Transcript define algebra

Common Core:
Preparing for the Assessments
Dr. Eric Milou
Rowan University
Department of Mathematics
[email protected]
856-256-4500 x3876
http://ericmilou.com
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Preparing for the Assessments
Know the content
Standards, practices, and progressions
Use Technology
Engage, motivate, and assess
Review Assessment Sample Items
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Common Core State Standards:
Let’s not just drink the Kool-Aid.
 Fewer, clearer, and higher, to best drive effective policy and practice;
 But definitely not fewer for grades 9-12!
 Clearer? Have you read these things?
 Aligned with college and work expectations, so that all students are
prepared for success upon graduating from high school;
 Does math for college = math for work?
 Inclusive of rigorous content and application of knowledge through high-
order skills, so that all students are prepared for the 21st century;
 Internationally benchmarked, so that all students are prepared for
succeeding in our global economy and society; and
 Singapore. Singapore. Singapore.
 Research and evidence-based.
 The research they liked.
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National Assessments 2014-15
 Partnership for Assessment of Readiness for College
and Careers (PARCC)
 19 states + DC, Achieve
 SMARTER Balanced Assessment Consortium
(SBAC)
 22 states, West Ed
 3 states undecided, 1 (Utah) lost interest
 5 states did not adopt the common core
PARCC and SBAC
PARCC & SBAC
 Online assessments for Grades 3-8 and high school
 Use of a mix of item types, including selected
response, constructed response, technology enhanced
and complex performance tasks.
 Two components, both given during final weeks of the
school year.
 Use of both electronic and human scoring, with results
expected within two weeks.
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FIXED FORM
ADAPTIVE
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Using Technology to Advance Assessment and
the Shifts
 Capturing complex student responses
through a device interface (e.g., using
drawing tools, symbol palettes, etc.)
 Machine scorable multi-step tasks are more
efficient to administer and score.
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Overview of Mathematics Task Types
Task Type
Description of Task Type
I. Tasks assessing
concepts, skills and
procedures
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•
•
•
II. Tasks assessing
expressing
mathematical
reasoning
• Each task calls for written arguments / justifications, critique of
reasoning, or precision in mathematical statements (MP.3, 6).
• Can involve other mathematical practice standards
• May include a mix of machine scored and hand scored responses
• Included on the Performance Based Assessment component
III. Tasks assessing
modeling /
applications
• Each task calls for modeling/application in a real-world context or
scenario (MP.4)
• Can involve other mathematical practice standards.
• May include a mix of machine scored and hand scored responses 12
• Included on the Performance Based Assessment component
Balance of conceptual understanding, fluency, and application
Can involve any or all mathematical practice standards
Machine scorable including innovative, computer-based formats
Will appear on the End of Year and Performance Based Assessment
components
Sample Released items
 http://www.parcconline.org
 http://www.smarterbalanced.org
 Balanced Assessment Project
http://balancedassessment.concord.org
 Mathematics Assessment Project (MAP)
http://map.mathshell.org/
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Big Ideas
Elementary K-2: Place Value & 10
Grades 3-5+: Fractions!
Grades 6-8: Algebra
High School: Modeling
Modeling links classroom mathematics and
statistics to everyday life, work, and decisionmaking.
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The Importance of Ten
8 + 7 = ?
How do we teach this?
x x x x x
x x x x x
x x x x
x x x
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Best Friends
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2
3
4
5
6
7
8
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8+7=?
8 + 7=?
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5
10 + 5 = 15
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17 - 8 =
0 17
1/ 7/
-8
2
7
8 --> --> 10 --> --> --> --> --> --> --> 17
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How Many Circles?
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More time on computation
but not the same old way
Engaging & Active
Arcademicskillbuilders.com
Sumdog.com
Less passive worksheets
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The Influence of Video Games
3.NF - Assessment Item
Which is closer to 1 on the number line,
4/5 or 5/4. Explain.
This can be seen as a multi-step problem
for grade 3:
Compare 4/5 to 5/5 (like denominators)
Compare 4/4 to 5/4 (like denominators)
Compare 1/4 to 1/5 (like numerators)
3.NF.1
4.NBT.5
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4.G.2
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4.G.3
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5.NF.4 and 6
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5.G.3 and 4
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5.NF.5
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 Grade 3
Fractions Summary
 Develop understanding of fractions as numbers.
