1. Successfully Implementing High-Level Math Tasks
Presented by
Jennifer Montgomery
and Grace Greenleaf
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes
Workshop Description and Title:
Successfully Implementing High-Level Math Tasks
Workshop Description w/attention getter statement:
As we continue our district focus on problem solving, site teams will engage in 21st century learning skills as they solve math tasks correlated to the common core state standards for mathematics. Participants will learn about and use the thinking through a lesson protocol as a guide to successfully implement high-level math tasks in the classroom. Throughout our discussions we will focus on the importance of building conceptual understanding and English language competence simultaneously.

2. Opener
Sometimes when we subtract one number from another number we “regroup”, and sometimes we don’t. For example, if we subtract 8 from 375, we can “regroup by converting a ten to 10 ones:
Page 1 of see handout
Opener 20 minutes with discussion

3. Opener Find a 3-digit number to subtract from 375 so that:
You don’t have to use regrouping (decompose).
You would naturally use regrouping from the tens to the ones place.
You would naturally use regrouping from the hundreds place to the tens place.
You would naturally use regrouping in all places.
In each case, explain how you chose your numbers and complete the problem.
Page 2 of 2--- see handout Opener = 20 minutes with discussion
Participants work for about 10 minutes on the task (or while we wait for the majority of the group to be present). As participants work, presenter reminds participants to explain their thinking in words. Participants may begin working together at any time. The presenter jots down a few key individuals to share their thinking with the entire group and asks them to go up in a particular order. Presenter asks questions to help participants use the correct vocabulary and explain completely. How is this task different from a practice page of subtraction problems?
How will teachers support their English Learners on this task? Is this a good task for ELL’s why or why not?
Pass out entire handout with sample solutions. Discuss the illustrative math project which is where this came from. The illustrative math project is a website where all of the k-12 math standards can be found with sample illustrations (tasks) for teachers to use with students. Teachers submit sample tasks for specific standards and others can comment on the sample tasks. The site is constantly adding and updating their tasks. These problems will be used again laster in the presentation.
4.NBT.B.4 (Numbers and Operations in Base Ten) – Fluently add
and subtract multi-digit whole numbers using the standard algorithm.

4. A good teacher makes you think even when you don’t want to.
(Fisher, 1998, Teaching Thinking)
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes

5. Objectives
Participants will….
Use the thinking through a lesson protocol to successfully plan for and implement a high-level math task to all students, including English Learners to bridge to CCSS implementation.
Create an implementation site plan for Fall 2013
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes
Participants will….
Implement key aspects of problem solving lessons in the classroom daily
Analyze the thinking through a lesson protocol as a guide to successfully plan for and implement high-level math tasks to all students, including English Learners.
Engage in a PLC to practice using the thinking through a lesson protocol
Discuss the stages of a PLC and determine site next steps to move to the next stage

6. Agenda Opener The CCSS for Mathematics
Example of a Problem Solving Lesson: A Pencil and a Sticker Problem
Thinking Through a Lesson Protocol
Group Practice
PLC Process
Reflection
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes

7. Common Core State Standards
For Mathematics
Slides 3 – 18 = 20 minutes

8. Common Core State Standards
Emphasize the 21st Century Learning Skills
Full implementation in with a new assessment
Students in grades 3-8 and grade 11 will be tested in
Test includes constructed and selected response questions focused mostly at DOK levels 3 and 4
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes
Review the 21st Century Learning Skills (The 5 Cs)
Creativity
Communication
Collaboration
Critical Thinking and Problem Solving
And the CA addition Making Connections
DOK (Depth of Knowledge)
How complex a task is: (not difficult)
Level 1 – Recall and Reproduction (Routine)
Level 2 - Basic Application of Skills/Concepts (two or more steps) (Routine)
Level 3 - Strategic Thinking (Non-Routine) (Often more than one solution or pathway to get to the solution)
Level 4 - Extended Thinking (non-routine) (Investigation, Students put their words into a presentation--- takes time)

9. Common Core State Standards
Mathematics has two set of standards
Standards for Mathematical Practice which occur throughout all grade levels
Content Standards that are specific for each grade level
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes

10. Standards for Mathematical Practice
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes
This is available electroncially.

11. Student Friendly Language
CCSS for Mathematical Practice
Student-friendly Language
Make sense and persevere in solving problems.
I can try many times to understand and solve a math problem.
Reason abstractly and quantitatively.
I can think about the math problem in my head, first.
Construct viable arguments and critique the reasoning of others.
I can make a plan, called a strategy, to solve the problem and discuss other students’ strategies too.
Model with mathematics.
I can use math symbols and numbers to solve the problem.
Use appropriate tools strategically.
I can use math tools, pictures, drawings, and objects to solve the problem.
Attend to precision.
I can check to see if my strategy and calculations are correct.
Look for and make use of structure.
I can use what I already know about math to solve the problem.
Look for and express regularity in repeated reasoning.
I can use a strategy that I used to solve another math problem.
Adapted from NCTM article– Slide Handout
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes

