October 1, 2010 1

Making Sense of ChangeMaking Sense of Change

VCTM Fall AcademyVCTM Fall AcademyOctober 1, 2010October 1, 2010

Making Sense of ChangeMaking Sense of Change

VCTM Fall AcademyVCTM Fall AcademyOctober 1, 2010October 1, 2010

Michael BollingMichael BollingMathematics Coordinator, VDOEMathematics Coordinator, VDOE

(and managing it)

October 1, 2010 2

Slide TitleSlide TitleSlide TitleSlide Title

October 1, 2010 3

Oil leaked from April 20 – July 15, 2010.

On July 15, the leak was stopped after releasing about 4.9 million barrels (7.8×105 m3) of crude oil.

It was estimated that 53,000 barrels per day (8,400 m3/d) were escaping from the well just before it was capped.

It is believed that the daily flow rate diminished over time, starting at about 62,000 barrels per day (9,900 m3/d) and decreasing as the reservoir of hydrocarbons feeding the gusher was gradually depleted.

The Deepwater Horizon was able to operate in waters up to 8,000 feet (2,400 m) deep and drill down to 30,000 feet (9,100 m).

BP estimated the worst case flow at 162,000 barrels per day (25,800 m3/d).

Internal BP documents estimated the flow could be as much as 100,000 barrels per day (16,000 m3/d).

October 1, 2010

Deepwater Horizon Oil SpillDeepwater Horizon Oil SpillDeepwater Horizon Oil SpillDeepwater Horizon Oil Spill

• What “What “I wonder…I wonder…” questions about ” questions about the mathematics would kids (or the mathematics would kids (or adults) ask?adults) ask?

• What jobs related to the spill What jobs related to the spill involve pertinent mathematics?involve pertinent mathematics?

• To which mathematics content To which mathematics content could this disaster be connected?could this disaster be connected?

• What “What “I wonder…I wonder…” questions about ” questions about the mathematics would kids (or the mathematics would kids (or adults) ask?adults) ask?

• What jobs related to the spill What jobs related to the spill involve pertinent mathematics?involve pertinent mathematics?

• To which mathematics content To which mathematics content could this disaster be connected?could this disaster be connected?

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October 1, 2010

Highlighted SOL ChangesHighlighted SOL ChangesHighlighted SOL ChangesHighlighted SOL Changes

• Awareness Awareness (curriculum and pacing guides, (curriculum and pacing guides, SOL Crosswalks, VDOE training institutes)SOL Crosswalks, VDOE training institutes)

• UnderstandingUnderstanding• Content Content (Curriculum Framework, technical (Curriculum Framework, technical

assistance documents)assistance documents)

• Connections Connections (Enhanced Scope and (Enhanced Scope and Sequence lesson, vertical articulation of Sequence lesson, vertical articulation of content)content)

• Awareness Awareness (curriculum and pacing guides, (curriculum and pacing guides, SOL Crosswalks, VDOE training institutes)SOL Crosswalks, VDOE training institutes)

• UnderstandingUnderstanding• Content Content (Curriculum Framework, technical (Curriculum Framework, technical

assistance documents)assistance documents)

• Connections Connections (Enhanced Scope and (Enhanced Scope and Sequence lesson, vertical articulation of Sequence lesson, vertical articulation of content)content)

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October 1, 2010 6

New from grade 8

Exponents/Squares/Square Roots

October 1, 2010 7

Comparing and Ordering

October 1, 2010 8

New from grade 7

New from grade 7

Expressions and Operations

October 1, 2010 9

New content

Modeling

New content

October 1, 2010 10

New content

Equations and Inequalities

October 1, 2010

What can you tell me?What can you tell me?What can you tell me?What can you tell me?

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Algebra IRelation or function?

Domain/range

Zeros

x- and y-intercepts

Function values for elements of the domain

Connections among representations

AFDA - addsLocal/absolute max/min

Intervals of increasing/ decreasing

End behaviors

asymptotes

Alg 2 - addsInverse functions

Composition of functions

October 1, 2010 12

New content New content

New content

New content

Technical Assistance Document for A.9 Published

Technical Assistance Document for AII.11 October 2010

October 1, 2010 13

New content

October 1, 2010 14

Each figure in the pattern below is made of hexagons that measure 1 centimeter on each side.

