VCTM Conference March 2014
Transcript of VCTM Conference March 2014
Rigor and Differentiation:
Pamela BaileyGeorge Mason University
Session 135 9:45–11:00 HHS 2202
Instructional Tasks to Meet All Student Needs
GOAL OF SESSIONExperience a differentiated, rigorous task suitable for the middle/high school classroom.
Examine the components, method of implementation, mode of differentiation, and habits of mind addressed in the task.
In small groups create a differentiated task using ideas discussed and experienced.
BACKGROUNDCURRICULUM & DEVELOPMENT COURSE AT MASON IN MATH ED LEADERSHIP
PERFORMANCE ASSESSMENTCLASS CONSTRUCTED TASKS NCTM PROCESS STANDARDS MATHEMATICAL PRACTICES (CCSS)DIFFERENTIATION TECHNIQUES
http://edci645curriculumtasks.pbworks.com and request access.
Types of Differentiation
Inquiry – Discovery (open-ended / RAFT)
Centers – StationsLearning Styles - Mult. Intelligences
MenusTiers – JigsawPathway Plan
Progression of Rigor
Typical question….
Given the following values determine the standard deviation. 2, 4, 12, 14
Increase the rigor in the question...
Given the following values determine the standard deviation. 2.4, 4.4, 12.4, 14.4 …
Progression of Rigor
Most Rigorous – Meeting Place Amy, Brad, Carol, and Denise walk to school every day and all live on Euclid Road. Euclid Road begins at their high school and goes east out of the city. Amy lives 2 blocks from school, Brad – 4 blocks, Carol – 12 blocks, and Denise – 14 blocks. They all want to go out for pizza at their favorite spot, Pi Pizzeria, and decide to meet at a central location among their homes.
Your task is to determine the average distance to the central location where they all can meet to go to their local pizza place.
Meeting PlaceENGAGE:
1.Measure of Center2.Graphs (might have discussed these earlier)
scatter plots histogramscircle graphs bar graphsnumber linesWhat might be a good way to illustrate this situation.
3.Have you ever wanted to meet up with your friends to go out?
4.How do you decide where to meet?
Meeting PlaceMeasures of Center
Engage:
Which Measure of Center Would You Use?1. The high temperatures for a 7day week in December in Sayre,
PA were 29°, 31°, 28°, 32°, 29°, 27°, and 55°.
2. How you would describe the overall batting averages of the baseball team (0.321, 0.234, 0.256, 0.333, 0.276, 0.290, 0.198, 0.222, 0.289, and 0.300.)
3. Company employees are concerned about salaries. Out of the 250 employees, 100 have a salary of $72,000 and the 3 CEO’s make at least $2,000,000. The remaining employees make above $50,000 and less than $85,000.
Median – Mean skews data due to 55 deg value
Mean – Median could also be used
Mode – comparing $72,000 with CEO income
MEETING PLACE ILLUSTRATE THE SITUTATION
Scatterplot
0 1 2 3 4 50
2
4
6
8
10
12
14
16
MEETING PLACE
Amy Brad Carol Denise
Blocks To School
Discussion about scenario:
Have you ever wanted to meet up with your friends to go out?
How do you decide where to meet?
MEETING PLACE
MEETING PLACEExplore: Measure of Spread
Want students to understand Mean Absolute Deviation and Standard Deviation as the average distance from the mean.
Use NCTM Process Standards: Connections and Multiple Representations
Mathematical Practice: Make sense and persevere
Differentiation: Inquiry / Discovery
MEETING PLACE
IN SMALL GROUPSWhat are we being asked to find?What do you already know?How might you illustrate what you are being asked to find?
MEETING PLACE
What are we being asked to find?
The central location from each of their homes.
Determine the average distance to the central location where they all can meet.
MEETING PLACEWhat do we already know?
Amy, Brad, Carol, and Denise walk to school every day
All live on Euclid RoadAll like to eat at Pi PizzeriaEuclid Road starts at the high schoolAmy is 2 blocks from school, Brad – 4 blocks, Carol – 12 blocks, and
Denise – 14 blocks.
MEETING PLACE
How will you illustrate the situation?
Find a solution to this situation using the illustration.
Be ready to explain / justify your approach to finding
a solution.
MEETING PLACE
NUMBER LINE
Blocks to school
0 2 4 6 8 10 12 14 16
Mean
6 64 4
6 + 4 + 4 + 6 = 5 4MEAN ABS DEVIATION
MEAN
1 2 3 40
2
4
6
8
10
12
14
16
BLOCKS
TO
SCHO
OL
6 4
64
MEETING PLACE6 + 4 + 4 + 6 = 5 4MEAN ABS DEVIATION
MEETING PLACEDISTANCE TO THE CENTRAL LOCATION WAS PREVIOUSLY DETERMINED USING ABSOLUTE VALUE. (DIFFERENCE)
IS THERE ANOTHER WAY WE CAN LOOK AT THE DISTANCE FROM THE CENTRAL LOCATION?
1 2 3 40
2
4
6
8
10
12
14
16
MEAN
BLOC
KS T
O SC
HOOL 6
-6
4
-4
How can we deal with the values so that we can work with them?
What does it mean geometrically?
Can you illustrate your thinking?
1 2 3 40
2
4
6
8
10
12
14
16
MEAN
BLOCKS
TO
SCHO
OL -6
-6
-4
-4
1 2 3 40
2
4
6
8
10
12
14
16
MEAN
BLOC
KS T
O SC
HOOL -
6
-6
-4
-436 u2
16 u2
36 u2
16 u2
MEETING PLACE
16 u2
1 2 3 40
2
4
6
8
10
12
14
16
MEAN
BLOC
KS T
O SC
HOOL -
6-4
-436 u2
16 u2
36 u2
16 u2
16 u2
MEETING PLACE“Level”
the squares so they all have the same area.
1 2 3 40
2
4
6
8
10
12
14
16
MEAN
BLOC
KS T
O SC
HOOL -
6-4
-436 u2
16 u2
36 u2
16 u2
AVG. AREA 26u2
Avg. distance to mean ≈ 5.099
STANDARD DEVIATION
16 u2
MEETING PLACE
DIFFERENTIATIONHow might you, the teacher, go about introducing (set up) and closing the task for students?How is differentiation met with this task?
Which of the NCTM Process Standards were addressed in the problem?Which of the habits of mind were addressed?
Doing – UndoingBuilding Rules to Represent FunctionsAbstracting from Computation
GEAR DOWN:Provide a table and blank graph.Provide graph paper to cut out the “squares/distance” or some type of blocks so that students can level the squares/distance.
Have students physically model the situation and the mean.
GEAR UP:Give values that include decimals and are larger.Give more values.Ask fewer prompting questions.
DIFFERENTIATION
OTHER IMPORTANT IDEAS
Communication – Math Discourse
Questioning
Making connection between the graphs, verbal explanations,
and computations.