NCCTM October 2014 2014-2015 NCDPI Secondary Mathematics Update Lisa Ashe Secondary Mathematics Consultant NC Department of Public Instruction.
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NCCTM October 2014
2014-2015NCDPI
Secondary Mathematics Update
Lisa AsheSecondary Mathematics ConsultantNC Department of Public Instruction
Goals
• Redesign of the DPI wiki
• New/updated documents
• Our current work
• What’s coming next
• Announcements
Welcome
“Who’s in the Room”
Navigation Changes
Announcements
Educator's Survey
• This fall the NC Department of Public Instruction begins the standards review process for the mathematics standards.
• We will be following our established State Board policy (GCS-F-012) that calls for a standards review of content standards every five years.
• As the NCDPI standards review process progresses, we look forward to gathering information from stakeholders to inform the work of the NCDPI Standards Review Committee. To gather input, NCDPI is administering two surveys this fall—one in October for educators and one in November for the broader community.
• We hope you will take this survey and provide your specific feedback regarding the current mathematics standards. Your feedback will be extremely valuable as we move through this process.
Educator’s Survey
The educators’ survey is now live for teachers and other educators to complete: http://ncdpireview.weebly.com The survey will be available until Friday, Nov. 21, at 5 p.m.
Middle School’s New Look
High School’s New Look
Page Organization
• DPI Specific Information and Resources
• Web Resources
• Descriptions of the resource with links and other information
Standards…
• Standards Documents by grade level (6-8) and course (Math I, II and III)
• Unpacking Documents
• Major Work of the Grade
• Mathematics Progression Documents
• Resources for Standards for Mathematical Practice
Instructional Resources…
• Lessons for Learning (6-8)
• Secondary math progression documents (6-12)
– Expressions, Equations and Functions
– Statistics and Probability Coming Soon
• Resources for NCFE 4th Level Courses
Assessment…
• Links to NCDPI Testing site for EOGs and EOCs
• Testing specifications
• Gridded response instructions and practice
• Web resources for assessment
Parent & Community…
• Communication tools and resources
• NCDPI Announcements Page
• Grade band listserv
–Special announcements
–Monthly updates
–Newsletter
Join Our Listserv1.Send an email to the Listserv to the following address within your email application:
join-msmathdpi@lists.dpi.state.nc.us [MS requests]
join-hsmathdpi@lists.dpi.state.nc.us [HS requests]
2.Leave the subject line and the body of the message blank.
3.Once successfully subscribed, a confirmation email will be sent.
Follow Us!
NC Mathematicswww.facebook.com/NorthCarolinaMathematics
@ncmathematics
http://maccss.ncdpi.wikispaces.net
Standards Review
Our Current Work
The State of the Standards in NC
• Standard Course of Study Development/Revision Process (GCS-F-012)
• A review committee to determine if revisions are needed. Committee will include NC DPI content specialists, teachers, administrators, parents, institutions of higher education, and business/industry
• Committee recommends if revision should take place based on data, research, surveys, and standards review
NC DPI REVIEW – DATA Phase
• Educator Survey
– Your opportunity to give input on as many standards as you can
• Will be analyzed for common themes and compiled
• The work will be analyzed and given to the review committee (yet to be named)
NC DPI REVIEW – DATA Phase
• Focus (work) groups in each region will be giving feedback on progression of standards in grade bands
• K-2, 3-5, 6-8, Math I, II, III
• Critical transition years will be included, for example 2nd to 3rd and 8th to Math I
Professional Development
Our Current Work
• Southern Regional Educational Board (sreb.org) consists of 13 states- 18 total using course
• Course implemented in NC 2014-15. Professional Development for teachers in 7 regions across North Carolina – funded through SREB grant.
• Two upcoming trainings – Raleigh CCRESA and Charlotte-Mecklenburg Schools
• Information will be out soon on registration
SREB Math Ready – Essentials of College Algebra
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Educators Evaluating Quality Instructional Products
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• Built on a collaborative effort of education leaders from Massachusetts, New York and Rhode Island facilitated by Achieve (formerly known as the Tri-State Rubric)
• An initiative designed to identify high-quality materials aligned to the college and career readiness standards.
