1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Grade 4 – Module 4

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons. Introduction to mathematical models and instructional strategies to support implementation of A Story of Units.

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Curriculum Overview of A Story of Units

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module Overview Take 8 minutes to read the Narrative, Standards, Lesson Objectives, and Vocabulary. What will you and your students be familiar with? What will you and your students be completely unfamiliar with?

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic A: Lines and Angles 4 lessons to draw and identify lines and angles. New Terms: point, line, segment, ray, angle (right, acute and obtuse), figure, vertex, perpendicular, parallel. Tools: right angle template, straightedge. 4.G.1

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Points, Lines, Segments, Rays and Angles Terms are bolded in the Concept Development at first use and again in the Debrief. Teach each term within a context to provide meaning and not simply its definition. Student work will vary during this and many of the following lessons. Lesson 1, Concept Development

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Right Angle Template Used in many lessons throughout the Module. Made from any piece of paper. Introduced in Lesson 2 to identify and draw right, acute and obtuse angles. Complete the Lesson 2 Problem Set. Lesson 2

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Physiometry Fluency Physical Geometry Reinforces many new terms like acute, right and obtuse angles, lines, segments, rays and more. Develops across lessons as new terms are introduced Introduced in Lesson 2

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Perpendicular Lines Draw perpendicular lines using a straightedge and a right angle template. Lesson 3

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Parallel Lines Draw parallel lines using a straightedge and a right angle template. Lesson 4

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Partner Debrief: Perpendicular and Parallel Lines 1.Choose one letter of the alphabet with parallel and/or perpendicular lines. 2.Have your partner identify the lines as parallel or perpendicular. 3.Label points to use for discussing the lines. 4.Explain why they are classified as parallel or perpendicular. Lesson 3-4

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic B: Angle Measurement 4 lessons to use a protractor to measure and draw angles. New Terms: Tools: protractors of various sizes. 4.MD.5, 4.MD.6

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Angles Lesson 5, Concept Development

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Angle Measure vs. Length Measure Lesson 6 Which angle is larger? A B

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Measure and Draw Angles Using Varied Protractors Complete Problem Sets 6 and 7. Use a variety of protractors. Share! Extend the length of angle segments with a ruler to measure. Lesson 6 and 7 Problem Sets

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic C: Problem Solving with the Addition of Angle Measures 4 lessons to draw and identify lines and angles. New Terms: complementary, supplementary, and vertical angles Tools: pattern blocks. 4.MD.7

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decompose Angles Lesson 9, Concept Development

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Addition of Adjacent Angles and Solving for Unknown Angles Lessons 10 and 11

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Addition of Adjacent Angles and Solving for Unknown Angles Lessons 10 and 11 90 + 120 + x = 360 90 + 120 = 210 360 – 210 = x x = 150

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic D: Two-Dimensional Figures and Symmetry 5 lessons to analyze, classify and draw two-dimensional figures. New Terms: symmetry, triangles (right, isosceles, obtuse, acute, equilateral, scalene),. Tools: right angle template, ruler, grid paper. 4.G.1, 4.G.2, 4.G.3

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lines of Symmetry Fold paper polygons to find lines of symmetry. Identify lines of symmetry in familiar figures. Draw lines of symmetry. Lesson 12, Concept Development

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze Triangles In partners or small groups: Cut out Triangles A-F. Investigate the triangles using rulers and protractors. Record your findings in the Attributes column of the Practice Sheet. Include measures of sides and angles. Sketch each triangle in the first column. Lesson 13, Concept Development

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Classify Triangles Side Length Equilateral Triangles – A Isosceles Triangles – B, E, F Scalene Triangles – C, D Angle Measure Right Triangles – D, E Obtuse Triangles – C, F Acute Triangles – A, B Lesson 13, Concept Development

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Define and Construct Triangles Graph paper and 3 non-collinear points helps to formalize a definition. Complete the Problem Set for Lesson 14. Students combine the 2 types of triangles to draw a specified triangle. Students reason about triangle attributes. Lesson 14, Concept Development

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Classify Quadrilaterals Participant Debrief What makes a square different from a rectangle? Why is it important to define a square as a rectangle with four equal length sides, and not as a quadrilateral with four equal length sides? Can a trapezoid be defined as a square? Can a square be defined as a trapezoid? We classified different quadrilaterals. Try classifying these words: woman, mother, aunt, sister. Or clothes, pants, jeans. Lesson 15, Concept Development

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Biggest Takeaway Turn and Talk: I now know… I can go back to school and… I need to figure out…

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points Points, lines, segments, rays and angles of the first topic support the rest of the module as students construct angles and figures. A degree is not a length measure. Analyzing attributes of figures leads to more formalized definitions. Spend time physically manipulating angles and figures. It will lead to a deeper understanding.