1. October 1, 2010 1 Making Sense of Change VCTM Fall Academy October 1, 2010 Making Sense of Change VCTM Fall Academy October 1, 2010 Michael Bolling Mathematics Coordinator, VDOE (and managing it)

2. October 1, 2010 2 Slide Title

3. 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 (7.8×10 5 m 3 ) of crude oil. It was estimated that 53,000 barrels per day (8,400 m 3 /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 m 3 /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 m 3 /d). Internal BP documents estimated the flow could be as much as 100,000 barrels per day (16,000 m 3 /d).

4. October 1, 2010 Deepwater Horizon Oil Spill What “I wonder…” questions about the mathematics would kids (or adults) ask?What “I wonder…” questions about the mathematics would kids (or adults) ask? What jobs related to the spill involve pertinent mathematics?What jobs related to the spill involve pertinent mathematics? To which mathematics content could this disaster be connected?To which mathematics content could this disaster be connected? What “I wonder…” questions about the mathematics would kids (or adults) ask?What “I wonder…” questions about the mathematics would kids (or adults) ask? What jobs related to the spill involve pertinent mathematics?What jobs related to the spill involve pertinent mathematics? To which mathematics content could this disaster be connected?To which mathematics content could this disaster be connected? 4

5. October 1, 2010 Highlighted SOL Changes Awareness (curriculum and pacing guides, SOL Crosswalks, VDOE training institutes)Awareness (curriculum and pacing guides, SOL Crosswalks, VDOE training institutes) UnderstandingUnderstanding Content (Curriculum Framework, technical assistance documents)Content (Curriculum Framework, technical assistance documents) Connections (Enhanced Scope and Sequence lesson, vertical articulation of content)Connections (Enhanced Scope and Sequence lesson, vertical articulation of content) Awareness (curriculum and pacing guides, SOL Crosswalks, VDOE training institutes)Awareness (curriculum and pacing guides, SOL Crosswalks, VDOE training institutes) UnderstandingUnderstanding Content (Curriculum Framework, technical assistance documents)Content (Curriculum Framework, technical assistance documents) Connections (Enhanced Scope and Sequence lesson, vertical articulation of content)Connections (Enhanced Scope and Sequence lesson, vertical articulation of content) 5

6. October 1, 2010 6 6.5 investigate/ describe positive exponents, perfect squares 7.1a) investigate/ describe negative exponents b) determine scientific notation for numbers greater than 0 d) determine square roots 8.5 a) determine if a number is a perfect square b) find 2 whole numbers btwn which a square root lies New from grade 8 Exponents/Squares/Square Roots

7. October 1, 2010 7 4.2 a) comp/ order fractions 4.3 c) comp/ order decimals 6.2 d) comp/order fractions, decimals, percents 7.1 c) comp/ order fractions, decimals, percents, scientific notation 5.2 b) compare/ order fractions and decimals Comparing and Ordering

8. October 1, 2010 8 5.7 Order of Operations 6.8 Order of Operations ( no { }, | | ) 7.13 evaluate algebraic expressions 7.3 operations with integers 8.1 simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties to justify Alg1.1 represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables New from grade 7 Expressions and Operations

9. October 1, 2010 9 3.3 b) model fractions 5.18 c) model solutions of one-step linear equations (+,-) 6.2 b) identify fract, decimal, percent from a representation 4.2 b) represent equiv fractions 4.3 d) write dec/fract from a model 6.4 represent multiplication and division of fractions 7.3 a) model operations (add/sub/mult/div) with integers New content Modeling New content

10. October 1, 2010 10 8.15 a) solve multistep linear equations 7.15 a) solve one-step inequalities/ b) graph on number line 8.16 graph linear equations in two variables Alg1.4 solve multistep linear and quadratic equations (2 variables) Alg1.5 solve multistep linear inequalities (2 variables) Alg1.6 graph linear equations and inequalities New content Equations and Inequalities 7.14 a) solve one- and two-step linear equations 6.20 graph inequalities on a number line

11. October 1, 2010 What can you tell me? 11 Algebra I Relation or function? Domain/range Zeros x- and y-intercepts Function values for elements of the domain Connections among representations AFDA - adds Local/absolute max/min Intervals of increasing/ decreasing End behaviors asymptotes Alg 2 - adds Inverse functions Composition of functions

12. October 1, 2010 12 5.16 Mean as Fair Share 6.15 Mean as Balance Point Alg1.9 Standard Deviation Alg2.11 Normal Distributions New content Technical Assistance Document for A.9 Published Technical Assistance Document for AII.11 October 2010

13. October 1, 2010 13 6.17 identify/ extend geometric/ arithmetic sequences 7.2 describe/ represent arithmetic/ geometric sequences using variable expressions Alg2.2 investigate/ apply properties of arithmetic/ geometric sequences/ series to solve real world probs New content

14. 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. NAEP Released Items – 2007 Grade 8 M7 #14 SCR Hard 29%

15. October 1, 2010 Perimeter Problem In what situation would this task be used?In what situation would this task be used? In which course/level would you use this task?In which course/level would you use this task? How would you adjust it for another course/level?How would you adjust it for another course/level? In what situation would this task be used?In what situation would this task be used? In which course/level would you use this task?In which course/level would you use this task? How would you adjust it for another course/level?How would you adjust it for another course/level? 15

16. October 1, 2010 Worthwhile task? Questions to ask yourself Does the problem challenge students to use higher-level critical thinking skills?Does the problem challenge students to use higher-level critical thinking skills? Is the problem clearly connected to the targeted mathematics?Is the problem clearly connected to the targeted mathematics? Are there multiple ways to solve this problem?Are there multiple ways to solve this problem? Is it accessible to all students?Is it accessible to all students? Does the problem challenge students to use higher-level critical thinking skills?Does the problem challenge students to use higher-level critical thinking skills? Is the problem clearly connected to the targeted mathematics?Is the problem clearly connected to the targeted mathematics? Are there multiple ways to solve this problem?Are there multiple ways to solve this problem? Is it accessible to all students?Is it accessible to all students? 16

