career Readiness math standards, NCTM released a new document titled Principles to Action: Ensuring Mathematical Success for All.
Read the slide.

9. Principles to Actions: Ensuring Mathematical Success for All
“Most important, it describes the actions required to ensure that all students learn to become mathematical thinkers and are prepared for any academic career or professional path they choose.” Principles to Action, NCTM, p.vii
Allow 1 minute
Read slide

10. Principles to Actions discusses and documents these realities:
Too much focus is on learning procedures without any connection to meaning, understanding, or the applications that require these procedures.
Too many students are limited by the lower expectations and narrower curricula of remedial tracks from which few ever emerge.
Too many teachers have limited access to the instructional materials, tools, and technology that they need.
Allow 2 minutes
Say: The book discusses some realities that exist in math education/classrooms.
Read bullets…

11. Principle on Teaching and Learning
The heart of the matter:
Teaching and Learning
An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically.
Allow 2 minutes
Say: Based on the work done in Principles to Action, some guiding principles for school math were developed. One of those principles is the Principle of Teaching and Learning.
Say: An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically.
NCTM, 2014, p. 7

12. Principle on Teaching and Learning
Mathematics Teaching Practices
Establish mathematics goals to focus learning.
Implement tasks that promote reasoning and problem solving.
Use and connect mathematical representations.
Facilitate meaningful mathematical discourse.
Pose purposeful questions.
Build procedural fluency from conceptual understanding.
Support productive struggle in learning mathematics.
Elicit and use evidence of student thinking.
Principles to Actions, NCTM, 2014
Allow 1 minute
Say: There are eight research-informed teaching practices that support the mathematics learning of all students.
The 1st Guiding Principle, Teaching & Learning, has 8 Essential Mathematics Teaching Practices and they are listed on this slide.

13. Implementing Tasks That Promote Reasoning and Problem Solving
Research indicates that student learning is increased when teachers regularly engage students in cognitively demanding tasks. (Boaler and Staples 2008; Hiebert and Wearne 1993; Stein and Lane 1996)
Allow 1 minute
Say: Our focus today is on the second math teaching practice: Implementing tasks that promote reasoning and problem solving. Read the slide

14. Implement Tasks that Promote Reasoning and Problem Solving
Mathematical tasks should:
Provide opportunities for students to engage in exploration or encourage students to use procedures in ways that are connected to concepts and understanding;
Build on students’ current understanding; and
Have multiple entry points.
There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics.
(Lappan & Briars, 1995, NCTM)
Allow 2 minutes
Say: Mathematical tasks should:
Provide opportunities for students to engage in exploration or encourage students to use procedures in ways that are connected to concepts and understanding;
Build on students’ current understanding; and
Have multiple entry points.
Emphasize the quote from Lappan and Briars

15. Math Tasks Modeling Activity
Allow 20 minutes
Pass out task handout “Pizza Toppings”
Facilitator will use the State’s Structure and Routines of a Lesson (handout provided)
Set up problem
Explore/private work time
Small Group problem solving
Share, Discuss and analyze

16. The Structures and Routines of a Lesson
Allow 2 minutes
Presenter note:
Explain the flow of the various stages of the lesson structure and point out how students should have private think time, small group explorations and time to share and discuss. Note how the arrows point to the left column which provides information about monitoring small group interactions and sharing, comparing, focusing and reflecting on the content.

17. Additional Tasks Resources
PtA (NCTM)
MARS
Illustrative Math
Tncore (tneducation fastestimproving)
NYC y/TasksUnitsStudentWork/default.htm
Dan Myer (search Dan Myer's Three-Act Math Tasks)
***Embedded in SCS Math Instructional Maps***
Allow 2 minutes
Say: Here are some additional resources for locating meaningful tasks. Also notice that tasks are embedded throughout the instructional maps.
If time permits click on a few links to show teachers what’s available.

18. Instructional Map -7th Grade
Review the Content and Tasks component of the curriculum maps
Stress the inclusion of math tasks embedded in the maps .

19. Resource Toolbox – 7th Grade
Note Resource Toolbox at the end of each quarter. Highlight the task resources that are available: Illustrative Math, MARS, TNCore, etc.

20. Instructional Map –Algebra I
Review the Content and Tasks component of the curriculum maps (HS example)
Stress the inclusion of math tasks embedded in the maps .

21. Resource Toolbox –Algebra I
Note Resource Toolbox at the end of each quarter. Highlight the task resources that are available: Illustrative Math, MARS, TNCore, etc. (HS example)

22. Revisit Objectives Know:
how to provide engaging mathematics with rigorous content
how to support and encourage critical thinking and problem solving
Understand:
the importance of developing and using higher-level tasks that build conceptual understanding and mathematical success
the importance of using the resources provided in the instructional map
Do:
integrate literacy strategies in solving mathematical tasks to facilitate communication, problem-solving, and conceptual understanding
develop and plan lessons that will engage students in cognitively demanding tasks
Time: 1-2 minutes
Say: Take just a moment to review our session objectives.

23. Next steps and activities for follow up
Collaborate with teachers in your grade-level or subject and examine task resources embedded in your instructional maps.
Plan and implement lessons that include the use of tasks to facilitate student conceptual understanding.
Throughout the school year plan to attend mathematics PD offerings that will continue to expand on the work that we’ve done today.
Allow 2 minutes.
Read the slide and emphasize expectations for follow-up upon teachers’ return to school.

24. Reflection: One minute paper on post-it
What resonated with you?
What are you going to change as a result of attending today’s session?
Jot down your “Take-Aways”
Consider what you need to know and be able to do to successfully implement what you have learned in this session.
What is still unclear?
What professional development or additional resources do you need?
Time: 5 minutes
Say: Take a few minutes to reflect on our session today. Jot any questions or comments that you have on post-its and place them on the “Parking Lot”.
Presenters please collect post-it notes at the end of each session.
Prepare an analysis of the responses and be prepared to share out in DLD debrief.

25. Math Instructional Advisors
Camilla S. Horton, Ed.D Emily B. Barbee, Ed.D.
Middle School Math High School Math
Say: You may contact your instructional advisor if you have any questions or comments.