Download - Making Sense Of The New Standards K-12 Alliance Staff Developer Training January 25, 2013
Making SenseOf The New Standards
K-12 Alliance Staff Developer Training
January 25, 2013
New Opportunities for All Learners
California Common Core State Standards (ELA and Math)
Next Generation Science Standards
21st Century Skills
Prior Knowlege
• With your group discuss what you know about 21st Century Skills, CCSS, and NGSS
• What connections do you see?• Chart your ideas. You will return to
your thinking on Sunday.
In The Classroom
Math Science
21st Century Skills
ELA
Activity
• Choose a secret number (don’t say it aloud) • add 5 to that number• double that sum• subtract 4 from that product• divide the results by 2 • subtract your secret number from the
quotient • you have 3.
How Did That Happen?
• What is behind this trick?• Is it foolproof?• Discuss your thoughts at your
table.
Explain this trick
Use the tools at your table to explain what you think is happening.Remember:•You may all have had different secret numbers.•No matter what number you selected, you all ended up with 3.
Transfer to a Whiteboard
• Think about how to use the tools to demonstrate how the trick was done.
• Use the white board to depict your demonstration.
Connect action to a direct model with a specific “Secret #” choice
Instructions What I did My model
Choose a secret number
I chose 2 beans •• (2 beans)
Add 5 I added 5 more •• •••••
Double that sum I multiplied by two •• ••••••• •••••
Subtract 4 Subtracted 4 beans ••••• •••••
Divide by 2 I pulled half away •••••
Subtract secret number
I pulled off 2 beans •••
You have three I was astonished!
Connect action to a model for any choice (A set of all secret numbers)
Instructions What I did My model
Choose a secret number
I chose a cup to represent “any”
Cup
Add 5 I added 5 beans Cup •••••
Double that sum I multiplied by two Cup •••••Cup •••••
Subtract 4 Subtracted 4 beans Cup •••Cup •••
Divide by 2 I pulled half away Cup •••
Subtract secret number
I pulled off the cup •••
You have three Voila!
Words Manipulatives Algebra Expressions/Result
Choose a secret number
Cup n
Add 5
Double that sum
Subtract 4
Divide by 2
Subtract secret number
You have three
Words Manipulatives Algebra Expressions/Result
Choose a secret number
Cup n
Add 5 Cup • • • • • N+5
Double that sum
Subtract 4
Divide by 2
Subtract secret number
You have three
Words Manipulatives Algebra Expressions/Result
Choose a secret number
Cup n
Add 5 Cup • • • • • N+5
Double that sum Cup •••••Cup •••••
2(n+5) = 2n + 10
Subtract 4
Divide by 2
Subtract secret number
You have three
Words Manipulatives Algebra Expressions/Result
Choose a secret number
Cup n
Add 5 Cup • • • • • N+5
Double that sum Cup •••••Cup •••••
2(n+5) = 2n + 10
Subtract 4 Cup•••Cup•••
2n + 10 – 4= 2n+6
Divide by 2
Subtract secret number
You have three
Words Manipulatives Algebra Expressions/Result
Choose a secret number
Cup n
Add 5 Cup • • • • • N+5
Double that sum Cup •••••Cup •••••
2(n+5) = 2n + 10
Subtract 4 Cup•••Cup•••
2n + 10 – 4= 2n+6
Divide by 2 Cup••• (2n+6)/2 = n + 3
Subtract secret number
You have three
Words Manipulatives Algebra Expressions/Result
Choose a secret number
Cup n
Add 5 Cup • • • • • N+5
Double that sum Cup •••••Cup •••••
2(n+5) = 2n + 10
Subtract 4 Cup•••Cup•••
2n + 10 – 4= 2n+6
Divide by 2 Cup••• (2n+6)/2 = n + 3
Subtract secret number
••• N + 3 – n = 3
You have three
Words Manipulatives Algebra Expressions/Result
Choose a secret number
Cup n
Add 5 Cup • • • • • N+5
Double that sum Cup •••••Cup •••••
2(n+5) = 2n + 10
Subtract 4 Cup•••Cup•••
2n + 10 – 4= 2n+6
Divide by 2 Cup••• (2n+6)/2 = n + 3
Subtract secret number
••• N + 3 – n = 3
You have three Yes, I do. 3
8th Grade Expectation
Words Results Cumulative Expression
Choose a secret number
n n
Add 5 N+5 N+5
Double that sum 2(n+5) = 2n+10 2(n+5)
Subtract 4 2n + 10 – 4 = 2n+6
2(n + 5) – 4
Divide by 2 (2n+6)/2 = n + 3 2
Subtract secret number
N + 3 – n = 3 2
You have three 3 2(n + 5) – 4 -n = 3 2
2(n + 5) – 4
2(n + 5) – 4 -n
Language Of Doing Math
Which of these words best describes what I asked you to do:•Represent •Solve •Evaluate•Simplify •Determine •Compare •Find •Explain
Instructional Words =implication for process
• Represent – To portray in another abstract way.• Solve – Finding an unknown quantity or expression.• Evaluate – To find the value of by substituting
