1. Ensuring Instructional Task Quality in Mathematics, Grades K-12
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Ensuring Instructional Task Quality in Mathematics, Grades K-12
Materials:
Sticky notes
Poster paper with tasks written on them
person copy of tasks
markers
personal copy of content guides- grades 4, 6, and Algebra I
Be ready to share how to find the content guides
Winter 2017

2. Where Have We Been? Focus:
ENSURING TASK QUALITY IN MATHEMATICS
Where Have We Been?
Focus:
Spend the most time on the most important stuff!
Rigor:
Balance conceptual understanding, procedure, and modeling/application.
Coherence:
Within-Grade: use multiple standards to leverage deeper understanding.
Across-Grade: use progressions to bridge gaps.
2 min.
Speaker Notes:
Ask: How do they make sense of problems?

3. Where Are We Going Today?
ENSURING TASK QUALITY IN MATHEMATICS
Where Are We Going Today?
Tying it All Together with the Task
2 min
Speaker Notes:
Talking points: The fundamental work that students do in math classes is to solve problems. Focus, coherence, and rigor are crucial for planning and for instruction and supervision. They also matter, though, in task design, which is where all of our work meets students directly.

4. Objectives and Agenda Morning Ice Breaker/Opener
ENSURING TASK QUALITY IN MATHEMATICS
Objectives and Agenda
Morning
Ice Breaker/Opener
Analysis Protocol and Task Analysis
Break
Task Analysis and Adaptation
Lunch
Afternoon
Task Analysis
Gallery Walk
Coaching, Planning, Wrap Up
Participants will be able to
Determine whether an instructional task is of high quality based three key indicators.
Coach teachers in choosing or adapting tasks to increase alignment.
6 min
Speaker Notes:
Say: Given this, here are our objectives today and how we’ll get there.
Read objectives and see if anyone has questions
Read agenda and see if anyone has questions.
8:30–9:30: Review, Objective, Agenda and Activator
9:30–10:30: Analysis protocol and task analysis
10:00 – 10:45: Break
10:45 – 12:00: Task Analysis and Adaptation
12:00 – 1:00: Lunch
1:00 – 2:15: Task Analysis
2:15 – 3:00: Gallery Walk
3:00 – 4:30: Coaching, Planning, Wrap Up

5. Activator: You Teach! The Task
ENSURING TASK QUALITY IN MATHEMATICS
Activator: You Teach!
The Task
Using chart paper and markers, design a 5 minute lesson that teaches your topic to an audience of standards skeptics. For your topic, you must:
Convey all key ideas accurately. Identify what it is—and what it isn’t.
Present a strong rationale of its importance.
Have an element of “stickiness” so the learning will be memorable.
Count off 1–6.
The Groups
1. Focus
2. Within-Grade Coherence
3. Across-Grade Coherence
4. Conceptual Understanding
5. Procedural Skill and Fluency
6. Application/Modeling
50 min. – Each group needs chart paper and markers.
Speaker Notes:
4 min. – Give directions and move into groups.
Say: The purpose here is to help you remember what you have already learned about standards-based mathematics, whether with us at an Institute or somewhere else.
<Click> Have the group count off 1-6.
<Click> to show the groups topic assignments
<Click> to show them the task.
10 min. to plan and groups will be chosen randomly to teach their topic
30 min. to present (1 min. transition between groups)
You may have the groups around the room rather than have groups come to the front if it will save time.

6. Is This a High-Quality Instructional Task? Why? Why Not?
ENSURING TASK QUALITY IN MATHEMATICS
Is This a High-Quality Instructional Task? Why? Why Not?
[6.EE.C.9]
Stephanie is helping her band collect money to fund a field trip. The band decided to sell boxes of chocolate bars. Each bar sells for $1.50 and each box contains 20 bars. Below is a partial table of monies collected for different numbers of boxes sold.
Complete the table above for the values of m.
Write an equation for the amount of money, m, that will be collected if b boxes of chocolate bars are sold. Which is the independent variable and which is the dependent variable?
Graph the equation using the ordered pairs from the table above.
Calculate how much money will be collected if 100 boxes of chocolate bars are sold.
The band collected $ from chocolate bar sales. How many boxes did they sell?
Boxes Sold b
Money Collected m 1
$30.00 2 3 4 5
$150.00 6 7 8
15 min.
Speaker Notes:
Facilitator presents the task. People work in groups to do the task and come up with reasons the task is quality or not.
SOURCE:
“Chocolate Bar Sales” by Illustrative Mathematics is licensed under CC BY 4.0.

