A Story of Units

1. A Story of Units Grade 2 – Module 8

2. Session Objectives • Examine the development of mathematical understanding across the module using a focus on Concept Development within the lessons. • Introduce mathematical models and instructional strategies to support implementation of A Story of Units. • Consider scaffolding to provide multiple entry points for students at all levels.

3. A Story of UnitsScaffolding Mathematics Instruction Key Points • Amplify Language • Move from Concrete to Representation to Abstract • Give Specific Guidelines for Speaking, Reading, Writing, or Listening

4. Amplify Language • Give clear mathematical definitions • Explain multiple meanings • Maintain consistency and point out interchangeable terminology

5. Move from Concrete to Representation to Abstract • Use familiar contexts • Visually organize thinking • Provide multiple representations

6. Give Guidelines for Speaking, Reading, Writing, or Listening • Provide structured opportunities to speak and write in English • Give explicit instructions in student-friendly language • Use visuals or examples in giving instructions.

7. Key Points • Amplify Language • Move from Concrete to Representation to Abstract • Give Guidelines for Speaking, Reading, Writing, or Listening

8. Agenda Introduction to the Module Concept Development Module Review

9. Curriculum Overview of A Story of Units

10. Module Overview • Read the narrative. • *key concepts • models and tools • Important vocabulary • How do composition and decomposition relate to time, shapes, and fractions?

11. Agenda Introduction to the Module Concept Development Module Review

12. Topic A • Attributes of Geometric Shapes • Why is the use of exemplars and variants important to students as they develop concepts about shapes?

13. Lesson 1 Application Problem Lesson Objective: Describe two-dimensional shapes based on attributes. Terrence is making shapes with 12 toothpicks. Draw 3 different shapes he could make using all of the toothpicks. How many other combinations can you find?

14. Lesson 1 Lesson Objective: Describe two-dimensional shapes based on attributes.

15. Lesson 1 Problem Set Lesson 1, Student Debrief • Tell your partner why you need to pay attention to more than how a shape looks when grouping shapes.

16. Turn and Talk • How does this task align with the Universal Design for Learning (UDL) in providing multiple options for: • Representation: the “what of learning” • Action/Expression: the “how” of learning • Engagement: the “why” of learning

17. Lesson 2 Application Problem Lesson Objective: Build, identify, and analyze two-dimensional shapes with specified attributes. How many triangles can you find?

18. Lessons 2 Lesson Objective: Build, identify, and analyze two-dimensional shapes with specified attributes.

19. Lesson 3 Lesson Objective: Use attributes to draw different polygons including triangles, quadrilaterals, pentagons, and hexagons.

20. Lesson 4 Lesson Objective: Use attributes to identify and draw different quadrilaterals including rectangles, rhombuses, parallelograms, and trapezoids.

21. Lesson 5 Lesson Objective: Relate the square to the cube, and describe the cube based on attributes.

22. Topic B • Composite Shapes and Fraction Concepts • What are composite shapes and how can they help students develop fraction concepts?

23. Topic B 3-5 Number and Operations – Fractions Progression Composite Shapes and Fraction Concepts The meaning of fractions In Grades 1 and 2, students use fraction language to describe partitions of shapes into equal shares.2.G.3 In Grade 3 they start to develop the idea of a fraction more formally, building on the idea of partitioning a whole into equal parts.

24. Lesson 6 Lesson Objective: Combine shapes to create a composite shape; create a new shape from composite shapes.

25. Lesson 7 Lesson Objective: Interpret equal shares in composite shapes as halves, thirds, and fourths.

26. Lesson 8 Lesson Objective: Interpret equal shares in composite shapes as halves, thirds, and fourths.

27. Lesson 8 Problem Set Lesson 8, Student Debrief How did knowing the attributes of each shape help you solve the problems?

28. Topic C • Halves, Thirds, and Fourths of Circles and Rectangles • How will students apply their spatial structuring from Module 6 to understand that equal shares of an identical whole do not have to be the same shape?

29. Lessons 9 Lesson Objective: Partition circles and rectangles into equal parts, and describe those parts as halves, thirds, or fourths.

30. Lesson 10 Lesson Objective: Partition circles and rectangles into equal parts, and describe those parts as halves, thirds, or fourths.

31. Lesson 11 Lesson Objective: Describe a whole by the number of equal parts including 2 halves, 3 thirds, and 4 fourths.

32. Lesson 11 Problem Set Lesson 11, Student Debrief Sangeeta says that 2 halves cannot equal 3 thirds. Explain why you agree or disagree.

33. Lesson 12 Lesson Objective: Recognize that equal parts of an identical rectangle can have different shapes.

34. Lesson 12 Problem Set Lesson 12, Student Debrief If you split two rectangles in half, will the halves always be the same shape? What must the rectangles have in common first?

35. Topic D • Application of Fractions to Tell Time • How does the work of Topic C prepare students to tell time in Topic D?

36. Turn and Talk • What difficulties would you anticipate with student understanding of the mathematics in this section? • What scaffolds would be effective for addressing those difficulties?

37. Lesson 13 Lesson Objective: Construct a paper clock by partitioning a circle into halves and quarters, and tell time to the half hour or quarter hour.

38. Lesson 14 Lesson Objective: Tell time to the nearest five minutes.

39. Lesson 15 Lesson Objective: Tell time to the nearest five minutes; relate a.m. and p.m. to time of day.

40. Lesson 16 Lesson Objective: Solve elapsed time problems involving whole hours and a half hour. How much time has passed?

41. Mid-Module Assessment Complete the mid-module assessment. Match each assessment question to the lesson where the content was taught.

42. Agenda Introduction to the Module Concept Development Module Review

43. Reflection • Turn and Talk: • How do composition and decomposition relate to time, shapes, and fractions? • What is the importance of sequencing fractions prior to time? • What units are students working with in M8? • How does thinking of fractions as units prepare students to add and subtract fractions in G3?

44. Key Points • In Module 8, students continue to develop their understanding of units within units as they describe and analyze 2-dimensional shapes and then combine polygons to build composite shapes. • Module 8 develops fraction concepts, extending student understanding of part/whole relationships to unit fractions as equal parts of a whole. • Students partition and describe equal shares of a whole as halves, thirds, and fourths, but they do not write, add, or subtract fractions; that is the domain of G3. • Students apply fraction concepts to telling time. They relate 30 minutes to a half hour and 15 minutes to a quarter hour.