If the pattern of adding one hexagon to each figure is continued, what will be the perimeter of the 25th figure in the pattern? Show how you found your answer.

October 1, 2010

Perimeter ProblemPerimeter ProblemPerimeter ProblemPerimeter Problem

• In what situation would this task be In what situation would this task be used? used?

• In which course/level would you In which course/level would you use this task?use this task?

• How would you adjust it for another How would you adjust it for another course/level?course/level?

• In what situation would this task be In what situation would this task be used? used?

• In which course/level would you In which course/level would you use this task?use this task?

• How would you adjust it for another How would you adjust it for another course/level?course/level?

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October 1, 2010

Worthwhile task?Worthwhile task?Questions to ask yourselfQuestions to ask yourself

Worthwhile task?Worthwhile task?Questions to ask yourselfQuestions to ask yourself

• Does the problem challenge students Does the problem challenge students to use higher-level critical thinking to use higher-level critical thinking skills?skills?

• Is the problem clearly connected to the Is the problem clearly connected to the targeted mathematics?targeted mathematics?

• Are there multiple ways to solve this Are there multiple ways to solve this problem? problem?

• Is it accessible to all students?Is it accessible to all students?

• Does the problem challenge students Does the problem challenge students to use higher-level critical thinking to use higher-level critical thinking skills?skills?

• Is the problem clearly connected to the Is the problem clearly connected to the targeted mathematics?targeted mathematics?

• Are there multiple ways to solve this Are there multiple ways to solve this problem? problem?

• Is it accessible to all students?Is it accessible to all students?

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October 1, 2010

Worthwhile task?Worthwhile task?Questions to ask yourselfQuestions to ask yourself

Worthwhile task?Worthwhile task?Questions to ask yourselfQuestions to ask yourself

• Does the problem promote Does the problem promote mathematical communication?mathematical communication?

• What might students struggle with?What might students struggle with?

• This would be an appropriate This would be an appropriate problem if you were studying… or if problem if you were studying… or if you have already studied…you have already studied…

• Does the problem promote Does the problem promote mathematical communication?mathematical communication?

• What might students struggle with?What might students struggle with?

• This would be an appropriate This would be an appropriate problem if you were studying… or if problem if you were studying… or if you have already studied…you have already studied…

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October 1, 2010

Where can I get worthwhile Where can I get worthwhile mathematical tasks?mathematical tasks?

Where can I get worthwhile Where can I get worthwhile mathematical tasks?mathematical tasks?

NAEP released items NAEP released items http://nces.ed.gov/nationsreportcard/

PISA released items PISA released items http://nces.ed.gov/surveys/pisa/educators.asp

APEC Mathematics Assessment Database APEC Mathematics Assessment Database http://hrd.apec.org/index.php/Mathematics_Assessments

Heinemann Mathematics (not free, but cheap) Heinemann Mathematics (not free, but cheap) http://books.heinemann.com/math/

NAEP released items NAEP released items http://nces.ed.gov/nationsreportcard/

PISA released items PISA released items http://nces.ed.gov/surveys/pisa/educators.asp

APEC Mathematics Assessment Database APEC Mathematics Assessment Database http://hrd.apec.org/index.php/Mathematics_Assessments

Heinemann Mathematics (not free, but cheap) Heinemann Mathematics (not free, but cheap) http://books.heinemann.com/math/

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October 1, 2010

Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills

Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills

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8.11The student will solve practical area and perimeter problems involving composite plane figures.

PAST FUTURE

Find the area of

the shaded region.

October 1, 2010

Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills

Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills

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8.5 b) The student will find the two consecutive whole numbers between which a square root lies.

PAST FUTURE

Between which two square roots does 5 lie?

October 1, 2010

Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills

Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills

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A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.

PAST

Which class had the most students scoring higher than 83?

FUTURE

Class A has 30 students and Class B has 20 students. Which class has more students scoring above 83?

