6-12 mathematics 1 © ccsesa, california, 2011. all rights reserved mathematics teacher overview

6-12 Mathematics

1© CCSESA, California, 2011. All rights reserved • Mathematics Teacher Overview

General Overview

◦ Focus and Coherence

◦ Mathematical Proficiency

ObjectivesObjectives

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Structure

◦ Organization

◦ Progression of Standards

◦ Grade 8 Options

Similarities Grade Shifts Next Steps

© CCSESA, California, 2011. All rights reserved • Mathematics Teacher Overview

Topics and performances are logical over time

Based on research about how students learn math over time

Reflect hierarchical nature of the content

Evolve from particulars to deeper structures


Define what students should understand and be able to do in their study of mathematics

◦ Understanding and procedural skill are equally important and can be assessed using tasks of sufficient richness

◦ Students will be expected to justify, appropriate to their math maturity

Are internationally benchmarked

◦ Reflect rigor, focus and coherence of standards in top-performing countries


Do:

◦Set grade-level standards K-8

◦Identify standards for 8th Grade Algebra 1

◦Provide conceptual cluster standards in high school

◦Provide clear signposts along the way toward the goal of college and career readiness for all students


Do provide common assessments

Grades 3-8 and 11

Online assessment using “smart” technology

Rapid reporting system to inform instruction

Teachers involved in development and scoring

Variety of item types Selected response Short and extended constructed response Technology enhanced Performance tasks

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Do not:

◦Define intervention methods or materials

◦Define the full range of supports for English learners, students with special needs and students who are well above or below grade level expectations

◦Dictate curriculum or teaching methods


Think about what you have learned so far.

What questions or comments come to mind?

Discuss with your table group.


Mathematical Practices- Recurring throughout the grades

Mathematical Content- Different at each grade level


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 mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in

repeated reasoning11

© CCSESA, California, 2011. All rights reserved • Mathematics Teacher Overview

Read your assigned Standard for Mathematical Practice

Highlight key words or phrases in your standard to share with the whole group.

With a partner, discuss:◦ Your “Aha’s”◦ A standard that you feel might be a challenge to

implement, and why


Reading the Grade Level Reading the Grade Level OverviewOverview

Domain

Cluster

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Reading the Grade Level Reading the Grade Level StandardsStandards


Domain

Cluster

Standards

California’s Additional 15%

Intended to:◦Include current California standards not in

the Common Core Standards◦Enhance the Common Core Standards◦Maintain alignment with California’s

current standards Created three courses specific to CA:

◦8th Grade Algebra 1◦Calculus◦AP Probability and Statistics

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Two sets of standards for grade 8 that will prepare students for college and career◦ Standards for Algebra 1, taken from 8th grade

Common Core, high school content clusters and CA Algebra 1standards

◦ 8th grade Common Core

Goal of grade 8 Common Core is to finalize preparation for students in high school

K-7 standards as augmented prepare students for either set of standards


Arranged by conceptual cluster (NOT by course):

•Number and Quantity

•Algebra

•Functions

• Modeling

• Geometry

• Statistics and Probability

Same K-8 structure of domain, cluster and standard

17© 2011 California County Superintendents Educational Services Association • Mathematics Teacher Overview

Specify the math that all students should study to be college and career ready

Identify additional math standards that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics. These are indicated by (+).

Development of suggested course pathways will be done by CDE as part of their long-range implementation plan

◦Traditional vs. Integrated


Modeling Standard

High School Example-Geometry Content Cluster


(+)Standard

Locate your grade level or course in your standards handout.

Choose one domain and one cluster of standards to review.

Pay attention to the language, content, and structure of the standards.

Share your reactions with a partner.



K 1 2 3 4 5 6 7 8 HS

Counting & Cardinality

Number and Operations in Base TenRatios and Proportional

RelationshipsNumber & Quantity

Number and Operations – Fractions

The Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and ProbabilityStatistics & Probability

Domains and Conceptual Domains and Conceptual Categories K-12Categories K-12

Choose a domain or conceptual category that covers at least two grade levels, including your own.

Read the standards in each domain or conceptual category.

What connections do you notice? Share with a partner.


6.EE.96.EE.9“…Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity…in terms of the other… Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.…”

Develop Conceptual Develop Conceptual Understanding Across Grade Understanding Across Grade LevelsLevels

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7.RP.2b7.RP.2b

“Identify the constant of proportionality (unit rate) in tables, graphs, …”

7.RP.2c7.RP.2c“Represent proportional relationships by equations.”

7.RP.2d7.RP.2d“Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points(0, 0) and (1, r) where r is the unit rate.”


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How do the skills and concepts involved in completing this task relate to the two previous tasks?

8.F.48.F.4 “Construct a function to model a linear relationship

between two quantities…Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values…Interpret the rate of change and initial value … in terms of the situation it models...”


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Connecting Standards for Math Practice with Standards for Content Balanced combination of procedure and

understanding

Build in complexity and provide more clarity for expected performance

“Understand” expectations connect practice to content

◦ Lack of understanding prevents students from engaging in the mathematical practices

◦ Weighted toward important concepts that most merit the time, resources, and focus


Grade California Standard Common Core

Sixth Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations ( a/b, a to b, a:b ).

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Seventh Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three is less than a number, half as large as area A).

Use variables to represent quantities in real-world and mathematical problems and construct simple equations and inequalities to solve problems about the quantities.


Grade/Course

California Standard Common Core

Seventh Construct and read drawings and models made to scale.

Solve problems involving scale drawings of geometric figures, including actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Algebra Algebra 1:

Solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

Algebra Content Cluster:

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Geometry

Geometry:

Use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.

Geometry Content Cluster:

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.


Grade Shifts: ExamplesGrade Shifts: Examples

Developed by SCFIRD

Concept 1997 Standards CCCS

Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle)

Grade2

K

Introduction to ProbabilityGrade

3Grade

7

Introduction of fractions as numbers

Grade2

Grade3

Add and subtract simple fractions

Grade3

Grade4

Introduction of integers Grade 4

Grade6


Continue to implement current CA standards, as there are more similarities than differences in the standards.

Emphasize developing student conceptual understanding.

Implement our current Math Reasoning Standards as this will support the Standards for Mathematical Practice.

Collaborate with colleagues for Common Core implementation.


6-12 mathematics 1 © ccsesa, california, 2011. all rights reserved mathematics teacher overview

Documents

gradelevel standards

grade level standards

grade algebra

coherence of standards

conceptual cluster standards

assigned standard

ahasa standard

reasoning of othersmodel