A Story of Units

1. A Story of Units Grade 4 – Module 4

2. 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. Agenda Introduction to the Module Concept Development Module Review

4. Curriculum Overview of A Story of Units

5. 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. Agenda Introduction to the Module Concept Development Module Review

7. Topic A: Lines and Angles 4.G.1 • 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.

8. Points, Lines, Segments, Rays and Angles Lesson 1, Concept Development • 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.

9. Right Angle Template Lesson 2 • 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.

10. Physiometry Fluency Introduced in Lesson 2 • 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

11. Perpendicular Lines Lesson 3 • Draw perpendicular lines using a straightedge and a right angle template.

12. Parallel Lines Lesson 4 • Draw parallel lines using a straightedge and a right angle template.

13. Partner Debrief: Perpendicular and Parallel Lines Lesson 3-4 Choose one letter of the alphabet with parallel and/or perpendicular lines. Have your partner identify the lines as parallel or perpendicular. Label points to use for discussing the lines. Explain why they are classified as parallel or perpendicular.

14. Topic B: Angle Measurement 4.MD.5, 4.MD.6 • 4 lessons to use a protractor to measure and draw angles. • New Terms: • Tools: protractors of various sizes.

15. Angles Lesson 5, Concept Development

16. Angle Measure vs. Length Measure Which angle is larger? B A Lesson 6

17. Measure and Draw Angles Using Varied Protractors Lesson 6 and 7 Problem Sets • Complete Problem Sets 6 and 7. • Use a variety of protractors. Share! • Extend the length of angle segments with a ruler to measure.

18. Topic C: Problem Solving with the Addition of Angle Measures 4.MD.7 • 4 lessons to draw and identify lines and angles. • New Terms: complementary, supplementary, and vertical angles • Tools: pattern blocks.

19. Decompose Angles Lesson 9, Concept Development

20. Addition of Adjacent Angles and Solving for Unknown Angles Lessons 10 and 11

21. Addition of Adjacent Angles and Solving for Unknown Angles 90 + 120 + x = 360 90 + 120 = 210 360 – 210 = x x = 150 Lessons 10 and 11

22. Topic D: Two-Dimensional Figures and Symmetry 4.G.1, 4.G.2, 4.G.3 • 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.

23. Lines of Symmetry Lesson 12, Concept Development • Fold paper polygons to find lines of symmetry. • Identify lines of symmetry in familiar figures. • Draw lines of symmetry.

24. Analyze Triangles Lesson 13, Concept Development • 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.

25. Classify Triangles Lesson 13, Concept Development • 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

26. Define and Construct Triangles Lesson 14, Concept Development • 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.

27. Classify Quadrilaterals Lesson 15, Concept Development • 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.

28. Agenda Introduction to the Module Concept Development Module Review

29. Biggest Takeaway • Turn and Talk: • I now know… • I can go back to school and… • I need to figure out…

30. 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.