October 1, 2010

Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills

Assessing Higher-level Assessing Higher-level Thinking Skills Thinking Skills

• Increased levels of complexity Increased levels of complexity in analysisin analysis

• Increased levels of complexity Increased levels of complexity in expressions and equationsin expressions and equations

• Comparing and contrasting of Comparing and contrasting of functions during analysisfunctions during analysis

• Increased levels of complexity Increased levels of complexity in analysisin analysis

• Increased levels of complexity Increased levels of complexity in expressions and equationsin expressions and equations

• Comparing and contrasting of Comparing and contrasting of functions during analysisfunctions during analysis

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October 1, 2010

New SOL BlueprintsNew SOL BlueprintsNew SOL BlueprintsNew SOL Blueprints

Mega-categories combine reporting Mega-categories combine reporting categoriescategories

• Grade 6 – from 5 to 4Grade 6 – from 5 to 4• Grade 7-8 – from 5 to 3Grade 7-8 – from 5 to 3• Algebra I – from 4 to 3Algebra I – from 4 to 3• Geometry and Algebra II – from 5 to Geometry and Algebra II – from 5 to

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Mega-categories combine reporting Mega-categories combine reporting categoriescategories

• Grade 6 – from 5 to 4Grade 6 – from 5 to 4• Grade 7-8 – from 5 to 3Grade 7-8 – from 5 to 3• Algebra I – from 4 to 3Algebra I – from 4 to 3• Geometry and Algebra II – from 5 to Geometry and Algebra II – from 5 to

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October 1, 2010 24

Note: Asterisk indicates that the SOL will be assessed in the non-calculator section.

October 1, 2010 25

New Formula SheetsNew Formula SheetsNew Formula SheetsNew Formula Sheets

October 1, 2010

Technology Enhanced ItemsTechnology Enhanced ItemsTechnology Enhanced ItemsTechnology Enhanced Items

Interactive questionsInteractive questions• Hot-spotsHot-spots

• Drag and dropDrag and drop

• Creation of graphsCreation of graphs

• Short responseShort response

Practice ePAT available by February 2011Practice ePAT available by February 2011

Interactive questionsInteractive questions• Hot-spotsHot-spots

• Drag and dropDrag and drop

• Creation of graphsCreation of graphs

• Short responseShort response

Practice ePAT available by February 2011Practice ePAT available by February 2011

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Beginning in

Spring 2011

October 1, 2010

New SOL Assessment TimelineNew SOL Assessment TimelineNew SOL Assessment TimelineNew SOL Assessment Timeline

Spring 2011Spring 2011• All SOL tests (live test items) based on All SOL tests (live test items) based on

2001 SOL 2001 SOL

• Field test items will be based on the Field test items will be based on the 2009 SOL2009 SOL

• Technology enhanced items will be field Technology enhanced items will be field tested in grades 6-8 and EOC SOL teststested in grades 6-8 and EOC SOL tests

Spring 2011Spring 2011• All SOL tests (live test items) based on All SOL tests (live test items) based on

2001 SOL 2001 SOL

• Field test items will be based on the Field test items will be based on the 2009 SOL2009 SOL

• Technology enhanced items will be field Technology enhanced items will be field tested in grades 6-8 and EOC SOL teststested in grades 6-8 and EOC SOL tests

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October 1, 2010

New SOL Assessment TimelineNew SOL Assessment TimelineNew SOL Assessment TimelineNew SOL Assessment Timeline

Fall 2011Fall 2011• EOC SOL tests will be based on EOC SOL tests will be based on

2009 SOL2009 SOL

Spring 2012Spring 2012• All SOL tests will be based on All SOL tests will be based on

2009 SOL2009 SOL

Fall 2011Fall 2011• EOC SOL tests will be based on EOC SOL tests will be based on

2009 SOL2009 SOL

Spring 2012Spring 2012• All SOL tests will be based on All SOL tests will be based on

2009 SOL2009 SOL

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October 1, 2010

What is our goal as teachers of What is our goal as teachers of mathematics?mathematics?

What is our goal as teachers of What is our goal as teachers of mathematics?mathematics?

• What will tomorrow’s jobs look What will tomorrow’s jobs look like?like?

• Teach kids how to use their Teach kids how to use their critical thinking and reasoning critical thinking and reasoning skills to adapt and overcome in skills to adapt and overcome in unfamiliar settingsunfamiliar settings

• What will tomorrow’s jobs look What will tomorrow’s jobs look like?like?

• Teach kids how to use their Teach kids how to use their critical thinking and reasoning critical thinking and reasoning skills to adapt and overcome in skills to adapt and overcome in unfamiliar settingsunfamiliar settings

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