Transcript Document

(and managing it)
Making Sense of Change
VCTM Fall Academy
October 1, 2010
Michael Bolling
Mathematics Coordinator, VDOE
October 1, 2010
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Slide Title
October 1, 2010
2
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).
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Deepwater Horizon Oil Spill
• What “I wonder…” questions
about the mathematics would
kids (or adults) ask?
• What jobs related to the spill
involve pertinent mathematics?
• To which mathematics content
could this disaster be
connected?
October 1, 2010
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Highlighted SOL Changes
• Awareness (curriculum and pacing
guides, SOL Crosswalks, VDOE training
institutes)
• Understanding
• Content (Curriculum Framework,
technical assistance documents)
• Connections (Enhanced Scope and
Sequence lesson, vertical articulation
of content)
October 1, 2010
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Exponents/Squares/Square Roots
New from grade 8
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
October 1, 2010
8.5 a)
determine if a
number is a
perfect square
b) find 2 whole
numbers btwn
which a
square root
lies
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Comparing and Ordering
4.2 a) comp/
order
fractions
4.3 c) comp/
order
decimals
5.2 b)
compare/
order
fractions and
decimals
October 1, 2010
6.2 d)
comp/order
fractions,
decimals,
percents
7.1 c) comp/
order
fractions,
decimals,
percents,
scientific
notation
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Expressions and Operations
8.1 simplify numerical
expressions involving
positive exponents,
using rational
numbers, order of
operations, and
6.8 Order
properties to justify
5.7 Order
of
Operations
Alg1.1 represent verbal
quantitative situations
algebraically/evaluate
7.13 evaluate
expressions for given
algebraic
replacement
values of
variables
expressions
of
Operations
( no { }, | | )
New from grade 7
New from grade 7
October 1, 2010
7.3
operations
with
integers
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Modeling
3.3 b) model
fractions
4.2 b)
represent
equiv
fractions
4.3 d) write
dec/fract
from a model
October 1, 2010
7.3 a) model
operations
(add/sub/mult/div)
with integers
5.18 c) model
solutions of
one-step
linear
equations
(+,-)
New content
6.2 b) identify
fract, decimal,
percent from a
representation
6.4 represent
multiplication
and division of
fractions
New content
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Equations and Inequalities
7.14 a) solve
one- and
two-step
6.20 graph
linear
inequalities
equations
on a number
line
7.15 a) solve
one-step
inequalities/
b) graph on
number line
New content
October 1, 2010
8.15 a) solve
multistep
linear
equations
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
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What can you tell me?
Algebra I
AFDA - adds
Alg 2 - adds
Relation or function?
Local/absolute max/min
Inverse functions
Domain/range
Zeros
Intervals of increasing/
decreasing
Composition of
functions
x- and y-intercepts
End behaviors
Function values for
elements of the domain
asymptotes
Connections among
representations
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Technical Assistance
Document for A.9
Published
5.16
Mean as
Fair
Share
6.15 Mean
as Balance
Point
New content
New content
Technical Assistance
Document for AII.11
October 2010
October 1, 2010
Alg1.9
Standard
Deviation
New content
Alg2.11
Normal
Distributions
New content
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6.17 identify/
extend
geometric/
arithmetic
sequences
7.2 describe/
represent
arithmetic/
geometric
sequences
using variable
expressions
New content
October 1, 2010
Alg2.2
investigate/
apply
properties of
arithmetic/
geometric
sequences/
series to solve
real world
probs
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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.
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NAEP Released Items – 2007 Grade 8 M7 #14 SCR Hard 29%
Each figure in the pattern below is made of hexagons that
measure 1 centimeter on each side.
Perimeter Problem
• In what situation would this task be
used?
• In which course/level would you use
this task?
• How would you adjust it for another
course/level?
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Worthwhile task?
Questions to ask yourself
• Does the problem challenge
students to use higher-level critical
thinking skills?
• Is the problem clearly connected to
the targeted mathematics?
• Are there multiple ways to solve
this problem?
• Is it accessible to all students?
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Worthwhile task?
Questions to ask yourself
• Does the problem promote
mathematical communication?
• What might students struggle with?
• This would be an appropriate
problem if you were studying… or if
you have already studied…
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Where can I get worthwhile
mathematical tasks?
NAEP released items
http://nces.ed.gov/nationsreportcard/
PISA released items
http://nces.ed.gov/surveys/pisa/educators.asp
APEC Mathematics Assessment Database
http://hrd.apec.org/index.php/Mathematics_Ass
essments
Heinemann Mathematics (not free, but cheap)
http://books.heinemann.com/math/
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Assessing Higher-level
Thinking Skills
8.11The student will solve practical area and perimeter
problems involving composite plane figures.
PAST
October 1, 2010
FUTURE
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Assessing Higher-level
Thinking Skills
8.5 b) The student will find the two consecutive whole
numbers between which a square root lies.
Between which two
whole numbers does
lie?
Between which two
square roots does 5
lie?
PAST
FUTURE
October 1, 2010
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Assessing Higher-level
Thinking Skills
A.10 The student will compare and contrast multiple
univariate data sets, using box-and-whisker plots.
Which class had the
most students scoring
higher than 83?
PAST
October 1, 2010
Class A has 30 students and Class B
has 20 students. Which class has
more students scoring above 83?
FUTURE
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Assessing Higher-level
Thinking Skills
• Increased levels of complexity
in analysis
• Increased levels of complexity
in expressions and equations
• Comparing and contrasting of
functions during analysis
October 1, 2010
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New SOL Blueprints
Mega-categories combine
reporting categories
• Grade 6 – from 5 to 4
• Grade 7-8 – from 5 to 3
• Algebra I – from 4 to 3
• Geometry and Algebra II – from
5 to 3
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Note: Asterisk
indicates that
the SOL will be
assessed in the
non-calculator
section.
October 1, 2010
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New Formula Sheets
October 1, 2010
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Technology Enhanced Items
Interactive questions
• Hot-spots
• Drag and drop
• Creation of graphs
• Short response
Practice ePAT available by February 2011
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New SOL Assessment Timeline
Spring 2011
• All SOL tests (live test items)
based on 2001 SOL
• Field test items will be based on
the 2009 SOL
• Technology enhanced items will
be field tested in grades 6-8 and
EOC SOL tests
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New SOL Assessment Timeline
Fall 2011
• EOC SOL tests will be based on
2009 SOL
Spring 2012
• All SOL tests will be based on
2009 SOL
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What is our goal as teachers of
mathematics?
• What will tomorrow’s jobs look
like?
• Teach kids how to use their
critical thinking and reasoning
skills to adapt and overcome in
unfamiliar settings
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