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

ALGEBRA I TEAM

DIRECT & INVERSE VARIATIONS

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.

5 Es

ENGAGEEXPLOREEXPLAIN

ELABORATEEVALUATE

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

NUMBER LINE

Blocks to school0 2 4 6 8 10 12 14 16

MEETING PLACE ILLUSTRATE THE SITUTATION

BAR GRAPH

1 2 3 40

2

4

6

8

10

12

14

16

Blocks to School

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

1 2 3 40

2

4

6

8

10

12

14

16

MEAN

BLOCKS

TO SC

HOOL

MEETING PLACE

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

16 u2

MEETING PLACE

When should you use

•Absolute value•Squaring

Why?

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.

YOUR TURNTypical question….

2x + 3y = 481x + 1y = 20

1.Raise the rigor of the question.2.How can you present the new question to students?

3.Student expectations? 4.Connections to be made?