Session 10, Part B:

In This Part: Exploring Standards | Examining Children's Reasoning

Here are scenarios from two different teachers' classrooms, each involving young children's developing ideas about number and operations. Snippets of students' discussions are given for each scenario. For each student, consider the following:

 • Understanding and Misunderstanding: What does the statement reveal about the student's understanding or misunderstanding of number and operations ideas? Which ideas are embedded in the student's observations? • Next Instructional Moves: If you were the teacher, how would you respond to this student? What questions might you ask so that the student would ground his or her comments in the context? What further tasks and situations might you present for the student to investigate? Note 4

Problem B5

Second graders Leland, Randy, and Reed are given the following problem: Kent and his dog Nikki weigh 194 pounds when they are together on the scale. Kent weighs 146 pounds. How much does Nikki weigh?

Below is a snippet of their conversation:

Reed: Nikki weighs 48 pounds. I did it in my head. I first added 2 to 194 to get 196. Then I counted backward by tens until I got to 146 -- 196, 186, 176, 166, 156, 146. That's 5 tens, or 50. Then I subtracted the 2 to get 48.

Leland: I didn't do it that way. I counted up by tens -- 146, 156, 166, 176, 186, 196. That's 50, and 2 less makes 48.

Randy: I wrote it down on a piece of paper, and 6 minus 4 is 2, and 9 minus 4 is 5, and 1 minus 1 is 0. So it's 52.

 a. What method did each student use to solve the problem? What does this tell you about how each student is thinking about the problem? b. Do you think each student is ready to learn a new method? Why or why not?

Problem B6

Second graders Daniel, Tarra, and Mariko are given the following problem: Antonio has 35 marbles. Helen has 52 marbles. How many more marbles does Helen have than Antonio?

Below is a snippet of their conversation:

Mariko: They have 87 marbles all together.

Tarra: Helen has 35, 45, 55 -- that's 20. Count back 55, 54, 53, 52. She has 17 more.

Daniel: Fifty-two, 42, 32, then 33, 34, 35 -- that's 23 more.

 a. What method did each student use to solve the problem? What does this tell you about how each student is thinking about the problem? b. Do you think each student is ready to learn a new method? Why or why not?

 Join the discussion! Post your answer to Problems B5 and B6 on Channel Talk; then read and respond to answers posted by others.

 Session 10, Grades K-2: Index | Notes | Solutions | Video