ccss-m task force: camte, cde, cisc, cmc, cmp
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CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Choose a partner.
Interview your partner:
Name, School, Grade level
What’s great about your work?
Who was your favorite math teacher and why?
Introduce partner to group.
Introductions
M1 A1
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Understanding why the number line is an
important representation for understanding
fractions and operations with / by fractions.
Elaborating definitions of fractions and operations.
Big Ideas Module 1
M1 A1
Module 1: Digging out of the “Whole”
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Activity 1: Opening / Welcome
Activity 2: Overview of Institute
Activity 3: What does 2/3 mean?
Activity 4: Why Emphasize the Number Line?
Activity 5: Comparing Two Lengths
Activity 6: Defining Fractions
Activity 7: Schemes
Activity 8: Additive to Multiplicative Thinking
Activity 9: Mathematical Practices
Activity 10: Summarize Module 1
Agenda Module 1
M1 A1Participant page 12
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
CMP Task Force
California Department of Education (CDE)
California Mathematics Council (CMC)
California Mathematics Project (CMP)
California Mathematics Teacher Educators
(CaMTE)
Curriculum & Instruction Steering Committee,
Math Subcommittee (CISC)
Overview of Institute
M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Focus on:
Common Core State Standards
Begin transition with:
Mathematical Practices
Restructuring Lessons
Overview of Institute
M1 A2 Appendix pages 126-199
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
CMP Task Forces developed 5 institutes:
Number Sense - Cardinality
Fractions on a Number Line
Transformational Geometry
Modeling – Math Practices
Modeling – High School
Overview of Institute
M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Institute Themes:
Changes in Content Emphasis in CCSS-M
CCSS Math Practices
Elaborating Definitions
Restructuring Current Instruction
Overview of Institute
M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Fractions on Number Line – Modules:
Overview of Institute
1. Digging Out of the “Whole”2. Get to the Point!3. All Things Being Equal4. Ordering and Comparing5. We “Halve” Assessments6. Addition as Iterating7. Subtraction as Difference8. Multiplication as Comparison9. Divide and Conquer 10. Wrapping It Up
M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
CCSS Fraction Domain
Overview of Institute
Participant pages13-16 M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
CCSS Number Line
Overview of Institute
Participant pages 7-10M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
CCSS Mathematical PracticesOverview of Institute
CCSS pp. 6-8
Make sense of problem and persevere in solving.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others. Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for & express regularity in repeated reasoning..
M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Overview of Institute
I have a friend who is a middle school math teacher.
This year he teaches all the “Far Below Basic” and
“Below Basic” students. He was frustrated as he asked
his students to locate 7/8 on the number line.
Where do you think the students put 7/8 on number line?
M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Overview of Institute
That night he went home to his 5th grade son,
and asked him the same question.
By the way, last year his son
got a perfect score on the CST.
Where do you think his son placed 7/8 on the number line?
M1 A2
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
What is a fraction?
What does 2/3 mean?
M1 A3
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Why emphasize the number line?
Rationale for Number Line in the Common Core State Standards
Read paragraphs #1 through #4 on page 3
M1 A4 Participant pages 3-10
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Why emphasize the number line?
“You can’t have the number line without fractions;you can’t have fractions without a number line.Number lines are not optional.”
Phil Daro, January 2011
M1 A4
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Comparing Two Lengths
What fraction of the white strip is the blue strip?
Catherine Lewis, Rebecca Perry
Fraction Toolkit, IES Grant
M1 A5 Materials: Paper strips
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Comparing Two Lengths
As a group, define “fraction”.
M1 A5
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Use the definition of fraction to explain what 1/5 means.
Defining Fractions
M1 A6
0
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Use the definition of fraction to explain what 3/5 means.
Defining Fractions
M1 A6
0 1(⅕) 2(⅕) 3(⅕) 4(⅕) 5(⅕)
⅗
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Unitizing
Partitioning
Iterating
Splitting
Fraction Schemes
M1 A7
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Fraction Schemes
M1 A7
Students make thoughtful mistakes.
Teachers and students courageouslyshare with us what they knowand have yet to learn.
Speak to evidence of what see and hear.
Protocols for Watching Videos
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
M1 A7
Scheme: Unit (whole)Unitizing (parts)
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Scheme: Partitioning
M1 A7
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
M1 A7
Clearly Iteration!
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
I had 375 candies. I sell 90 of them. How
many do I have left?
Schemes
I was taking a trip to visit my sister. I drive 90
miles then stop to rest. The total distance to my
sister’s house is 375 miles. How much farther
do I have to go?
M1 A7 Participant page 17
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
M1 A7
Scheme: Iterate 100’sPartition 10’s0’s
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
M1 A7
Scheme: Splitting
Additive to Multiplicative Thinking
M1 A8
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
M1 A8
Insert > Movie > Place 35 on a Number Line 0 to 35
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
M1 A8
Tally MarksIncrementsScale
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Predict how many sections there will be when fold paper.four times. Now fold paper.
# of folds # of sections
0 11234.n
Additive to Multiplicative Thinking
M1 A8Materials: Meter paper strips
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Describe the growth pattern of sections.
# of folds # of sections
0 11 22 43 84 16.n
Additive to Multiplicative Thinking
M1 A8
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Where in paper folding do you see:
Multiplication?
Division?
Fractions?
Exponents?
In other words,
where do you see multiplicative thinking?
Additive to Multiplicative Thinking
M1 A8
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
CCSS Mathematical Practices
Math Practices
Participant pages 18-19
Make sense of problem and persevere in solving.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others. Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for & express regularity in repeated reasoning.
M1 A9
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
“Hung-Hsi Wu attempts to bring coherence to the teaching and learning of fractions by beginning with the definition of a fraction as a length on the number line (1998). This approach eliminates the ‘conceptual discontinuity’ (2002) encountered moving from work with whole numbers to fractions; it also brings coherence to the various meanings of fractions and allows for both conceptual work to operations on fractions (2008). Wu asserted that ‘The number line is to fractions what one’s fingers are to whole numbers…’”
Summary
M1 A10
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
Summary
Compare what we have done in
Module 1 with the previous quote.
M1 A10 Participant page 20
Quick Write:
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
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