CCSS 101: Standards for Mathematical Practice

CCSS 101: Standards for Mathematical Practice Class 3 March 14, 2011

Journal Review by Your Peers • Read and react to each other’s journal entries about the Math Talk (Chapter 2) reading • Use Post-it-Notes to record your comments in each journal • Pass the journals to the right until you get your own journal back • Discuss as a group – What stands out after reading all the journals?

Discussion of “Math Talk” • Share your group’s reflections on the journals you read • What important ideas are surfaced in the “Math Talk” reading?

Learning Intentions We Are Learning To … • analyze students’ thinking on a Continuum of Student Thinking and Understanding. • advance students’ thinking by asking good questions and making adaptations and modifications to move students to the next stage or stages.

Success Criteria We will know we are successful when we can understand the components of the Continuum of Student Thinking and Understanding and fill in the form after analyzing student work.

Common Core State Standards Alignment • Present your task to the teachers at your table. • Summarize the work that you brought for this task. • What did you see and hear when your students worked on this task?

Analyzing Students’ Thinking • Sort your student samples according to their stage on the Continuum of Student Thinking and Understanding • Use Post-it notes to make reasoning comments on the sortings of other members of your group

Analyzing Students’ Thinking • Re-sort your student samples, if necessary, after reflecting on your colleague’s comments • Complete part 2 of the Continuum template for your student samples

Advancing Students’ Thinking • Complete part 3 of the Continuum template for your student samples • What questions will I ask? • What modifications or adaptations will I do?

Asking Questions Problem Comprehension Can students understand, define, formulate, or explain the problem or task? Can they cope with poorly defined problems? • What is the problem about? What can you tell me about it? • Would you please explain that in your own words? • What do you know about this part? • Is there something that can be eliminated or that is missing? • What assumptions do you have to make? Approaches and Strategies Do students have an organized approach to the problem or task? How do they record? Do they use tools (manipulatives, diagrams, graphs, calculators, computers, etc.) appropriately? • Where would you find the needed information? • What have you tried? What steps did you take? What did not work? • How did you organize the information? Do you have a record? • Did you have a system? A strategy? A design? • Would it help to draw a diagram or make a sketch? • How would it look if you used these materials? Solutions Do students reach a result? Do they consider other possibilities? • Is that the only possible answer? • How would you check the steps you have taken, or your answer? • Is there anything you have overlooked? • Is the solution reasonable, considering the context? • How did you know you were finished?

Summary We Are Learning To … • analyze students’ thinking on a Continuum of Student Thinking and Understanding. • advance students’ thinking by asking good questions and making adaptations and modifications to move students to the next stage or stages. We will know we are successful when we can understand the components of the Continuum of Student Thinking and Understanding and fill in the form after analyzing student work.

Break

Learning Intentions We are learning to identify grade-band progressions within a given content domain in the CCSS, and connect those progressions with a math task.

Success Criteria We will know we are successful when we can • articulate at least one strength and one weakness in a CCSS content progression • Describe how an understanding of that progression can be used to guide classroom instruction within a school

Review of Area Turn and talk: What is area? What are the moving and combining principles for area?

Area Principles Combining Principle: The total area of two (or more) non-overlapping shapes is the sum of their individual areas. Moving Principle: the area of a shape is not changed if the shape undergoes a rigid motion.

Exploring the Area of Polygons Using Grid Paper, Dot Paper or a Geo-board, determine the area of the given shape.

Developing an Area Conjecture • Draw a right-angled triangle near the center of a sheet of grid paper • You should draw the triangle with two of its sides parallel to grid lines • Draw a square on each side of the triangle

Developing an Area Conjecture • Your figure should look something like this:

Developing an Area Conjecture • Find the area of each of your 3 squares • When you are done, write your results on the chart paper at the front of the room

Developing an Area Conjecture • Find the area of each of your 3 squares • When you are done, write your results on the chart paper at the front of the room • What do you observe? • (Carefully) state a conjecture that you are prepared to make on the basis of the class results

Proving your Conjecture How do these figures prove your conjecture?

Unfortunately, we were scooped… If a right triangle has legs of length a and b, and hypotenuse of length c, then a2 + b2 = c2.

Unfortunately, we were scooped… If a right triangle has legs of length a and b, and hypotenuse of length c, then a2 + b2 = c2. (Pythagoras’ Theorem)

What Content Standard Did We Address? • Look for Content Standards in the CCSS (Grades 6-8) that were addressed by today’s task. • Do you see a coherent progression from Grade 6 through Grade 8?

Standards for Mathematical Practice • Identify any Standards for Mathematical Practice that you saw as we carried out today’s task. • Use specific examples to explain the connection between the content and practice standard you identified.

What practices did you see?

Understanding Understanding • Some of the standards start with the word Understand • What does that verb mean in these math standards?

Summary We are learning to identify grade-band progressions within a given content domain in the CCSS, and connect those progressions with a math task. We will know we are successful when we can • articulate at least one strength and one weakness in a CCSS content progression • Describe how an understanding of that progression can be used to guide classroom instruction within a school

CCSS 101: Standards for Mathematical Practice