1. Implementing the Common Core Through Increased Rigor
Lisa Choate Cannon County High School Woodbury, Tennessee

2. Only high school in our county
650 +/- students
Middle Tennessee
Only high school in our county

3. Proficient and Advanced
Algebra one progress
This represents a 455% increase over the last 3 years!
50%
Proficient and Advanced
31% 9%

4. Proficient and Advanced
Algebra Two Progress
This represents a 224% increase over the last year!
Proficient and Advanced

5. Algebra Lab for struggling freshmen math students
How did we do iT?
Algebra Lab for struggling freshmen math students
Failure is not an option
Standards-based grading
Formative Assessment Lessons

6. http://map.mathshell.org/materials/download.php?fileid =700

7. What a formative assessment is…
Students demonstrate what they know
Students apply knowledge in new situations
Assessment AS learning

8. What a formative assessment is not…
A test

10. Lesson structure

11. Assessment (Pre and Post)

12. Review pre-assessments Group homogeneously 2 or 3 in a group
Grouping
Review pre-assessments Group homogeneously 2 or 3 in a group

13. The keys to success are…
Allow productive struggle. Do not give away anything.
MP1
Press for justification.
Ask advancing questions.
MP3

15. Disclaimer: I don’t baby step.
Task
Disclaimer:
I don’t baby step.
At this point, the script suggests you review the different forms of quadratics, but I believe that decreases the rigor. I use the task as a review of quadratics.

18. Justification
I use legal paper and include 5 blank cards for them to include their justifications.
Justification
Justification
Justification
I don’t give them tape until they have justified every match.
Justification

19. The teacher should be circulating around the groups as an OBSERVER.
Facilitation notes
The teacher should be circulating around the groups as an OBSERVER.
This is when you can ask the assessing and advancing questions.

23. e
If you focus on “right” answers, as soon as the “right” answer is revealed, everyone shuts down.
Multiple solution paths!
You may do this using a document camera or having students hold up their work in front of the class.

24. Assessment (Pre and Post)

25. Ball Toss Vertical Projectile Motion h(t) = -1/2 gt2 + vt + h
Where
g = gravity (9.8 m/sec)
t = time
h = height
v = initial velocity
h(t) = height for given time
This is a short task that we do in one day.
Y= x x

26. Recognizing the level of thinking as demonstrated by students
Rigor is…
Scaffolding thinking
Planning for thinking
Assessing thinking
about content
Recognizing the level of
thinking as demonstrated
by students
Managing the teaching/
learning level for the
desired thinking level
Rigor is not…
More or harder
worksheets
AP or honors
courses
More homework
Only for “smart” students
Source:

27. Where do I get these rigorous tasks?

28. What is the maximum? {hint: The maximum is the y-value of the vertex.}
Textbook problem
Too much scaffolding
f(x) = -16x2 +200x
Graph the parabola.
Identify the vertex.
What is the maximum? {hint: The maximum is the y-value of the vertex.}
What will a student remember from this problem?
No room for multiple solution paths
No real-world connection

29. Superman is jumping over a 612 foot
Modified for added rigor
Superman is jumping over a 612 foot
high building. He has an initial velocity
of 200 feet/second. Will Superman
clear the building? Defend your
conclusion by proving it at least 2 ways.
Students will remember this problem
Real-world connections
No scaffolding, but it can be added for students who need it
Requires multiple solution paths
Although we will probably have to provide the equation “f(x) = -16x x” students will be required to THINK about what the equation and its individual parts actually means.

30. 4. Model with mathematics.
Textbook problem
f(x) = -16x2 +200x
Graph the parabola.
Identify the vertex.
What is the maximum? {hint: The maximum is the y-value of the vertex.}
CCSS
A-REI.10
F-IF.4
F-IF.7 MP
4. Model with mathematics.

