Presentation is loading. Please wait.

Presentation is loading. Please wait.

Stones of the Standards

Published byJesse Chandler Modified over 5 years ago

Similar presentations

Presentation on theme: "Stones of the Standards"— Presentation transcript:

1 The Language and Structure of the Common Core State Standards for Mathematics

2 Stones of the Standards
or, Geology of the CCSS Or, Stones of the Standards Oops… I’m in an effluvial delta!

3 Monolithic structures from a distance
Lots of words to describe what in the end are rocks A lot of work to scale Close up, individual pieces are visible, one distinct from the other Hard to push up against a big rock to get it to move… but you can work with smaller, individual rocks. But if you just focus on the smaller individual rocks, you miss the big picture. Eventually time, erosion and a lot of liquid will change the way it looks

4 “The Standards” Not what we teach Not the curriculum
We teach mathematics The standards are the goals Tweet about it using hashtag #ccssm Not the things we do day by day … although some administrators perceive it that way The standards are discrete but also critical parts of a whole Different places for different people… if you’re already a pro, if you’re already comfortable, examine how you would explain it well to others (critique me… tweet about it…) each one of us becomes the expert Tweet about it #ccssm And now… the Standards

5 The Common Core State Standards for Mathematics
Oh wait… too far away. It still looks monolithic

6 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra The Standards… from somewhat far away Ribbons of rocks running through the students’ academic careers River of magma? Multiple streams feeding through to the large river of high school mathematics Conflict : triburaries (roads not followed) Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

7 Conceptual Categories
These categories reach back to the beginning of the students’ academic careers … Okay… this is a really high-school perspective Drilling in to the structure

8 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

9 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Counting and Cardinality (K) Know number names and the count sequence Count to tell the number of objects Compare numbers Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra How MONUMENTAL counting is It’s the atomic structure of every other rock. throughout the rest of the monolith, right? Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

10 The Common Core State Standards in Mathematics
K Modeling Number and Operations in Base Ten (K – 5) Place value understanding Develop base-ten algorithms using place value and properties of operations Computation competencies (fluency, estimation) Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Bedrock of mathematics To really understand things, have to move back and forth (increase professionalism) Notice how the strict dependencies light up.. Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

11 The Common Core State Standards in Mathematics
K Modeling Operations and Algebraic Thinking (K-5) Concrete uses and meanings of the basic operations (word problems) Mathematical meaning and formal properties of the basic operations Prepare for later work with expressions and equations in middle school Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

12 The Common Core State Standards in Mathematics
K Modeling Number and Operations Fractions (3 – 5) Enlarge concept of number beyond whole numbers, to include fractions Use understanding of the four operations to extend arithmetic to fractions Solve word problems related to the equation ax = b (a and b fractions) Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Understanding fractions Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

13 The Common Core State Standards in Mathematics
K Modeling The Number System (6 – 8) Build concepts of positive and negative numbers Work with the rational numbers as a system governed by properties of operations Begin work with irrational numbers Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra How numbers work Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

14 The Common Core State Standards in Mathematics
K Expressions and Equations (6 – 8) Treat expressions as objects to reason about (not as instructions to compute an answer) Transform expressions using properties of operations Solve linear equations Use variables and equations as techniques to solve word problems Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

15 The Common Core State Standards in Mathematics
K Modeling Algebra (9 - 12) Seeing Structure in Expressions Arithmetic with Polynomials & Rational Expressions Creating Equations Reasoning with Equations and Inequalities Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

16 The Common Core State Standards in Mathematics
K Modeling Number and Quantity (9 – 12) The Real Number System Quantities The Complex Number System Vector and Matrix Quantities Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra And how the same streams lead in to Number and Quantity in Highschool Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

17 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Geometry (K – 8) Ascend through progressively higher levels of logical reasoning about shapes Reason spatially with shapes, leading to logical reasoning about transformations Connect geometry to number, operations, and measurement via notion of partitioning Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

18 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Geometry (9 – 12) Congruence Similarity, Right Triangles, and Trigonometry Circles Expressing Geometric Properties with Equations Geometric Measurement and Dimension Modeling with Geometry Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

19 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Ratios and Proportional Relationships (6 – 8) Extend work on multiplication and division; consolidate multiplicative reasoning Lay groundwork for linear functions in Grade 8 by studying quantities that vary together Solve a wide variety of problems with ratios, rates, percents Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

20 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Functions (8) Extend and formalize understanding of quantitative relationships from Grades 3-7 Lay groundwork for more extensive work with functions in High School Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

21 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Functions (9 – 12) Interpreting Functions Building Functions Linear Quadratic and Exponential Models Trigonometric Functions Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

22 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Measurement and Data (K – 5) Emphasize the common nature of all measurement as iterating by a unit Build understanding of linear spacing of numbers and support learning of the number line Develop geometric measures Work with data to prepare for Statistics and Probability in middle school Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

23 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Statistics and Probability (6 – 8) Introduce concepts of central tendency, variability, and distribution Connect randomness with statistical inference Lay foundations for High School Statistics and Probability Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

24 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Statistics and Probability (9 - 12) Interpreting Categorical and Quantitative Data Making Inferences and Justifying Conclusions Conditional Probability and the Rules of Probability Using Probability to Make Decisions Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

25 The Common Core State Standards in Mathematics
K Modeling Modeling (9 – 12) Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

26 The Common Core State Standards in Mathematics
K Modeling Statistics and Probability Measurement and Data Statistics and Probability Functions Ratios and Proportional Relationships F Number and Operations Fractions CC Number and Quantity The Number System Number and Operations in Base Ten Algebra Operations and Algebraic Thinking Expressions and Equations Geometry Geometry

27 The Common Core State Standards in Mathematics
Turn/flip to page 5 No copy? Required image is on next slide so don’t panic!

