nc naep project module 2 - activity 2 whose problem structure is it? examining problems from the...

NC NAEP Project NC NAEP Project

Module 2 - Activity 2Whose Problem Structure is It? Examining Problems from the Perspective of the Expert and of the Student

Elementary Module 2, Activity 2

GoalsGoalsBased on videotaped examples,

develop understanding of common student approaches to single-step and multi-step problems.

Become aware of a variety of instructional approaches for teaching these topics that are research-based.

Practice predicting student thinking on a particular task or item.

Elementary Module 2, Activity 2

Solve These Problems:Solve These Problems:

Connor has 10 cars. He gives 3 cars to Tristan. How many cars does Connor have left?

Connor has 3 cars. How many more cars does he need to have 10 cars?

Connor has 3 cars. Tristan has 10 cars. How many more cars does Tristan have than Connor?

Elementary Module 2, Activity 2

DiscussionDiscussion

How would you solve these problems?

How might a first grader solve these problems?

What strategies might a first grader use to arrive at the answer ?

Elementary Module 2, Activity 2

Cognitively Guided Cognitively Guided Instruction (CGI Join Instruction (CGI Join Problems)Problems)

Join: Result Unknown◦Sandra had 8 pennies. George gave her four

more. How many pennies does Sandra have altogether?

Join: Change Unknown◦Sandra had 8 pennies. George gave her some

more. Now, Sandra has 12 pennies. How many did George give her?

Join: Initial Unknown◦Sandra had some pennies. George gave her 4

more. Now Sandra has 12 pennies. How many pennies did Sandra have to begin with?

Elementary Module 2, Activity 2

Cognitively Guided Cognitively Guided Instruction (CGI Separate Instruction (CGI Separate Problems)Problems)

Separate: Result Unknown◦Sandra had 12 pennies. She gave 4 pennies to

George. How many pennies does Sandra have now?

Separate: Change Unknown◦Sandra had 12 pennies. She gave some to

George. Now she has 8 pennies. How many did she give George?

Separate: Initial Unknown◦Sandra had some pennies. She gave 4 to

George. Now Sandra has 8 pennies left. How many pennies did Sandra have to begin with?

Elementary Module 2, Activity 2

Cognitively Guided Cognitively Guided Instruction (CGI Part-Part Instruction (CGI Part-Part Whole Problems)Whole Problems)

Part-Part-Whole: Whole Unknown◦George had 4 pennies and 8 nickels. How

many coins does he have?◦George has 4 pennies and Sandra has 8

pennies. They put their pennies into a piggy bank. How many pennies did they put into the bank?

Elementary Module 2, Activity 2

Cognitively Guided Cognitively Guided Instruction (CGI Part-Part Instruction (CGI Part-Part Whole Problems)Whole Problems)

Part-Part-Whole: Part Unknown◦George has 12 coins. Eight of his coins

are pennies and the rest are nickels. How many nickels does George have?

◦George and Sandra put 12 pennies into the piggy bank. George put in 4 pennies. How many pennies did Sandra put in?

Elementary Module 2, Activity 2

Cognitively Guided Cognitively Guided Instruction (CGI Compare Instruction (CGI Compare Problems)Problems)

Compare: Difference Unknown◦George has 12 pennies and Sandra has 8

pennies. How many more pennies does George have than Sandra?

◦George has 12 pennies. Sandra has 8 pennies. How many fewer pennies does Sandra have than George?

Elementary Module 2, Activity 2

Cognitively Guided Cognitively Guided Instruction (CGI Compare Instruction (CGI Compare Problems)Problems)

 Compare: Larger Unknown◦George has 4 more pennies than Sandra.

Sandra has 8 pennies. How many pennies does George have?

◦Sandra has 4 fewer pennies than George. Sandra has 8 pennies. How many pennies does George have?

Elementary Module 2, Activity 2

Cognitively Guided Cognitively Guided Instruction (CGI Compare Instruction (CGI Compare Problems)Problems)

 Compare: Smaller Unknown◦George has 4 more pennies than Sandra.

George has 12 pennies/ How many pennies does Sandra have?

◦Sandra has 4 fewer pennies than George. George has 12 pennies. How many pennies does Sandra have?

Elementary Module 2, Activity 2

Questions Following Gallery Questions Following Gallery WalkWalk

1. Are there any questions? 2. What did you notice? 3. Is there something that you

are unsure about?

Elementary Module 2, Activity 2