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Geometry K-6

Geometry K-6. Elko County School District CCSS Math Professional Development Module 3, Week 2 Digging into the CCSS, part 1. Video: Beauty is Number in Nature: The Geometry of Beauty Discovery Education.

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Geometry K-6

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  1. Geometry K-6 Elko County School District CCSS Math Professional Development Module 3, Week 2 Digging into the CCSS, part 1

  2. Video:Beauty is Number in Nature: The Geometry of BeautyDiscovery Education Science has found that the elegance of mathematics often underlies the beauty of nature. Mathematics can be used to explain the shape of the world around us, particularly geometry.

  3. Step 1: Target a Standard Domain: Geometry, K-6 “Like core knowledge of number, core geometrical knowledge appears to be a universal capability of the human mind. Geometric and spatial thinking are important in and of themselves, because they connect mathematics with the physical world, and play an important role in modeling phenomena whose origins are not necessarily physical…” -The Common Core Standards Writing Team Teacher Task: Read through your grade level standards.

  4. Today’s Agenda We will… • Target a mathematics domain. • Chunk the main categories within the standard. • Identify the developmental progression of the standards. • Identify the standard components in Operations and Algebraic Thinking (K-5) and Expressions and Equations (Grade 6) • Use the Progressions Document to understand how domains are connected across grade levels.

  5. Unpacking and Repacking “To increase student achievement by ensuring educators understand specifically what the new standards mean a student must know, understand and be able to do. (Unpacking) may also be used to facilitate discussion among teachers and curriculum staff and to encourage coherence…(Unpacking), along with on-going professional development is one of many resources used to understand and teach the CCSS.” -North Carolina Dept of Public Instruction Week 2 Step 1: Target a standard Step 2: Chunk the Main Categories Step 3: Identify all standard components Step 4: Identify the Developmental Progression Week 3 Step 5: Identify Key Vocabulary Step 6: Add Clarifying Information Critical Areas of Focus

  6. 2.G.3 Partition circles and rectangles into two, three, or four equal shares Describe Recognize Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Recognize that equal shares of identical wholes need not have the same shape 2.G.3 Partition Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Fourths Fourth of Identical whole Builds on 1.G.3 Thirds Third of Needed for 3.G.2 whole partition rectangle Halves Half of Partition a shape into fourths in different ways Pattern Blocks Fraction Bars/Circles 2/2 = one whole Equal shares circle

  7. Why are we Unpacking Standards? • To understand what the standards are asking students to know, understand, and be able to do • To make time for professional discussion about the standards • To build upon and use common terminology when discussing the implementation of the standards Unpacking is standards is not a substitute document for the Common Core Standards, it is a record of the conversation of those who are involved in the process of digging into the standards.

  8. Step 2: Chunk the Main Categories • All Standard(s) in the cluster(s) • Identify Key Verbs Example 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. 2.G.3 Partition circles and rectangles into two, three, or four equal shares Describe Recognize Partition

  9. Step 3: Identify all standard components blue Components from CCSS: • Analyze nouns and verbs What do students need to do? • Include bullets, examples, footnotes, etc. • Take standard apart according to the verb to separate skills within the standard What do the students need to know?

  10. Step 4: Identify the Developmental Progression How would you utilize these chunks (blue) for scaffolding toward mastery of the entire standard? • Where would you start when teaching this standard? • What is the chunk that demonstrates the highest level of thinking? Rearrange/Sequence the standard components.

  11. Example 2.G.3 Partition circles and rectangles into two, three, or four equal shares Partition Describe Recognize Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Recognize that equal shares of identical wholes need not have the same shape 2.G.3

  12. Progressions Document The Progressions Document is a narrative description about how a particular domain plays out across the grade levels. (McCallum 2011) Read: • Scan to find your grade level within the Progressions Document. • Read and code the text. • If time permits, read the grades above and below your own grade level. ? = Question I have ! = Ah Ha

  13. “They(Geometric and spatial thinking) are also important because they support the development of number and arithmetic concepts and skills. Thus, geometry is essential for all grade levels for many reasons: its mathematical content, its roles in physical sciences, engineering, and many other subjects, and its strong aesthetic connections.” -The Common Core Standards Writing Team

  14. Vertical Alignment Using the progression document(s) from Ohio Department of Education and CCSS Writing Team: • Look to the grade level(s) below to see if the standard is introduced. • Look to the grade level(s) above to see if the standard is continued. Code each standard on the poster with: • builds on • introduced • needed for • or mastered and the grade level to which the standard aligns.

  15. 2.G.3 Partition circles and rectangles into two, three, or four equal shares Partition Describe Recognize Recognize that equal shares of identical wholes need not have the same shape 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Builds on 1.G.3 Introduced? Mastered? Needed for? Builds on? Needed for 3.G.2

  16. Wrap Up: Reflection • How did today’s training impact your understanding of these standards? • No impact • Some impact • Significant impact • What ah-ha’s did you have today? • What questions do you still have about this domain?

  17. Reference Burke, Kay. 2010 Balanced Assessment: From Formative to Summative. Solution Tree Press. Bloomington, IN. The Common Core Standards Writing Team. May 2011. Progressions for the Common Core State Standards in Mathematics (draft): K, Counting and Cardinality; K-5, Operations and Algebraic Thinking. Available Online: commoncoretools.wordpress.com Ohio Department of Education. February 2012. K-8 Standards Progression. Available Online: education.ohio.gov

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