Math Resources! Problems, tasks, strategies, and pedagogy. An hour of my 90-min session on math task design at Cal Poly Pomona for a group of teachers (mainly elementary school).

1. Task Design
Engaging Students Through Equity-based Practices
and Issues of Social Justice.
CMP @ CPP June 13, 2018

2. Gif artist

3. Peek into #MTBoS / #iteachmath
Explore Classroom Chef, This livebinder
has even more
Engaging Students Through Equity-based Practices
and Issues of Social Justice.
CMP @ CPP June 13, 2018
Archivist activist
Task Design

4. Archivist activist
#mathchat
#math
#iteachmath
#MTBoS

5. Goals
• Build Trust
• Do Math Together
• Share Strategies and Resources

6. Guidelines
• Be mindful of intent and impact
• Engage from a place of compassion (open heart)
• Replace judgement with curiosity (open mind)
• Challenge ideas not people

7. 2 3
Subtract

8. 2 3
How many combinations
can you make?
a) Use digits 0-9 to fill in
the tens and ones
Subtract

9. 2 3
Subtract
How many combinations
can you make?
a) Use digits 0-9 to fill in
the tens and ones
a) Use digits 0-9 to fill in
the hundreds, tens and
ones

10. 0 2 3
How many combinations
can you make?
a) Use only tens and ones
a) Use only hundreds, tens
and ones
Subtract

11. What features do
effective mathematical
tasks have?

12. What features do effective
mathematical tasks have?
The task needs _____ in order to _____

13. Design Feature Purpose
Curiosity
Familiarity with context
Engaging (persistence)
Multiple entry points
Collaboration
Diversity in the task
Not just one way of solving
Recognizable pattern
Relevancy / Student Interest
Manipulatives
Movement / Music / Modalities
Drives questions and creates a context for new learning
So Ss can comprehend
Keep Ss wanting to explore and try
Kids hanging on can stay in it - advanced kid can take it further
Confidence and creativity
Differentiate (advanced/lower) so not to get boring
So you know you get multiple solutions
Seeing repetition of pattern
Increases engagement and buy-in
See it and feel it to understand
Engage kinesthetic learning, visual learning

15. need for certainty
need for causality
need for computation
need for communication
need for connection and structure
http://math.ucsd.edu/~jrabin/publications/ProblemFreeActivity.pdf (pg. 4)
Need to Know

16. Teaching Style

17. How do you structure your lessons?
a) Across a conceptual unit
a) Within a single lesson

18. Share with a partner
Why do you organize them this way?
Find common features
How do you structure your lessons?

20. 1)Introductory Task
2)Provision Expert Model
3)Deliberate Practice
4)Transfer Task
Lesson Stages
http://cheesemonkeysf.blogspot.com/2015/09/how-people-learn-and-how-people-learn.html

21. 1-3 Standards from Textbook
Familiar “Map” to a Unit of Instruction
Intro
Lecture
Endof
UnitTest
Practice
Topic1
Review
Mid-Unit
Quiz
Lecture
(Topic
2)
Practice
Topic2
Lecture
(Topic
3)
Practice
Topic3
Fun(?)
Project
Familiar Unit “Map”

22. Big Ideas, Essential Questions, & Valued Learning Goals
≈3-5 Weeks
Alternative Unit “Map”

23. Big Ideas, Essential Questions, & Valued Learning Goals
Summative
(Diagnostic)
Task
≈3-5 Weeks
Summative Tasks (≈1-5 days) are tasks or series
of tasks that provide students final opportunities to
demonstrate understandings, knowledge, and
skills related to unit content.
Alternative Unit “Map”

24. Big Ideas, Essential Questions, & Valued Learning Goals
One “Map” to a Unit of Instruction
Adapted from SVMI
Formative
(Diagnostic)
Task
Summative
(Diagnostic)
Task
≈3-5 Weeks
Formative Tasks (≈2-5 days) are open-ended tasks that provide
students’ opportunities to deepen conceptual understandings of the
unit content AND that provide specific feedback to the teacher on
student progress.
Alternative Unit “Map”

25. One “Map” to a Unit of Instruction
Adapted from SVMI
Alternative Unit “Map”
Big Ideas, Essential Questions, & Valued Learning Goals
≈3-5 Weeks
Entry
Task
Formative
(Diagnostic)
Task
Summative
(Diagnostic)
Task
Entry Tasks (≈1-3 days) are open-ended tasks that uncover what
students understand, know, and can do related to the big ideas of
the unit. They should be highly accessible to ALL students.

