1. 1 Overview of Class #7 Teaching Segment #3: Warm-up problem Introduction to base-ten blocks Analysis of student thinking using samples of students’ written work Wrap up

2. 2 A student solved the problem 92 - 37 in the following way: Analyze the student’s method, and explain why it gives the incorrect answer. Why might a student think this method would work? How could you modify this method to make it work? (That is, how can you start with 92-40=52, and arrive at the correct answer?) What are some other erroneous subtraction methods that students might come up with? I know that 92 – 40 = 52. Since 37 is 3 less than 40, I need to take 3 away from 52. So the answer is 49.

3. 3 What is a Warm-up Problem? A short problem (5-10 minutes) Students should be able get started and work on it independently Should engage each student productively -- not too easy or too difficult –Examples: multiple solutions or solution strategies; no real “end” Task can be publicly displayed for students to copy, or on a handout for students to complete Brief discussion after students have worked for a while

4. 4 Purposes of Warm-up Problems Managing transitions Variety of instructional goals: –To review or practice skills that have been previously taught –To reinforce concepts or practice skills that students are currently learning –To refresh a concept or skill that students will be using in that day’s lesson –To provide enrichment on content not regularly part of the curriculum –To motivate or interest students in mathematics

5. 5 Practice for Teaching Segment #3 Work with your cooperating teacher to choose or modify a warm-up problem. –Use your curriculum materials or other resources. Plan for the discussion of the problem. Carry out the warm-up problem and collect artifacts. Write an entry about your work. –Design, implementation, reflection

6. 6 Where are we in the course? Why are we working on what we’re working on? Modeling place value, numeration, computation; moving into decimals and upper elementary content: –Learning to produce clear explanations, make meaning visible, help students make solid connections –Filling in what teachers’ guides will not provide –Teaching this content well will give you leverage as a beginning teacher in about 3/4 of the elementary curriculum Learning to make judgments about students’ mathematical proficiency –Diagnosis, to be able to match mathematical focus to where students are is absolutely crucial to effective teaching –Communicating clearly, and backing up with examples and evidence, about students’ progress (parents, other teachers, specialists, students themselves) is essential to professional work of a teacher

7. 7 Base Ten Blocks Trading model Highlights geometry of number and number relationships (Little) cube, rod, flat, big cube Micro-, mini-, super-, mega- as prefixes for extending the blocks Unit can change Expensive Flexible across K - 8 and beyond

8. 8 Modeling with Base Ten Blocks Work with a partner Use language of base ten blocks Remember to model the steps of the conventional algorithm and make the meaning clear Attend to the way you are representing addition and subtraction

9. 9 Our Work on Student Thinking We’ve been focusing on: eliciting listening probing interpreting We’re now going to add: evaluating responding using

10. 10 Analysis of Third Grade Quiz 1.Answer each of the questions on the quiz yourself. 2.Use handout to analyze particular questions (#8, #4 & #5, #9 & #10, then your choice): What is the purpose of the question and the core mathematical ideas addressed? What are characteristics of “good” answers at the third grade level?

11. 11 Analysis of Student Work Read each of the three student responses to a particular question (starting with #8, #4 & #5, and #9 & #10). For each question discuss the following: 1.What does each student’s response tell you about his or her mathematical understandings? 2.What follow-up questions would you like to ask each student?

12. 12 Analyzing Student Work Samples from Field Placement For each question: 1.Answer the questions yourselves. 2.Analyze the question: –What is the purpose of the question and the core mathematical ideas addressed? –What are characteristics of “good” answers at that grade level? 3.Read the student responses to that question: –What does each student’s response tell you about his or her mathematical understandings? –What follow-up questions would you like to ask each student?

13. 13 Assignments Reading: Lampert, Chs 5-6 Midterm course comments –– why these are important and how I will use them; Download, and email as attachments, before next class, to: Brenda Ely elyb@umich.eduelyb@umich.edu Begin Teaching Segment #3