ccss-m task force: camte, cde, cisc, cmc, cmp

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


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”


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


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


Presenter

Presentation Notes

Collaboration of CA groups invested in math education Groups committed to implementation even in dire economic times

Focus on:

Common Core State Standards

Begin transition with:

Mathematical Practices

Restructuring Lessons


M1 A2 Appendix pages 126-199


Presenter

Presentation Notes

Can Begin work by: Learning and teaching students how to engage in Math Practices Unit planning with existing texts. What’s there? What’s missing? Cut back amount of review and teach well. Focus on important ideas of unit and then connect lessons to. Changing to chunky problems Begin to use assessments: MARS tasks, Massachusetts multiple choice

CMP Task Forces developed 5 institutes:

Number Sense - Cardinality

Fractions on a Number Line

Transformational Geometry

Modeling – Math Practices

Modeling – High School


M1 A2


Institute Themes:

Changes in Content Emphasis in CCSS-M

CCSS Math Practices

Elaborating Definitions

Restructuring Current Instruction


M1 A2


Fractions on Number Line – Modules:


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 Fraction Domain


Participant pages13-16 M1 A2


CCSS Number Line


Participant pages 7-10M1 A2


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



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



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


Presenter

Presentation Notes

What questions do you have? What did this vignette make you think about? What issues did it raise? Is this a social issue?

What is a fraction?

What does 2/3 mean?

M1 A3


Presenter

Presentation Notes

What questions do you have? What did this vignette make you think about? What issues did it raise? Is this a social issue?

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


Presenter

Presentation Notes

Why would Phil Daro have said this? Why is the number line “not an option”?

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


Presenter

Presentation Notes

Why would Phil Daro have said this? Why is the number line “not an option”?

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


Presenter

Presentation Notes

How many people don’t think it is half? Why? Any other fractions that you know it is not? How do you know? Continue working What is the value of the blue strip? What understandings did you use to figure this out? What knowledge did you bring to the problem? What definition of fractions did you use?

Comparing Two Lengths

As a group, define “fraction”.

M1 A5


Presenter

Presentation Notes

How many people don’t think it is half? Why? Any other fractions that you know it is not? How do you know? Continue working What is the value of the blue strip? What understandings did you use to figure this out? What knowledge did you bring to the problem? What definition of fractions did you use?

Use the definition of fraction to explain what 1/5 means.

Defining Fractions

M1 A6

0


Presenter

Presentation Notes

Use the definition of a fraction to explain what 1/5 means. Why is it important to emphasize that we have equal sized pieces / lengths? How many people think this diagram could be useful to make a picture of 3/5? Can you see 3/5 in more than one place? If I put a zero over here so this is now a number line, what is the value of this point? Where on the number line should we put 3/5? Explain to your partner how you would locate 4/7 on a number line?

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


Presenter

Presentation Notes

Use the definition of a fraction to explain what 1/5 means. Why is it important to emphasize that we have equal sized pieces / lengths? How many people think this diagram could be useful to make a picture of 3/5? Can you see 3/5 in more than one place? If I put a zero over here so this is now a number line, what is the value of this point? Where on the number line should we put 3/5? Explain to your partner how you would locate 4/7 on a number line?

Unitizing

Partitioning

Iterating

Splitting

Fraction Schemes

M1 A7


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


M1 A7

Scheme: Unit (whole)Unitizing (parts)


Presenter

Presentation Notes

- We assume that identifying the unit is obvious. But actually we don’t make obvious to students. We give them sets of objects and ask to identify half of them. We ask to divide by 2 so get 1 ½. We see much confusion over dividing by 2 and ½. Where are they the same and when are they different?


Scheme: Partitioning

M1 A7


M1 A7

Clearly Iteration!


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


M1 A7

Scheme: Iterate 100’sPartition 10’s0’s


M1 A7

Scheme: Splitting

Additive to Multiplicative Thinking

M1 A8


Presenter

Presentation Notes

Other examples of additive student work Compare the first number line placing 7 between 0 and 10 and the second number line placing 35 between 0 and 100. We also see additive thinking in the last number line that continue to add on to the line to get the numbers on in counting sequence.

M1 A8

Insert > Movie > Place 35 on a Number Line 0 to 35


Presenter

Presentation Notes

What does this student know about number line? What does she have yet to learn? Try to elicit that student is using as a counting strip. Thinking additively 1 + 1 + 1 …. 35 Does not yet have a sense that the difference between distance between 0 and 35 has anything to do with the distance between 35 and 100

M1 A8

Tally MarksIncrementsScale


Presenter

Presentation Notes

Students using number line as line with tally marks needed to represent quantity of one Some sense that counting by groups 5, 10s would make the work more efficient. Cameron had typical counting issue … if trying to make ten draw eleven marks. Do count 0 tick mark as 1? Last student was transitioning. Making intervals of 20, but then couldn’t solve a problem calling for ones. Much to learn about the number line itself.

Predict how many sections there will be when fold paper.four times. Now fold paper.

# of folds # of sections

0 11234.n


M1 A8Materials: Meter paper strips


Presenter

Presentation Notes

Don’t open How many folds? How many sections? Value of each section? Where is additive thinking? Where is multiplicative thinking?

Describe the growth pattern of sections.

# of folds # of sections

0 11 22 43 84 16.n


M1 A8


Presenter

Presentation Notes

-Doubling or twice the previous answer - Two folds is 4 sections or 2 times 2, three folds is 8 sections or 2 x 2 x 2 - # of folds becomes the power to 2. Three folds is 23 ; four folds is 24 n folds is 2n Explain 0 folds

Where in paper folding do you see:

Multiplication?

Division?

Fractions?

Exponents?

In other words,

where do you see multiplicative thinking?


M1 A8


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


Presenter

Presentation Notes

Which standards of mathematical practice did you engage in the previous activity? How could the activity be amended so that additional standards of mathematical practice could be employed?

“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


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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