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.


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?


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 ?


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?


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?


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?


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?


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?



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?



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?


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?


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