values in an expression or function.• Simplify – To make a math expression simpler.• Determine – Find or choose• Compare – Relate values of 2 or more expressions• Explain – Describe a process.• Justify – Support the logic of a process or solution
Standards for Mathematical Content K-8
How the grade level standards are organized
• Standards • Clusters • Domains
7th Grade Common Core Standard Connection
7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Common Core Connections7 ------> 6
• 7th Grade (p. 31) 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
• 6TH: (P. 26) 6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Follow the Standard Back5—4—3—2—1—Kinder!
• Keep track of the standards you determine to be in the line from Kindergarten to 5th grade and on to Middle school.
• Remember the key idea is representing (modeling) a mathematical idea in a manner chosen by the student.
Common Core Standards for Mathematics
Two Types of Standards•Mathematical Practice (recurring
throughout the grades)•Mathematical Content (different at
each grade level)
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.3. Construct viable arguments and
critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in
repeated reasoning
Which of These Describe your work on the “Trick”?
Common Core Math Standards
1997 CA. Math Standards
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CCSS Requires Three Shifts in Mathematics
1. Focus: Focus strongly where the standards focus.
2. Coherence: Think across grades, and link to major topics
3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application
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Shift #1: Focus Strongly where the Standards Focus
• Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom.
• Focus deeply on what is emphasized in the standards, so that students gain strong foundations.
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GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2Addition and subtraction - concepts, skills, and problem solving and place value
3–5Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
6Ratios and proportional reasoning; early expressions and equations
7Ratios and proportional reasoning; arithmetic of rational numbers
8 Linear algebra
Key Areas of Focus in Mathematics
Grade Shifts: Examples
Concept1997
Standards
CCSS
Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle)
Grade2
K
Introduction to ProbabilityGrade
3Grade
7
Introduction of fractions as numbers
Grade2
Grade3
Add and subtract simple fractions
Grade3
Grade4
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Shift #2: Coherence: Think Across Grades, and Link to Major Math Topics Within Grades
• Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years.
• Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.
Shift #3: Rigor: Expect fluency, deep understanding, and application
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• The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving
situations
• Pursuit of all threes requires equal intensity in time, activities, and resources.
Solid Conceptual Understanding
• Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives
• Students are able to see math as more than a set of mnemonics or discrete procedures
• Conceptual understanding supports the other aspects of rigor (fluency and application)
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Fluency
• The standards require speed and accuracy in calculation.
• Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts
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Required Fluencies in K-6
GradeStandard
Required Fluency
K K.OA.5 Add/subtract within 51 1.OA.6 Add/subtract within 10
22.OA.22.NBT.5
Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100
33.OA.73.NBT.2
Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000
4 4.NBT.4 Add/subtract within 1,000,0005 5.NBT.5 Multi-digit multiplication
6 6.NS.2,3Multi-digit divisionMulti-digit decimal operations
Application
• Students can use appropriate concepts and procedures for application even when not prompted to do so.
• Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.
• Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of
and access science content.38