7. Traits of Task Quality Alignment/Embodiment of the Standard(s)
ENSURING TASK QUALITY IN MATHEMATICS
Traits of Task Quality
Alignment/Embodiment of the Standard(s)
It elicits reasoning and/or modeling and expects communication of it.
It minimizes processing demands.
15 min.
Speaker Notes:
After participants have had the chance to work the task and come up with why it is good, have them share their thoughts on why it was good (this can be popcorned). Then show this slide, which will summarize with these points. Ask them to compare/contrast.
Responses may include traits that are good, but not the main point of our work today (and are often too granular):
It’s real world; true, but not all tasks need to have this characteristic.
It focuses on Major Work of the Grade: True, but many strong tasks will be aligned to more than one standard, which may include supporting/additional work; or, they may be aligned to supporting/additional work only. In both cases, this does not affect the quality of task; rather, it reflects on the instructional context.
It’s mathematically correct: this is taken as a non-negotiable prerequisite. If the math is bad, the task must not be used as-is.
Others may come up too, but should have their importance judged based on applicability and context.
1: State this one, but also say that we’ll come back to it in more detail shortly
2: Say: Rather than just doing the math—which is perfectly reasonable as students approach fluency—we need tasks to be written in a manner that elicits reasoning (or modeling) where appropriate. This helps us see not only where students are doing well, but where they make mistakes and what misconceptions may be behind those mistakes.
3: By processing demands, we mean attributes of the task which are ancillary or superfluous to the mathematics, yet which require students to deal with it.
Say: For our task, here’s what we saw:
It is aligned to the standards.
It requires students to reason and/or model and to communicate that reasoning and modeling through the creation and use of graph and equation; and the task itself is accessible (low processing demand and scaffolding on ramps: only the important information is in the task; and, there is nice scaffolding. Teacher could help, if needed to populate 2).

8. Is This a High-Quality Instructional Task? Why? Why Not?
ENSURING TASK QUALITY IN MATHEMATICS
Is This a High-Quality Instructional Task? Why? Why Not?
[A-REI.C.5]
15 min.
Speaker Notes:
Facilitator presents the task. People work in groups to do the task and come up with reasons the task is quality or not.
SOURCE:
“Equations in Two Unknowns” by Illustrative Mathematics is licensed under CC BY 4.0.

9. Traits of Task Quality Alignment/Embodiment of the Standard(s)
ENSURING TASK QUALITY IN MATHEMATICS
Traits of Task Quality
Alignment/Embodiment of the Standard(s)
It elicits reasoning and/or modeling and expects communication of it.
It minimizes processing demands.
15 min.
Speaker Notes:
After participants have had the chance to work the task and come up with why it is good, have them share out their thoughts on why it was good (this can be popcorned). Then show this slide, which will summarize with these points. Ask them to compare/contrast.
Responses may include traits that are good, but not the main point of our work today (and are often too granular):
It’s real world: True, but not all tasks need to have this characteristic.
It focuses on Major Work of the Grade: True, but many strong tasks will be aligned to more than one standard, which may include supporting/additional work; or, they may be aligned to supporting/additional work only. In both cases, this does not affect the quality of task; rather, it reflects on the instructional context.
It’s mathematically correct: this is taken as a non-negotiable prerequisite. If the math is bad, the task must not be used as-is.
Others may come up too, but should have their importance judged based on applicability and context.
1: State this one, but also say that we’ll come back to it in more detail shortly
2: Say: Rather than just doing math- which is perfectly reasonable as students approach fluency- we need tasks to be written in a manner that elicits reasoning (or modeling) where appropriate. This helps us see not only where students are doing well, but where they make mistakes and what misconceptions may be behind those mistakes.
3: Say: By processing demands, we mean attributes of the task which are ancillary or superfluous to the mathematics, yet which require students to deal with it.
Say: For our task, here’s what we saw:
It is aligned to the standards;
It requires students to reason and/or model and to communicate that reasoning and modeling through the use of “explain”; and the task itself is accessible (low processing demand and scaffolding on ramps; only the important information is in the task; and, there is nice scaffolding through all the information given. Teacher could help, if needed to initiate the equation writing).

