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Making Sense Of The New Standards

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Making Sense Of The New Standards K-12 Alliance Staff Developer Training January 25, 2013 – PowerPoint PPT presentation

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Title: Making Sense Of The New Standards


1
Making Sense Of The New Standards
  • K-12 Alliance Staff Developer Training
  • January 25, 2013

2
New Opportunities for All Learners
California Common Core State Standards (ELA and
Math)
Next Generation Science Standards
21st Century Skills
3
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.

4
In The Classroom
Math
Science
ELA
21st Century Skills
5
Activity
  • Choose a secret number (dont 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.

6
How Did That Happen?
  • What is behind this trick?
  • Is it foolproof?
  • Discuss your thoughts at your table.

7
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.

8
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.

9
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!
10
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!
11
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
12
Words Manipulatives Algebra Expressions/Result
Choose a secret number Cup n
Add 5 Cup N5
Double that sum
Subtract 4
Divide by 2
Subtract secret number
You have three
13
Words Manipulatives Algebra Expressions/Result
Choose a secret number Cup n
Add 5 Cup N5
Double that sum Cup Cup 2(n5) 2n 10
Subtract 4
Divide by 2
Subtract secret number
You have three
14
Words Manipulatives Algebra Expressions/Result
Choose a secret number Cup n
Add 5 Cup N5
Double that sum Cup Cup 2(n5) 2n 10
Subtract 4 Cup Cup 2n 10 4 2n6
Divide by 2
Subtract secret number
You have three
15
Words Manipulatives Algebra Expressions/Result
Choose a secret number Cup n
Add 5 Cup N5
Double that sum Cup Cup 2(n5) 2n 10
Subtract 4 Cup Cup 2n 10 4 2n6
Divide by 2 Cup (2n6)/2 n 3
Subtract secret number
You have three
16
Words Manipulatives Algebra Expressions/Result
Choose a secret number Cup n
Add 5 Cup N5
Double that sum Cup Cup 2(n5) 2n 10
Subtract 4 Cup Cup 2n 10 4 2n6
Divide by 2 Cup (2n6)/2 n 3
Subtract secret number N 3 n 3
You have three
17
Words Manipulatives Algebra Expressions/Result
Choose a secret number Cup n
Add 5 Cup N5
Double that sum Cup Cup 2(n5) 2n 10
Subtract 4 Cup Cup 2n 10 4 2n6
Divide by 2 Cup (2n6)/2 n 3
Subtract secret number N 3 n 3
You have three Yes, I do. 3
18
8th Grade Expectation
Words Results Cumulative Expression
Choose a secret number n n
Add 5 N5 N5
Double that sum 2(n5) 2n10 2(n5)
Subtract 4 2n 10 4 2n6 2(n 5) 4
Divide by 2 (2n6)/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
19
Language Of Doing Math
  • Which of these words best describes what I asked
    you to do
  • Represent
  • Solve
  • Evaluate
  • Simplify
  • Determine
  • Compare
  • Find
  • Explain

20
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

21
Standards for Mathematical Content K-8
  • How the grade level standards are organized

Standards Clusters Domains
22
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.

23
Common Core Connections 7 ------gt 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.

24
Follow the Standard Back 54321Kinder!
  • 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.

25
Common Core Standards for Mathematics
  • Two Types of Standards
  • Mathematical Practice (recurring throughout the
    grades)
  • Mathematical Content (different at each grade
    level)

26
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?
27
Common Core Math Standards
28
1997 CA. Math Standards
29
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

30
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.

31
Key Areas of Focus in Mathematics
Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K2 Addition and subtraction - concepts, skills, and problem solving and place value
35 Multiplication and division of whole numbers and fractions concepts, skills, and problem solving
6 Ratios and proportional reasoning early expressions and equations
7 Ratios and proportional reasoning arithmetic of rational numbers
8 Linear algebra
32
Grade Shifts Examples
Concept 1997 Standards CCSS
Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle) Grade 2 K
Introduction to Probability Grade 3 Grade 7
Introduction of fractions as numbers Grade 2 Grade 3
Add and subtract simple fractions Grade 3 Grade 4
33
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.

34
Shift 3 Rigor Expect fluency, deep
understanding, and application
  • 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.

35
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)

36
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

37
Required Fluencies in K-6
Grade Standard Required Fluency
K K.OA.5 Add/subtract within 5
1 1.OA.6 Add/subtract within 10
2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100
3 3.OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within 1000
4 4.NBT.4 Add/subtract within 1,000,000
5 5.NBT.5 Multi-digit multiplication
6 6.NS.2,3 Multi-digit division Multi-digit decimal operations
38
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.
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