• Intended to build the capacity of educators to evaluate and improve the quality of instructional materials for use in their classrooms and schools.
• Designed to increase the supply of high-quality lessons and units aligned to the CCSS that are available to elementary, middle and high school teachers as soon as possible.
Overview of the EQuIP rubric:
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The EQuIP Rubric for Mathematics – The 1-Page Version
NCTM Strategic Priorities• Access and Equity
• Advocacy
• Curriculum, Instruction, and Assessment
• Professional Development
• Research
• Technology
Principles to Actions: Ensuring Mathematical Success for All
The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards.
Principles to Actions: Ensuring Mathematical Success for All
The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards.
Guiding Principles for School Mathematics
1. Teaching and Learning
2. Access and Equity
3. Curriculum
4. Tools and Technology
5. Assessment
6. Professionalism
Essential Elementsof Effective Math
Programs
Spring Regional Sessions
• Region 1-March 18
• Region 2-February 12
• Region 3-January 21
• Region 4-March 3
• Region 5-February 25
• Region 6-February 24
• Region 7-March 12
• Region 8-March 11
Announcements
• RFP (Request for Proposals) is being reviewed for posting with Federal monitor
If approved as written, will be similar to:
• Regional Content Academy Framework that serves teachers by grade bands…Focus on mathematics content using conceptual models
• Professional development to prepare teachers to be local teacher leaders who can lead development of local curriculum aligned to Standard Course of Study
Math and Science Partnerships
Nominate An Outstanding Teacher
Website: www.paemst.orgKitty.rutherford@dpi.nc.gov
Let’s DO math!
As you do the tasks, think about how they exemplify Standard for Mathematical Practice #7:
“Look for and Make Use of Structure”
Ticket to Ride
Malia is at an amusement park. She bought 14 tickets, and each ride requires 2 tickets.
a.Write an expression that gives the number of tickets Malia has left in terms of x, the number of rides she has already gone on. Find at least one other expression that is equivalent to it.
b.14 – 2x represents the number of tickets Malia has left after she has gone on x rides. How can each of the following numbers and expressions be interpreted in terms of tickets and rides?
14
–2
2x
http://www.illustrativemathematics.org/illustrations/1450
Ticket to Ride, cont’d
c. 2(7 − x) also represents the number of tickets Malia has left after she has gone on x rides. How can each of the following numbers and expressions be interpreted in terms of tickets and rides?
7
(7 – x)
2
http://www.illustrativemathematics.org/illustrations/1450
Profit of a company
The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If p is the price of the item, then three equivalent forms for the profit are:
Standard form: −2p2 + 24p − 54
Factored form: −2(p − 3)(p − 9)
Vertex form: −2(p − 6)2 + 18.
Which form is most useful for finding
•The prices that give a profit of zero dollars?
•The profit when the price is zero?
•The price that gives the maximum profit?
http://www.illustrativemathematics.org/illustrations/434
Look for and make use of structure
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x- y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
Look for and make use of structure
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x- y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
Where else can we find information about Look for and Make Use of Structure?
Interpret the structure of expressions
A-SSE.1 Interpret expressions that represent a quantity in terms of its context.★
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
Write expressions in equivalent forms to solve problems
A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
A-SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.★
Seeing Structure in Expressions
Interpret the structure of expressions
A-SSE.1 Interpret expressions that represent a quantity in terms of its context.★
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
Seeing Structure in Expressions
Interpret the structure of expressions
A-SSE.1 Interpret expressions that represent a quantity in terms of its context.★
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
Is Seeing Structure only in HS?
8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
What questions do you have?
Contact Us….
Lisa AsheSecondary Mathematics ConsultantNorth Carolina Department of Public
Instruction919-807-3909
lisa.ashe@dpi.nc.gov
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