17. October 1, 2010 Worthwhile task? Questions to ask yourself Does the problem promote mathematical communication?Does the problem promote mathematical communication? What might students struggle with?What might students struggle with? This would be an appropriate problem if you were studying… or if you have already studied…This would be an appropriate problem if you were studying… or if you have already studied… Does the problem promote mathematical communication?Does the problem promote mathematical communication? What might students struggle with?What might students struggle with? This would be an appropriate problem if you were studying… or if you have already studied…This would be an appropriate problem if you were studying… or if you have already studied… 17

18. October 1, 2010 Where can I get worthwhile mathematical tasks? NAEP released items http://nces.ed.gov/nationsreportcard/ http://nces.ed.gov/nationsreportcard/ PISA released items http://nces.ed.gov/surveys/pisa/educators.asp http://nces.ed.gov/surveys/pisa/educators.asp APEC Mathematics Assessment Database http://hrd.apec.org/index.php/Mathematics_Ass essments http://hrd.apec.org/index.php/Mathematics_Ass essments http://hrd.apec.org/index.php/Mathematics_Ass essments Heinemann Mathematics (not free, but cheap) http://books.heinemann.com/math/ http://books.heinemann.com/math/ NAEP released items http://nces.ed.gov/nationsreportcard/ http://nces.ed.gov/nationsreportcard/ PISA released items http://nces.ed.gov/surveys/pisa/educators.asp http://nces.ed.gov/surveys/pisa/educators.asp APEC Mathematics Assessment Database http://hrd.apec.org/index.php/Mathematics_Ass essments http://hrd.apec.org/index.php/Mathematics_Ass essments http://hrd.apec.org/index.php/Mathematics_Ass essments Heinemann Mathematics (not free, but cheap) http://books.heinemann.com/math/ http://books.heinemann.com/math/ 18

19. October 1, 2010 Assessing Higher-level Thinking Skills 19 8.11The student will solve practical area and perimeter problems involving composite plane figures. PAST FUTURE Find the area of the shaded region.

20. October 1, 2010 Assessing Higher-level Thinking Skills 20 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? Between which two whole numbers does lie?

21. October 1, 2010 Assessing Higher-level Thinking Skills 21 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?

22. October 1, 2010 Assessing Higher-level Thinking Skills Increased levels of complexity in analysisIncreased levels of complexity in analysis Increased levels of complexity in expressions and equationsIncreased levels of complexity in expressions and equations Comparing and contrasting of functions during analysisComparing and contrasting of functions during analysis Increased levels of complexity in analysisIncreased levels of complexity in analysis Increased levels of complexity in expressions and equationsIncreased levels of complexity in expressions and equations Comparing and contrasting of functions during analysisComparing and contrasting of functions during analysis 22

23. October 1, 2010 New SOL Blueprints Mega-categories combine reporting categories 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 3Geometry and Algebra II – from 5 to 3 Mega-categories combine reporting categories 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 3Geometry and Algebra II – from 5 to 3 23

24. October 1, 2010 24 Note: Asterisk indicates that the SOL will be assessed in the non-calculator section.

25. October 1, 2010 25 New Formula Sheets

26. October 1, 2010 Technology Enhanced Items Interactive questions Hot-spotsHot-spots Drag and dropDrag and drop Creation of graphsCreation of graphs Short responseShort response Practice ePAT available by February 2011 Interactive questions Hot-spotsHot-spots Drag and dropDrag and drop Creation of graphsCreation of graphs Short responseShort response Practice ePAT available by February 2011 26 Beginning in Spring 2011

27. October 1, 2010 New SOL Assessment Timeline Spring 2011 All SOL tests (live test items) based on 2001 SOLAll SOL tests (live test items) based on 2001 SOL Field test items will be based on the 2009 SOLField test items will be based on the 2009 SOL Technology enhanced items will be field tested in grades 6-8 and EOC SOL testsTechnology enhanced items will be field tested in grades 6-8 and EOC SOL tests Spring 2011 All SOL tests (live test items) based on 2001 SOLAll SOL tests (live test items) based on 2001 SOL Field test items will be based on the 2009 SOLField test items will be based on the 2009 SOL Technology enhanced items will be field tested in grades 6-8 and EOC SOL testsTechnology enhanced items will be field tested in grades 6-8 and EOC SOL tests 27

28. October 1, 2010 New SOL Assessment Timeline Fall 2011 EOC SOL tests will be based on 2009 SOLEOC SOL tests will be based on 2009 SOL Spring 2012 All SOL tests will be based on 2009 SOLAll SOL tests will be based on 2009 SOL Fall 2011 EOC SOL tests will be based on 2009 SOLEOC SOL tests will be based on 2009 SOL Spring 2012 All SOL tests will be based on 2009 SOLAll SOL tests will be based on 2009 SOL 28

29. October 1, 2010 What is our goal as teachers of mathematics? What will tomorrow’s jobs look like?What will tomorrow’s jobs look like? Teach kids how to use their critical thinking and reasoning skills to adapt and overcome in unfamiliar settingsTeach kids how to use their critical thinking and reasoning skills to adapt and overcome in unfamiliar settings What will tomorrow’s jobs look like?What will tomorrow’s jobs look like? Teach kids how to use their critical thinking and reasoning skills to adapt and overcome in unfamiliar settingsTeach kids how to use their critical thinking and reasoning skills to adapt and overcome in unfamiliar settings 29