10. More on “Alignment” What does it mean?
ENSURING TASK QUALITY IN MATHEMATICS
More on “Alignment”
What does it mean?
How do you know it exists or not?
What do you need to know to be able to answer that question?
15 min.
Speaker Notes:
First bullet: popcorn
Say: “Alignment” often glosses over the subtle misalignments. So, we use the word embodiment as well, to ensure that the task aligns to the letter and spirit of the standard. This is fairly simple with respect to fluency. But procedure, which requires an understanding of the logical, reasonable, and reversible steps taken, should use tasks where students can say why they engaged in the procedure they did. This is similar to tasks that focus on conceptual understanding.
Second bullet: TPS
Third bullet: popcorn
Say: The Content Guides provide us a wonderful tool to better understand alignment and embodiment. By going into much more detail about the standards, how they’re connected, and what they look like in action, they teach us—and our teachers—what the standards actually mean.
Say: There are three parts: The first part focuses on the major work of the grade—a set of standards that could reasonably be the focus for a unit of instruction. The second part focuses on coherence—those standards which reasonably support the primary standards. The third part focuses on progressions of ideas—before and after content.
Go back to task from the start of the day and ask them to provide more details from CG as to how the tasks embody the standards.
Note: if the standards in question are not found in the content guide, then the standards themselves are the reference.

11. Is This a High-Quality Instructional Task? Why? Why Not?
ENSURING TASK QUALITY IN MATHEMATICS
Is This a High-Quality Instructional Task? Why? Why Not?
[6.EE.C.9]
Stephanie is helping her band collect money to fund a field trip. The band decided to sell boxes of chocolate bars. Each bar sells for $1.50 and each box contains 20 bars. Below is a partial table of monies collected for different numbers of boxes sold.
Complete the table above for the values of m.
Write an equation for the amount of money, m, that will be collected if b boxes of chocolate bars are sold. Which is the independent variable and which is the dependent variable?
Graph the equation using the ordered pairs from the table above.
Calculate how much money will be collected if 100 boxes of chocolate bars are sold.
The band collected $ from chocolate bar sales. How many boxes did they sell?
Boxes Sold b
Money Collected m 1
$30.00 2 3 4 5
$150.00 6 7 8
15 min.
Speaker Notes:
Say: For our work today, please turn to page 17 of the Grade 6 Content Guide and read pages 17 and 18 (the section on “Expressions & Equations: Representing relationships between two variables.” Then, go back to the task and look for evidence of alignment or not.

12. Is This a High-Quality Instructional Task? Why? Why Not?
ENSURING TASK QUALITY IN MATHEMATICS
Is This a High-Quality Instructional Task? Why? Why Not?
[A-REI.C.5]
15 min.
Speaker Notes:
Say: For our work today, please turn to page 13 of the Algebra I Content Guide and read pages 13 to 15, the section titled “Systems of equations.” Then, go back to the task and look for evidence of alignment or not.

13. Take a break… Reconvene in 15 minutes. IMAGE CREDITS:

14. Is This a High-Quality Instructional Task? Why? Why Not?
ENSURING TASK QUALITY IN MATHEMATICS
Is This a High-Quality Instructional Task? Why? Why Not?
Is it Aligned? Let’s do the task first and then analyze it:
What content and performance demands does the task make on students?
What is the purpose of the task?
Which CCSS or your state’s (CCR) standards seem to be targeted by the task?
Does it elicit Reasoning and/or Modeling? Does it expect students to communicate it?
What types of student reasoning are required by the task?
For mathematics: which Standards for Mathematical Practice might be addressed by the task?
Does it minimize processing demand?
10 min.
Speaker Notes:
Say: Let’s do this again, but with a little more structure.
Note that we have been asking simple questions, but want to dig in more deeply. Then, read through the slide.