28 Vocabulary (pg. 5) Within each conceptual category are domains, clusters, and standards. This is a snapshot taken from the CCSS-M to define the structure and notation used. From the NCTM PowerPoint presentation, domains are the “Overarching ‘big ideas’ that connect topics across grades.” (NCTM PowerPoint presentation, Slide 17) Clusters “may appear in multiple grade levels” with increasing difficulty and reflect what students should know and be able to do. (NCTM PowerPoint presentation, Slide 18) The standards give more specific skills and concepts related to the cluster. Use this diagram to introduce the notation of domain, cluster, and standards.

29 F.BF-1a What does this notation mean?
Where is it? (Hint: It’s in the standards somewhere!) What does it mean? And, when you get there... hey, what's up with the star? Periods versus Dashes blah blah CTRL F Get them to find it in the CCSS document. What does it mean (in terms of coding) and what does it mean, 2nd time, in terms of mathematics Answer will appear after CLICK

30 4.MD-3 What does this notation mean? Where is it? What does it mean?
Need to look back and forth to situate the meaning. How much, how deep?

31 Will this be on the test? Yes but you’ll have plenty of practice

Download ppt "Stones of the Standards"

Similar presentations

Professional Development Module Common Core Math Shift: Focus Grade 6.

Professional Development Module Common Core Math Shift: Focus Grade 6.
Common Core State Standards for Mathematics: Coherence Grade 7 Overview.

Common Core State Standards for Mathematics: Coherence Grade 7 Overview.
Common Core State Standards for Mathematics: Coherence

Common Core State Standards for Mathematics: Coherence
Common Core State Standards for Mathematics: Coherence Grade 8 Overview.

Common Core State Standards for Mathematics: Coherence Grade 8 Overview.
Kindergarten Instructional Shifts-Focus. Why Common Core? Initiated by the National Governors Association (NGA) and Council of Chief State School Officers.

Kindergarten Instructional Shifts-Focus. Why Common Core? Initiated by the National Governors Association (NGA) and Council of Chief State School Officers.
K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics © Copyright 2011 Institute for Mathematics and Education Welcome to a clickable.

K The Common Core State Standards in Mathematics © Copyright 2011 Institute for Mathematics and Education Welcome to a clickable.
Mathematics Grade Level Considerations for High School.

Mathematics Grade Level Considerations for High School.
Transition to CCSS Math What it means and what are the expectations for learning? Middle School Parent Meeting March 26, 2014.

Transition to CCSS Math What it means and what are the expectations for learning? Middle School Parent Meeting March 26, 2014.
Common Core State Standards

Common Core State Standards
December 14, 2010 Proportionality Through Similarity and Geometry.

December 14, 2010 Proportionality Through Similarity and Geometry.
History & Vision.  The new standards are rigorous, research- based, and designed to prepare every student for success in college and the workforce. 

History & Vision.  The new standards are rigorous, research- based, and designed to prepare every student for success in college and the workforce. 
©2001 CBMS Math Preparation of Teachers Teachers need to study the mathematics of a cluster of grade levels, both to be ready for the various ways in which.

©2001 CBMS Math Preparation of Teachers Teachers need to study the mathematics of a cluster of grade levels, both to be ready for the various ways in which.
Unit 1 Focusing on the Major Work of the Levels Produced under U.S. Department of Education Contract No. ED-VAE-13-C-0066, with StandardsWork, Inc. and.

Unit 1 Focusing on the Major Work of the Levels Produced under U.S. Department of Education Contract No. ED-VAE-13-C-0066, with StandardsWork, Inc. and.
Number and Operations Standard Instructional programs from prekindergarten through grade 12 should enable all students to— Understand numbers Understand.

Number and Operations Standard Instructional programs from prekindergarten through grade 12 should enable all students to— Understand numbers Understand.
College and Career Readiness Mathematics at Middle School Poway Unified School District 2014.

College and Career Readiness Mathematics at Middle School Poway Unified School District 2014.
2010 New Math Standards. Mathematical Practices 1. Attend to precision 2. Construct viable arguments and critique the reasoning of others 3. Make sense.

2010 New Math Standards. Mathematical Practices 1. Attend to precision 2. Construct viable arguments and critique the reasoning of others 3. Make sense.
BUILDING LEARNING PROGRESSIONS WITH THE COMMON CORE By Marcia Torgrude.

BUILDING LEARNING PROGRESSIONS WITH THE COMMON CORE By Marcia Torgrude.
Module 1: A Closer Look at the Common Core State Standards for Mathematics High School Session 2: Matching Clusters of Standards to Critical Areas in one.

Module 1: A Closer Look at the Common Core State Standards for Mathematics High School Session 2: Matching Clusters of Standards to Critical Areas in one.
Common Core State Standards The Wisconsin State Standards.

Common Core State Standards The Wisconsin State Standards.
Numbers and Quantity Extend the Real Numbers to include work with rational exponents and study of the properties of rational and irrational numbers Use.

Numbers and Quantity Extend the Real Numbers to include work with rational exponents and study of the properties of rational and irrational numbers Use.

Similar presentations

Ads by Google