26. Big Ideas, Essential Questions, & Valued Learning Goals
One “Map” to a Unit of Instruction
Adapted from SVMIEntry
Task
Formative
(Diagnostic)
Task
Summative
(Diagnostic)
Task
Expert
Task
≈3-5 Weeks*
Expert Tasks (≈3-10 days) are investigations or projects that
provide students opportunities to develop mathematical ideas
and construct viable arguments to compare and contrast their
ideas with others.
Alternative Unit “Map”

27. Big Ideas, Essential Questions, & Valued Learning Goals
One “Map” to a Unit of Instruction
Adapted from SVMIEntry
Task
Formative
(Diagnostic)
Task
Summative
(Diagnostic)
Task
Lesson
Series
#1
Lesson
Series
#2
Lesson
Series
#3
Expert
Task
≈3-5 Weeks*
27
Lesson Series (≈1-5 days) connect assessments and are the flesh
of the unit. Ideally they begin with re-engagement lessons
designed using data gathered from entry, expert, and diagnostic
tasks.
Alternative Unit “Map”

28. Geoff's Problem-Based Curriculum Maps offer some strong
Math Tasks organized in units
Summit Learning Platform has a similar effort with more
support

29. Intro Task
Starts with something students know
Leads to a burning question
Preparation for future learning
Can be a hands-on experience

30. https://vimeo.com/56821540

32. Act 1: Inquiry - What do we Notice and Wonder
Choose a question to solve, make estimates
What information do we need?
Act 2: Provide requested information
Allow for computation
Act 3: Reveal - Resolve dissonance
Possible extensions
3-Acts

33. Robert
Kaplinksy's
lessons
His Open Middle
worksheet tracks
student attempts
rather than
assuming that
students do it
correctly once

34. Agree or Disagree Math

35. Why?
Which One Doesn't Belong?

36. Math Talks (Number and Pattern)

37. Math Mistakes

38. Step 1 Step 2 Step 3 Step 4
How many squares in step 43?
Visual Patterns

39. A great webinar by Desmos Instructional Designer Michael
Fenton on how he uses visual pattern problems to get
students to make predictions and share their thinking. His
questions,
What comes next? What else might come next?
What comes before? What else might come before?
What comes between? What else might come between?
Showed some really great variations on the classic visual pattern activity.

40. Would You Rather
Math

41. Play With Your Math

42. www.estimation180.com

43. Deliberate Practice
Immediate Feedback
Rehearsing Expert Model
Interleave worked examples
Spiral material throughout the year

44. Marbleslides
Putt Putt Golf
are examples of purposeful practice by adding a goal state
and some context
Desmos

45. Marilyn Burns

46. 90-min Lessons
1) Assessment Task
2) Common Issues are presented with suggested prompts
3) Collaborative Activity
4) Whole-class Discussion
5) Suggested teacher moves throughout
6) Students address questions on their pre-assessment
MARS Lessons
MARS Lessons

47. Here are some points in the plane:
(4, 1), (17, 27), (1, -5), (8, 9), (13, 19), (-2, -11)
(20, 33), (7,7), (-5, -17), (10, 13)
Choose any two of these points. Check with your neighbor to be
sure that you didn’t both choose the same pair of points. Now find
the rate of change between the first and the second point. Share
publicly. What do you notice?
WTF Problems

48. Variety Matters. Change it up
Walk with your
notebook and find a
partner. Write the
equation of the line
passing between your
points. Repeat 3 times.

49. Making Open Questions - Method 1
- Write down a question and work out the answer.
- Make up a new question that includes the answer as
part of the question.
339
+ 173
3 * *
+ * 7 *
512
Closed Open
Closed Open
40º
Find the missing angles
in this trapezoid.
What are possible
angles in this trapezoid?

50. Making Open Questions - Method 2
- Write down a complete question including the answer.
- Remove some of the question parts or provide
alternative solutions.
Tina earned the
following scores on
her last 5 exams:
83, 93, 78, 95, 81.
Find the average
test score.
Tina’s average test
score over the last
five exams was 86.
The highest score
was a 95, what
might the other
scores have been?
Closed Open
Johnny solved
2x + 4 = 8 and got 2.
Susie solved the
equation and got 6.
Who is correct and
why?
Closed Open
Solve for x
2x + 4 = 8

51. 1hr webinar on open questions by Ontario
learning coordinator Mishaal Surti. It has many
actionable tips - and some great comments from
the educators who were in attendance.
link to his materials revealed at the end ;)

58. Open Middle

59. Let’s Practice
1) Select a sample problem to make open
SBAC practice items
1) Share with your partner to give and receive feedback
on your redesign
Repeat this process 2-4 times (time permitting)
Find more examples and advice at Open Assessment in Math

60. Be Less Helpful

62. 1) What type of community of mathematicians and teachers do
you view as valuable and why?
1) What type of resources would you like to have shared/share
with others in such a community?
1) What kinds of opportunities would you want?
1) What do you wish mathematicians understood about
teachers?

63. Questions

64. How many squares
can be drawn by
connecting 4 points
in this 6x6 grid?
Organize your thinking
Discussion in 8min

65. What mathematical
features do we need?

66. Transfer Tasks
An inspiring transfer task takes a learner seriously
as a professional, and offers him or her an
engaging, in-context opportunity to apply their new
learning with all its glorious, messy, gravity-driven
moving parts

67. MARS Tasks
MARS tasks
Summative Assessment
Includes Rubric and Scored student work

68. Illustrative Mathematics Tasks
Illustrative
Mathematics

69. Heather Kohn on Engineering Design Process
Engineering
Design Process

70. Buck Institute for
PBL
Buck Institute Resources

71. We aren’t alone - Share your practice
Explore Classroom Chef for more
This livebinder has even more
Thank you
Evan Rushton
@E_Rushton