15. ENSURING TASK QUALITY IN MATHEMATICS
Analysis
Suppose the task was intended to be aligned to 7.RP.A.2d. Answer the questions:
Is it aligned (check the Content Guide!)?
Does it elicit Reasoning and/or Modeling? Does it expect students to communicate it?
Does it minimize processing demand?
20 min.
Speaker Notes:
Participants analyze the task and come to agreement in their groups about what’s wrong with it.
Say: What if I told you this task was said to align to 7.RP.A.2d?
It’s about determining whether relationships are proportional using a table, graphing, and finding the constant of proportionality (7.RP.A.2a). Yet, the target is 7.RP.A.2d. and the Internet search came up as such. Yikes!
No. No expectation that students explain anything.
Processing demand is okay.
SOURCE:
Problem is an original from Doug Sovde for purposes of this deck only.

16. Is This a High-Quality Instructional Task? Why? Why Not?
ENSURING TASK QUALITY IN MATHEMATICS
Is This a High-Quality Instructional Task? Why? Why Not?
Is it Aligned? Let’s do the task first and then analyze it:
What content and performance demands does the task make on students?
What is the purpose of the task?
Which CCSS or your state’s (CCR) standards seem to be targeted by the task?
Does it elicit Reasoning and/or Modeling? Does it expect students to communicate it?
What types of student reasoning are required by the task?
For mathematics: which Standards for Mathematical Practice might be addressed by the task?
Does it minimize processing demand?
10 min.
Speaker Notes:
Say: Let’s do this again, but with a little more structure.
Note that we have been asking simple questions, but want to dig in more deeply. Then, read through the slide.

17. ENSURING TASK QUALITY IN MATHEMATICS
Analysis
Suppose the task was intended to be aligned to A-REI-A.1. Answer the questions:
Is it aligned (check the Content Guide!)?
Does it elicit Reasoning and/or Modeling? Does it expect students to communicate it?
Does it minimize processing demand?
20 min.
Speaker Notes:
Participants analyze the task and come to agreement in their groups about what’s wrong with it.
Say: What if I told you this task was said to align to A-REI.A.1?
It’s about showing work in solving linear equations—not reasoning A-REI.B.3. Yet, the target is A-REI-A.1, and the Internet search came up as such. Yikes!
Yes, there is explanation, but it’s all procedural; no conceptual understanding.
Processing demand is okay.
SOURCE:
Problem is an original by Doug Sovde for purposes of this deck only.

18. What Now? Two Options: Work with (or ask) the teacher to fix it.
ENSURING TASK QUALITY IN MATHEMATICS
What Now?
Two Options:
Work with (or ask) the teacher to fix it.
What are the dependencies that need to be in place to make this work?
Deep knowledge of the standards (including the mathematics)
Time to do it.
Point the teacher to replacement tasks!
Use IM or ENY
7.RP.A.2d
A-REI.A.1
30 min.
Speaker Notes:
Say: Okay. So that was a bad task. What can we do about it? What can we tell staff to do about it?
Direct them to go find 3 viable replacements and explain why they chose the replacements.

19. Lunch break… 1 hour Speaker Notes:
Prep posters for tasks at this time if they have not been pre-prepped.
IMAGE CREDITS:

20. ENSURING TASK QUALITY IN MATHEMATICS
Practice!
At your tables is a stack of 5 tasks for each grade band (6-8 and 9-12). Get through as many as you can using our protocol to determine whether this is a high-quality task or not. If you deem it is not, suggest a viable replacement.
Add your thoughts to the posters around the room using stickies—one for each task.
75 min. (about 15 mn per task)
Speaker Notes:
Review the work of the morning—understanding what task quality traits are, analyzing tasks for them, and then finding replacements.
Now, folks get to practice!