12. Math Solutions-Look Fors as Classroom Indicators
What students should be doing for each practice
What teachers should be doing for each practice
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes
Handout

13. Understanding Language: Judit Moschokovich University of CA, Santa Cruz
Slides 3 – 18 = 20 minutes

14. Language Functions in the Standards for Mathematical Practice
Read, locate and highlight language functions in the standards for mathematical practice.
Use the margins to make any inferences you make.
Note: A language function refers to the purpose for which speech or writing is being used.
Slides 3 – 18 = 20 minutes

15. Standards for Mathematical Practice
What standards for mathematical practice did you use as you solved the opening problem? Explain your thinking.
How are the standards
for mathematical practice
helpful for English Learner’s?
Using the handouts ask participants the questions on the slide:
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes The bulk of the time should be spent on this discussion slide

16. Content Standards The standards for mathematics:
Are focused, coherent, and rigorous
Aim for clarity and specificity
Stress conceptual understanding of key ideas
Balance mathematical understanding and procedural skill
Are internationally benchmarked
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes

17. Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes
Handout that is black and white

18. Reading the Content Standards
Content standards define what students should understand and be able to do.
Clusters are groups of related content standards.
Domains are larger groups of related content standards that progress across grade levels.
Standard
from
Grade 3
Opening and CCSS Slides: Numbers 3 – 18 = 20 minutes

19. High-Level Math Tasks as the Center of All Instruction
Problem Solving
High-Level Math Tasks as the Center of All Instruction
Slides = 15 minutes
Daily!

20. Problem Solving
“When students do computation, their thinking should be high-level, critical thinking--- including the same math strategies that many adults in the United States employ in their daily lives.”
“Small Steps, Big Changes: Eight Essential Practices for Transforming Schools Through Mathematics” Chris Confer and Marco Ramirez”
Slides = 15 minutes

21. Try Solving This Problem
“You are shopping at a grocery store. You have a twenty-dollar bill in your pocket. You find a frozen pizza for $10.00, a bag of apples for $5.55, and a box of cereal for $ Do you have enough money to buy everything?”
Slides = 15 minutes
Ask the group. Did you solve the problem mentally or did you use pencil and paper? What would you do at the grocery store? Participants explain the ways that they solved the problem mentally. This type of discussion is what the common core standards are all about. Our math program must change for students experience problem solving on a daily basis.

22. “Problem Solving requires a degree of intellectual struggle
“Problem Solving requires a degree of intellectual struggle. Good math problems make students want to do that kind of mental exercise. Good math problems encourage students to think back to similar problems they’ve done in the past, and try out tools and models that could help them. Most important of all, intellectual struggle develops persistence.”
“Small Steps, Big Changes: Eight Essential Practices for Transforming Schools Through Mathematics” Chris Confer and Marco Ramirez”
Slides = 15 minutes
This is SMP 1

23. Math Task – A Pencil and a Sticker
Solve the problem in as many ways as you can.
Math Task and Presentations
30 minutes = Slides 21 and 22

24. A Pencil and a Sticker
A pencil costs 59 cents, and a sticker costs 20 cents less. How much do a pencil and a sticker cost together?
Math Task and Presentations
30 minutes = Slides 21 and 22
Model the five steps for orchestrating productive discussions here:
Anticipant Solutions (Create a chart with the headers of anticipated solutions, participants and order)
The headers for this problem might include:
Using a diagram, base ten blocks, number line, hundred chart or manipulative
Subtract then add using our traditional algorithm
Subtract then add using a non-traditional algorithm
Other
Monitor Participants
(Ask and answer questions, but don’t give away the solution or lead to the solution in any way) No telling!
3. Select Participants
(Ask participants to share a particular piece of the work that they’ve done)
Sequencing the Participants and having them present
Making connections between each of the presentations

25. Thinking Through a Lesson Protocol
Focused Lesson Planning
BREAK minutes
TTLP Introduction and Sample Slides = 20 minutes

26. Thinking Through a Lesson Protocol (TTLP)
Provides a framework for developing lessons that uses students’ mathematical thinking as the critical ingredient in developing their understanding of key disciplinary ideas.
Helps teachers anticipate what students will do and generate questions to ask that will promote student learning.
TTLP Introduction and Sample Slides = 20 minutes
Additional Notes:
Developed by Margaret S. Smith, Victoria Bill and Elizabeth Hughes who are all college professors at the Universities of Pittsburgh and Northern Iowa.
Intended for teachers to use as a process to further the use of cognitively challenging tasks.