 Grade 4
 Extend understanding of fraction equivalence and ordering.
 Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers.
 Understand decimal notation for fractions, and compare decimal fractions.
 Grade 5
 Use equivalent fractions as a strategy to add and subtract fractions.
 Apply and extend previous understandings of multiplication and division
to multiply and divide fractions.
 Grade 6
 Apply and extend previous understandings of multiplication and division
to divide fractions by fractions.
 Compute fluently with multi-digit numbers and find common factors and
multiples.
 Apply and extend previous understandings of numbers to the system of 32
rational numbers.
Number Line Task
a-b
b-a
0
a+b
a
b
Where is a+b on the number line?
Where is b-a?
Where is a-b?
What about (a/b)?
(Need to know where 1 is.)
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How Much Space?
 Janie’s Ipod holds 10 Mb of music. Janie
downloaded songs that were 2 Mbs. How many
songs can she fit on her Ipod?
 Richard also has an Ipod that holds 10 Mb of
music. He downloaded shorter songs that were
only ½ Mb. How many songs can he fit on his
Ipod?
Picture of 10 ÷ ½
|--------------------- 10 MB---------------------|
Grade 6: EE, CR
Grade 6: EE, TE
Grade 7: EE, CR
Grade 7: Number, ER
Grade 7: Geometry, TE
Grade 8: Geo, CR
Grade 8: Geo, CR
Technology Resources
 Khan Academy
 Of course, teachers aren’t “pissed off” because Sal Khan is the
world’s teacher. They’re concerned that he’s a bad teacher
who people think is great; that the guy who’s delivered over
170 million lessons to students around the world openly
brags about being unprepared and considers the
precise explanation of mathematical concepts to be
mere “nitpicking.” Experienced educators are concerned
that when bad teaching happens in the classroom, it’s a crisis;
but that when it happens on YouTube, it’s a “revolution.”
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Khan Academy does Angry Birds
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Using Technology in Lessons
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What do you need to know?
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Tall & Skinny
Volume = (Area of Base) x H
 Height = 10 cm
 Diameter = 5.5cm
 Radius = 2.75cm
 Area Base = π (2.75)2 = 23.75 cm2
 Volume = 237.5 cm3
 1 cm3 = 0.0338 oz
 Volume = 8.03 oz
Short & Fat
Volume = (Area of Base) x H
 Height = 3 cm
 Diameter = 7 cm
 Radius = 3.5 cm
 Area Base = π (3.5)2 = 38.47 cm2
 Volume = 115.4 cm3
 1 cm3 = 0.0338 oz
 Volume = 3.9 oz
Reveal
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High School
 Define “ALGEBRA”
The intensive study of the last three letters of the
alphabet.
using variables to replace something significant in a
problem
equations, formulas, numbers, headaches
using letters such as x to represent an unknown
number and solving for that letter
The class between prealgebra and geometry
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Algebra - CR
Number & Quantity: ER
Algebra - SR
Geometry - TE
Define “ALGEBRA”
 The intensive study of the last three letters of the
alphabet.
 using variables to replace something significant in
a problem
 equations, formulas, numbers, headaches
 using letters such as x to represent an unknown
number and solving for that letter
 The class between prealgebra and geometry
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Modeling: Drug Steady State
 10 mg Zrytec daily
 50% of Zrytec is eliminated daily
 How many mg of Zrytec is in the body after ….
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10mg Daily of Zrytec
Day
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2
3
4
5
6
Mg. of Zyrtec
10
15
17.5
18.75
19.375
19.6875
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 Turn on Common Core Math
Resources
 Ohio Model Curriculum
 NY state aligned tasks
 Dana Center Toolbox
 Common Core Progressions
 Illustrative Project
 Achieve the Core Website
 Common Core Resources (NCTM)
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http://ericmilou.com/
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Things to Consider in Summary
 Is modeling and contexts a part of daily instruction?
 Depth of content especially fractions in grades 3-6.
 Use of technology to engage, motivate, and assess
 Be wary of extraneous context.
 Embedded Mathematical Practices including
discourse, scaffolding, and reasoning. (Not word
problems at the end of the lessons.)
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Thank You
Dr. Eric Milou
Rowan University
[email protected]
http://ericmilou.com/
http://digitsmath.com/
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