21. Gallery Walk and Break What trends did you see with respect to:
ENSURING TASK QUALITY IN MATHEMATICS
Gallery Walk and Break
What trends did you see with respect to:
Alignment/Embodiment
Reasoning/Modeling and Communication Thereof
Processing Demands
35min.
Speaker Notes:
Debrief using this slide, too. Answers to these questions are found in the tasks handout.

22. ENSURING TASK QUALITY IN MATHEMATICS
What If?
All’s well, but there is no expectation for reasoning/modeling or communication?
5 min.
Speaker Notes:
Debrief using this slide too. Ask participants, in their groups to TPS on how they would address.
Responses should include things like:
First question is whether the task needs it—remember, fluency does not!
If it does, questions like, “Explain your reasoning” can be added to address the gap.

23. What If? All’s well, but too much processing?
ENSURING TASK QUALITY IN MATHEMATICS
What If?
All’s well, but too much processing?   
5 min.
Speaker Notes:
Debrief using this slide, too. Ask participants in their groups to TPS on how they would address.
Cut out unnecessary words.
Use shorter sentences.
Use smaller/shorter words.
Caution: some modeling questions require a bit more language to help students set assumptions and constraints, the purpose of task needs to be clear.

24. Coaching Role Play
1 min.
Speaker Notes: this is a transition slide. Use it shift people from the content deep work they’ve done to now discuss putting it to use in a coaching role play.

25. Coaching Role Play: Purpose and Scenario
ENSURING TASK QUALITY IN MATHEMATICS
Coaching Role Play: Purpose and Scenario
The objective of this activity is to give leaders practice coaching a teacher on quality math tasks in the context of an authentic lesson planning situation.
You stop by a teacher’s room and ask how math is going. The teacher holds up one of the poor-quality tasks you just evaluated and is excited that there is a whole website with many other activities just like this one. You have 5 minutes before you have to meet with the PTA—what do you do?
2 min.
Speaker Notes:
State the purpose of this role play: leaders have to practice talking about the changes they want to see. Leaders have to practice talking about content as well – especially if you don’t consider yourself a “math person”
Provide an overview of the process:
You will have 4 minutes to prepare to coach the teacher on one of the poor quality tasks you just evaluated. This will be quiet preparation time.
You will pair up, choose who goes first.
First role play, coach shares goals for the coaching sessions and sets the “heat” level.
5 min. role play
1 min. to gather your reflections and evidence for feedback
5 min, reflection and feedback
Say: This will be intentionally quick – most leaders do not have a ton of time to debrief a quick observation, so we are practicing doing this quickly and efficiently.
Say: I will manage time and signal when you move to a different part of the protocol.

26. Coaching Role Play: Purpose and Process
ENSURING TASK QUALITY IN MATHEMATICS
Coaching Role Play: Purpose and Process
The objective of this activity is to give leaders practice coaching a teacher on quality math tasks in the context of an authentic lesson planning situation.
Get Ready (4 min.)
Pair Up (2 min.)
Role Play & Feedback #1 (11 min.)
Role Play & Feedback #2 (11 min.)
2 min.
Speaker Notes:
State the purpose of this role play: leaders have to practice talking about the changes they want to see. Leaders have to practice talking about content as well—especially if you don’t consider yourself a “math person.”
Provide an overview of the process:
You will have 4 minutes to prepare to coach the teacher on one of the poor quality tasks you just evaluated. This will be quiet preparation time (see next slide for full directions).
You will pair up, choose who goes first.
First role play, coach shares goals for the coaching sessions and sets the “heat” level.
5 min. role play
1 min. to gather your reflections and evidence for feedback
5 min. reflection and feedback
Say: This will be intentionally quick—most leaders do not have a ton of time to debrief a quick observation, so we are practicing doing this quickly and efficiently.
Say: I will manage time and signal when you move to a different part of the protocol.