27. Why Lesson Planning?
The effectiveness of a lesson depends significantly on the care with which the lesson plan is prepared.
(Brahier, 2000)
Good planning “shoulders much of the burden” of teaching by replacing “on-fly-decision making” during a lesson with careful investigation into the what and how of instruction before the lesson is taught (Stigler & Hiebert, 1999, p.156)
TTLP Introduction and Sample Slides = 20 minutes 27

28. Why Lesson Planning?
“During the planning phase, teachers make decisions that affect instruction dramatically. They decide what to teach, how they are going to teach, how to organize the classroom, what routines to use, and how to adapt instruction for individuals”
(Fennema & Franke, 1992, p. 156).
TTLP Introduction and Sample Slides = 20 minutes 28

29. Thinking Through a Lesson Protocol (TTLP)
Divided into three sessions:
Part 1: Selecting and Setting Up a Mathematical Task
Part 2: Supporting Students’ Exploration of the Task
Part 3: Sharing and Discussing the Task
Pass out handout of the TTLP
TTLP Introduction and Sample Slides = 20 minutes

30. Part 1: Selecting and Setting Up A Mathematical Task
Teachers will…
Identify the mathematical goals
Select a high-level math task
Anticipant student solutions
Locate tools or resources that students will use
Discuss how the task will
be introduced and how
they know that all students
understand the context of
the task
TTLP Introduction and Sample Slides = 20 minutes
Have teachers read through part 1 and discuss together. What do they notice?

31. Part 2: Supporting Students’ Exploration of the Task
Teachers will..
Monitor students (no telling)
Anticipate questions that they will ask to get a group started or make progress on the task
Generate questions that will focus students’ thinking on the key math ideas in the task
TTLP Introduction and Sample Slides = 20 minutes
Have teachers read through part 2 and discuss together. What do they notice?

32. Part 3: Sharing and Discussing the Task
Teachers will..
Strategically select and sequence students to present their ideas in an order that allows access for all
Make connections
between the
presentations and
to the math goals
for the lesson
TTLP Introduction and Sample Slides = 20 minutes
Have teachers read through part 3 and discuss together. What do they notice?

33. Thinking Through a Lesson Protocol Planning Template Sample
Standards and Goals
Challenges for ELL’s
Task and Possible Solutions and Strategies
Questions the teacher may ask
Ideal order of presentations and why
Next Steps
TTLP Introduction and Sample Slides 19 – 27 = 20 minutes
Have teachers read through part 1 and discuss together. What do they notice?
This sample was written from the Pencil and sticker problem they just experienced. Don’t read this question by question but highlight some of the essential pieces. One piece to include is the EL question in part one and the frayer model. See handout.

34. Group Practice In a small group begin to
practice using the Thinking Through a Lesson Protocol
You will be given a grade level standard and an optional corresponding task that you can choose to use or you may use your own materials.
Be prepared to share your experience with the process, your questions and thoughts with the large group.
Slide 32 = 30 minutes plus share out
Standards and corresponding tasks are available for grades K, 2, 4 and 6.
Handout – extra blank copy for group of the TTLP

35. Seven Stages of Teacher Collaboration
Slides = 15 minutes

36. Seven Stages of Teacher Collaboration
Title 1
Filling the time 2
Sharing personal practice 3
Planning, planning, planning 4
Developing common assessments 5
Analyzing student learning 6
Adapting instruction to student needs 7
Reflecting on instruction
Slides = 15 minutes
Handout… Describe each stage. Below is the paragraph below the chart in the book which describes the stages in more detail.
In the first three stages teachers are trying to understand what they are supposed to accomplish as a team. They may need help bringing a focus to their work, setting up agendas, and learning to plan for the unit by unit work of them team (calendars, assignment, projects, timing of review days, etc.)
Teams in stages 3 and 4 are coordinating common planning of instruction and assessment, developing common assessments and tasks and analyzing student results. Teams may not take collective action on those results, but they are coordinating the generation and use of common learning targets, mathematical tasks, and assessments.
It is in the final two stages that teams are actually collaborating as members take collective responsibility for the learning of all students, differentiating instruction based on their collective understanding of students progress and designing assessments based on students need by reflection on the questions, “Which practices are most effective with our students?” If, after analyzing the data from the unit common assessment, your teams develop a differentiated lesson design to either extend the knowledge and reasoning of students who have mastered the learning target or to provide targeted support for struggling learners, then a more authentic and interdependent collaboration is under way. Collaborative teams achieve stage seven when they regularly make adjustments to instruction based on learner needs and discuss and implement instructional and assessment strategies that have the greatest impact on student learning.
Common Core Mathematics in a PLC at work:
Leaders Guide Tim Kanold and Matt Larson

37. Seven Stages of Teacher Collaboration
In what stage do you think using the Thinking Through a Lesson Protocol would most appropriately fit? Why?
What stages are the PLC teams typically functioning at your site? Why? What could be done to push them to the next stage?
Slides = 15 minutes
Stage Five – As long as you are coming back and analyzing the students work.

38. Reflection As a team discuss the following related to today’s
training and be prepared to share:
What will you personally use next school year?
What are the math needs at your site?
Where should your site begin?
Create an implementation plan for the thinking through protocol with as many details as possible, such as dates and topics for training, planning time, etc.
Slide 36 Reflection – 10 min or remaining time