31. Superman is jumping over a 612 foot
Modified for added rigor
Superman is jumping over a 612 foot
high building. He has an initial velocity
of 200 feet/second. Will Superman
clear the building? Defend your
conclusion by proving it at least 2 ways.
CCSS
A-SSE.1
A-CED.1
F-IF.4
F-IF.5
*F-IF.2
*F-IF.7
*F-IF.8.a
*potentially MP
Make sense of problems and persevere in solving them.
3. Construct a viable argument and critique reasoning of others.
4. Model with mathematics.
7. Look for and make use of structure.
Although we will probably have to provide the equation “f(x) = -16x x” students will be required to THINK about what the equation and its individual parts actually means.

32. Strategies for modifying textbook tasks
Include a prompt
instructing students to
represent the
solution another way
(table, graph…) and
to write about their
insights gained from looking
at the new representation.
Ask students to create a real-world story for “naked number” problems.

33. Strategies for modifying textbook tasks
Eliminate components
of the task that
provide too
much scaffolding.
3. Use a task “out of sequence” before students have memorized a rule or practiced a procedure that can be routinely applied.

34. Strategies for modifying textbook tasks
5. Adapt a task so as to provide more opportunities for students to think and reason-let students figure out things for themselves.

35. Find the solutions of the equation for x=0 and y = 0.
swimming
Original
37. If you swim the backstroke, you burn 9 cal/min. If you swim the butterfly stroke, you burn 12 cal/min. The equation 9x+12y = 360 models how you can burn 360 calories by swimming the backstroke for x minutes and the butterfly stroke for y minutes.
Find the solutions of the equation for x=0 and y = 0.
Explain what the solutions mean.
Graph the solutions you found in part A. Draw a line through the points.
Use your graph from part B. If you swim the butterfly stroke for 10 min., how long should you swim the backstroke to burn 360 calories?

36. Swimming
Modified
If you swim the backstroke, you burn 9 cal/min. If you swim the butterfly stroke, you burn 12 cal/min. You want to burn 360 calories.
Determine a way to find all the combinations of swimming the butterfly stroke and the backstroke that will meet this goal.
Write and graph an equation that represents the relationship you described in part A.
If you swim the butterfly stroke for 10 minutes, how long must you swim the backstroke to burn 360 calories?
Notice the student must determine the equation.

37. Find the solutions of the equation for x=0 and y = 0.
swimming
Original
37. If you swim the backstroke, you burn 9 cal/min. If you swim the butterfly stroke, you burn 12 cal/min. The equation 9x+12y = 360 models how you can burn 360 calories by swimming the backstroke for x minutes and the butterfly stroke for y minutes.
Find the solutions of the equation for x=0 and y = 0.
Explain what the solutions mean.
Graph the solutions you found in part A. Draw a line through the points.
Use your graph from part B. If you swim the butterfly stroke for 10 min., how long should you swim the backstroke to burn 360 calories?
What learning happens here?

38. Swimming
Modified
If you swim the backstroke, you burn 9 cal/min. If you swim the butterfly stroke, you burn 12 cal/min. You want to burn 360 calories.
Determine a way to find all the combinations of swimming the butterfly stroke and the backstroke that will meet this goal.
Write and graph an equation that represents the relationship you described in part A.
If you swim the butterfly stroke for 10 minutes, how long must you swim the backstroke to burn 360 calories?
What learning happens here?

39. We cannot get high cognitive demand from a low-level task
We cannot get high cognitive demand from a low-level task. What do we say to our students when we give them a low-level task?

40. But you don’t know MY students…
“Every morning in Africa, a gazelle wakes up. It knows it must run faster than the fastest lion or it will be killed. Every morning a lion wakes up. It knows it must outrun the slowest gazelle or it will starve. Moral: It doesn’t matter whether you are a lion or a gazelle, when the sun comes up, you had better be running.” ---African Proverb

41. Other Resources
ex.php (official CC website) (PARCC website) dy/dan (Dan Meyer’s amazing blog)