27. Coaching Role Play 4 min. – Everybody gets ready. 2 min. – Pair up.
ENSURING TASK QUALITY IN MATHEMATICS
Coaching Role Play
The objective of this activity is to give leaders a chance to practice coaching a teacher
on quality math tasks in the context of an authentic lesson planning situation
4 min. – Everybody gets ready.
Identify your goals for this coaching session.
What do you want the teacher to know and be able to try as a result of this interaction?
Draft entry question(s), clarifying questions, and probing questions.
Draft key learning and next steps you want the teacher to walk away ready to try.
2 min. – Pair up.
Choose a partner.
Identify who will go first.
Role Play #1 shares goals and the level of “heat” you’d like to practice coaching.
11 min.
Speaker Notes:
Click though each part at the time stated.
<Click> and give them 4 minutes to get ready.
<Click> and give them 2 minutes to partner and choose who goes first.
Next slide <Click> and give them 5 minutes for the role play.

28. Role Play #1 – 5 Minutes ENSURING TASK QUALITY IN MATHEMATICS 5 min.
IMAGE CREDITS:

29. Role Play #1 – Reflect and Feedback
ENSURING TASK QUALITY IN MATHEMATICS
Role Play #1 – Reflect and Feedback
1 min. – Each role writes reflections of effectiveness of coaching conversation from their point of view.
2 min. – Identify what worked.
Coach first:
Start with stating your goal(s) for the discussion and 1-2 moves you made that supported that goal.
Share 1-2 other pluses that you can identify.
Teacher:
Share 1-2 moves the coach made that deepened your understanding of quality math tasks.
2 min. – Identify suggestions for improvement.
Share 1-2 things you’d like to do differently or improve.
Share 1-2 things the coach should consider to strengthen practice.
5 min.
Speaker Notes:

30. Transition to Role Play #2
ENSURING TASK QUALITY IN MATHEMATICS
Transition to Role Play #2
Review preparation notes.
Share coaching goals and the level of “heat” you’d like to practice coaching.
1 min.
Speaker Notes:
Say:
Time to switch roles.
#2, share your goals and level of heat.
Be ready on my signal.
IMAGE CREDITS:

31. Role Play #2 – 5 Minutes ENSURING TASK QUALITY IN MATHEMATICS 5 min.
Speaker Notes:
IMAGE CREDITS:

32. Role Play #2 – Reflect and Feedback
ENSURING TASK QUALITY IN MATHEMATICS
Role Play #2 – Reflect and Feedback
1 min. – Each role writes reflections of effectiveness of coaching conversation from their point of view.
2 min. – Identify what worked.
Coach first:
Start with stating your goal(s) for the discussion and 1-2 moves you made that supported that goal.
Share 1-2 other pluses that you can identify.
Teacher:
Share 1-2 moves that the coach made that deepened your understanding of quality math tasks.
2 min. – Identify suggestions for improvement.
Share 1-2 things you’d like to do differently or improve.
Share 1-2 things the coach should consider to strengthen practice.
5 min.
Speaker Notes:

33. ENSURING TASK QUALITY IN MATHEMATICS
Now What?
5 min. – Individually write what you intend to do with what you have learned today:
What will you do?
With whom?
When?
How?
10 min. – Discuss it with a colleague. Colleagues should probe the plans they hear, helping to make the plans better and stronger.
15 min.
Speaker Notes:

34. Feedback
Please fill out the survey located here:
-Click “February Institute” on the top right
-Click “Details” on the center of the page
5 min.
Speaker’s Notes:
Please fill out the survey to help us improve!

35. ENSURING TASK QUALITY IN MATHEMATICS Reference List
Slide
Source 6
Grade 4, Module 3, Lesson 11 from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0. 8
“Chocolate Bar Sales” by Illustrative Mathematics is licensed under CC BY 4.0. 10
“Equations in Two Unknowns” by Illustrative Mathematics is licensed under CC BY 4.0. 18
Newark Public Schools.
20, 22
Doug Sovde

36. Image Credits ENSURING TASK QUALITY IN MATHEMATICS
Slide 3: Source: usnews.com
Slides 16, 24, 39:
Slides 33, 35, 37: