1. This module was developed by Carrie Ziegler, Nathan Auck, and Steve Jackson. They are the three principle designers of the course, Principles to Actions, in the UEN and Utah State Office of Education Professional Learning Series. USOE Professional Learning Series Principles to Actions 24 Shapes I can compose squares from shapes and label each part with a fraction. USOE Professional Learning Series Principles to Actions 24 Shapes I can compose squares from shapes and label each part with a fraction.

2. Overview of the Task Solve and discuss the task, 24 Shapes. As you engage in the task, think about and record what you would do and ask as the teacher- the teacher moves. Connect the task to the Effective Mathematics Teaching Practices.

3. Task: 24 Shapes

4. 24 Shapes

5. Task: 24 Shapes  Which squares did you find the most difficult to make? The least difficult? Why? Explain your thinking.  What strategies did you use to complete the task? Explain your thinking.  What properties of shapes did you attend to in order to compose the squares? Why? Explain your thinking.

6. 24 Shapes Task 2: Your task is to take each of the shapes and figure out what fractional part of the square it is.

7. 24 Shapes What fraction of the square is…

8. Use and Connect Mathematical Representations Different Representations should: Be introduced, discussed, and connected; Focus students’ attention on the structure or essential features of mathematical ideas; and Support students’ ability to justify and explain their reasoning. Strengthening the ability to move between and among these representations improves the growth of children’s concepts. Lesh, Post, Behr, 1987

9. Mathematical Representations

10. Support Productive Struggle in Learning Mathematics Productive Struggle should: Be considered essential to learning mathematics with understanding; Develop students’ capacity to persevere in the face of challenge; and Help students realize that they are capable of doing well in mathematics with effort. By struggling with important mathematics we mean the opposite of simply being presented information to be memorized or being asked only to practice what has been demonstrated. Hiebert & Grouws, 2007, pp. 387-388

11. Support Productive Struggle In Learning Mathematics: Teacher and Student Actions What are teachers doing? Anticipating what students might struggle with during a lesson and being prepared to support them productively through the struggle. Giving students time to struggle with tasks, and asking questions that scaffold students’ thinking without stepping in to do the work for them. Helping students realize that confusion and errors are a natural part of learning, by facilitating discussions on mistakes, misconceptions, and struggles. Praising students for their efforts in making sense of mathematical ideas and perseverance in reasoning through problems. What are students doing? Struggling at times with mathematics tasks but knowing that breakthroughs often emerge from confusion and struggle. Asking questions that are related to the sources of their struggles and will help them make progress in understanding and solving tasks. Persevering in solving problems and realizing that is acceptable to say, “I don’t know how to proceed here,” but it is not acceptable to give up. Helping one another without telling their classmates what the answer is or how to solve the problem.

12. Consider the Teacher and Student Actions Required to Support Productive Struggle What will you need to work on in order to support productive struggle in your own classroom? Where will you start?

13. Effective Mathematics Teaching Practices 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking.