Application Exercise 2.1: Observing and Responding to Student Thinking

Click the link below to watch an eighth-grade student solve the problem, "Ron's recycle shop started when Ron bought a used paper-shredding machine. Business was good, so Ron bought a new shredding machine. The old machine could shred a truckload of paper in 4 hours. The new machine could shred the same truckload in only 2 hours. How long will it take to shred a truckload of paper if Ron runs both shredders at the same time?" then answer the questions that follow.

Analyzing a Situation: Two Machines, One Jobhttp://mediaplayer.pearsoncmg.com/assets/chapter_2…

*Predict approximately how much time you think it should take the two machines to shred a truckload of paper. For example, will it be closer to 1 hour or closer to 4 hours? What facts about the situation lead you to this estimated time? Is there a way to check your estimate and determine if a solution isreasonable?

**What question(s) might you pose to help the student continue to reason about this problem?

***Describe a method for modeling and solving this problem.

Application Exercise 9.1: Reasoning Strategies for Multiplication and Division Facts

Apply your understanding of the learning from this chapter. When finished, submit your answers.

Watch as this teacher works with her students on a multiplication strategy. Click the link to watch the video and then answer the accompanying questions.

Ashley Lyons Classroom: Arrays and repeated additionhttp://mediaplayer.pearsoncmg.com/assets/ClassWork…

*How does Ms. Lyons use tools and guiding questions to build her students understanding of what three times four represents?

**The chapter introduces approaches to teaching basic facts. What strategy is evident in Ms. Lyons small group lesson?

***Based on observing the students working at the table, what developmental phase of basic fact learning would you identify these students are working? Explain using evidence you saw in the video.

Application Exercise 10.1: Base-Ten Models for Place Value

Apply your understanding of the learning from this chapter. When finished, submit your answers.

Watch this diagnostic interview of Freddie and apply your understanding of place-value development. Click the link to watch the video and then answer the accompanying questions.

Freddie 400-150, 150 + ? =400http://mediaplayer.pearsoncmg.com/assets/_video.tr…

*Explain what level of place-value understanding Freddie demonstrates in this interview.

**What error pattern is he making on his written work and how does this add to his confusion after he uses the base-ten blocks?

***Based on what you observed what strategies, methods, or materials would you use to support Freddie's place-value development?*

Application Exercise 11.1: Standard Algorithms for Addition and Subtraction

Apply your understanding of the learning from this chapter. When finished, submit your answers.

Watch this diagnostic interview of Hally and apply your understanding of invented strategies versus the standard algorithm. Click the link to watch the video and then answer the accompanying questions.

Hally 1000 – 4, 1000 – 1http://mediaplayer.pearsoncmg.com/assets/0156_iPad

*Explain what Hally is demonstrating in the first part of the interview when she is subtracting with zeros.

**The interviewer asked Hally if she could solve 1000minus−1 a different way and she said, "I don't know." Based on what you have learned about inventedstrategies, what method would have been effective for her to use with these subtraction problems.

***In the second part of the interview, Hally is adding using the procedural addition algorithm. Explain what she is demonstrating about her knowledge of place value.

****Hally added 286 + 149 with the standard algorithm. What invented strategies would be beneficial for her to use with this type of problem?

Application Exercise 12.1: Invented Strategies for Multiplication

Apply your understanding of the learning from this chapter. When finished, submit your answers.

Watch this class discussion involving a variety of student strategies for solving 251times×12.

Click the link to watch the video and then answer the accompanying questions.

Mental Multiplication, 2nd Grade/http://mediaplayer.pearsoncmg.com/assets/_video.tr…

*How do the teacher's questions encourage students to share their thinking?

**Based on the chapter, explain what strategies the children using to solve the multiplication problem.

***Why do you think the teacher asks students how the strategies are different and how they are the same?