Math Pathways for Instruction Aligned with the Common Core

State StandardsLCHS 7/8 MATH NIGHT

APRIL 15, 2014

AgendaInformational Power Point

7th Grade Teachers Mr. Kim & Mr. Savage7th Grade Student Daniel Landesman

8th Grade Teachers Mrs. Dornian & Mrs. Wright8th Grade Student Jeremy Herron

Q & A  

Traditional vs. Integrated ApproachTraditional

• Uses a horizontal model with first-year algebra, geometry and second-year algebra taught in a linear fashion.

• Lesson begins with the presentation of a math concept and ends with students attempt to apply the concept.

• Students apply the model given to solve the problem.

• Teacher provides direct instruction and is primarily a lecturer.

• Traditional assessments tools are used (formal tests, quizzes, etc.).

Integrated

• Uses a vertical model that interweaves the three.

• Lesson begins with context-based problem and concepts emerge as students attempt to solve the problem.

• Students analyze data and make and test conjectures about math models.

• Teacher is a facilitator who uses probing questions to stimulate students and interact with them.

• Uses a small group cooperative learning model.

• Technology is used regularly to enhance instruction

• A variety of assessment tools are used (written journals, extended group projects, etc.).

Courses in higher level mathematics: Precalculus, Calculus, Advanced Statistics, Discrete Mathematics,

Advanced Quantitative Reasoning, etc.

Standards for Mathematical Practice

The Eight Standards for Mathematical Practice place an emphasis on student demonstrations of learning that describe the thinking processes, habits of mind, and dispositions that students need to develop.

adapted from Briars & Mitchell (2010)Getting Started with the Common Core State Standards

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them…start by explaining the meaning of a problem and looking for entry points to its solution

2. Reason abstractly and quantitatively…make sense of quantities and their relationships to problem situations

3. Construct viable arguments and critique the reasoning of others…understand and use stated assumptions, definitions, and previously established results in constructing arguments

4. Model with mathematics…can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace

2011 © CA County Superintendents Educational Services Association

Standards for Mathematical Practice

5. Use appropriate tools strategically…consider the available tools when solving a mathematical problem

6. Attend to precision…communicate precisely using clear definitions and calculate accurately and efficiently

7. Look for and make use of structure…look closely to discern a pattern or structure

8. Look for and express regularity in repeated reasoning…notice if calculations are repeated, and look for both general methods and for shortcuts

2011 © CA County Superintendents Educational Services Association

The Key to Drive Successful Implementation

TeacherProfessional

Development andOn-Going Support

Teacher Development Group-TDG

• Best practice seminars (4 days) focused on Habits of Mind and Habits of Interaction

• 4 Studio Cycles to plan a lesson, observe it in action and analyze instruction

• Resident Coaching (Individualized support) for teachers

• Ongoing on line support and communication with consultant and colleagues

• Leadership coaching for administration

Habits of Mind• Generalize• Justify Why• Make Sense• Mathematical Representations• Metacognition Reflection• Regularity, Patterns, Structure• Connections• Mistakes & Stuck Points• Persevere & Seek More

Habit of Interaction• Listen to Understand• Genuine Questions• Private Reasoning Time• Explore Multiple Pathways• Compare our Logic & Ideas• Critique & Debate• Math Reasoning is the Authority• Explain my Reasoning

Next steps

• Continued professional development to support implementation of CCSS

• Strategic planning and alignment of master schedule with teacher expertise to maximize student learning

• Designing Common Core aligned instructional pacing guides, unit and lesson plans and assessments

• Rewriting course outlines to reflect the implementation of CCSS in our curriculum and submission for UC/CSU approval

Current 7/8 Math Offerings and Percent of Students Currently Enrolled

* It is anticipated that the number of 7th grade studentsenrolled in Algebra 1 will drop significantly from its currentlevel since there are now two courses instead of onebetween 6th grade CC math and Algebra 1 CC.

2014-15 7th Grade Math Offerings

1. 7th grade Common Core2. 7th grade Advanced (CC + First ½ of 8th grade

Common Core)3. Algebra 1 (Second ½ of 8th grade Common Core and

Algebra 1)• Students will be placed in options 1 or 2 based upon

6th grade teacher recommendation (current practice)• Students will be placed in option 3 only if they pass

the created Algebra 1 entrance test showing mastery of 7th grade CC AND 8th grade CC standards

2014-15 8th Grade Math Offerings

1. 8th grade CC2. 8th grade Advanced/Algebra 1 (Second half of 8th

grade CC + Algebra 1 CC)3. Geometry CC or Honors Geometry• Students will be placed in options 1 or 2 based

upon the 7th grade teacher’s recommendation• Students will be placed in option 3 only if they

successfully passed Algebra 1 CC as a 7th grade student

2014-15 Incoming 9th Grade Math Offerings

Incoming 2014 9th grade students (current 8th grade students) will have the following offerings:

1.Algebra 1 CC (after completing 8th grade CC)2.Geometry CC (after completing Algebra 1 CC)3.Algebra 2 CC (after completing Geometry CC or Honors Geometry)

Population Estimation with the “Capture-Recapture” Method

“Capture-Recapture” is a method commonly used to estimate an animal population’s  size. The method is most useful when it is not practical to count all the animals in the population.

Students did the following: Captured and tagged some beans. Set them free after being tagged.

Recaptured a set of beans. Counted how many of those were tagged.

Used the ratio of tagged beans in the set to generate a proportion.

Used the proportion to estimate the total population of beans.

( )

Number of beans marked in a sample Total number of beans marked

Total number of beans in a sample x Total population of beans