Cognitively Guided Instruction – Problem Type Chart 

 

JOIN 

Result Unknown 

Connie had 5 marbles. Juan gave her 8 more 
marbles. How many marbles does Connie 
have altogether? 

Change Unknown 

Connie has 5 marbles. How many more 
marbles does she need to have 13 marbles 
altogether? 

Start Unknown 

Connie had some marbles. Juan gave her 5 
more marbles. Now she has 13 marbles. 
How many marbles did Connie have to start 
with? 

SEPARATE 


Result Unknown 

Connie had 13 marbles. She gave 5 marbles 
to Juan. How many marbles does she have 
left? 

 

 

Change Unknown 

Connie had 13 marbles. She gave some to 
Juan. Now she has 5 marbles left. How many 
marbles did Connie give to Juan? 

Start Unknown 

Connie had some marbles. She gave 5 to 
Juan. Now she has 8 marbles left. How many 
marbles did Connie have to start with? 

PART-PART-
WHOLE 


Whole Unknown 

Connie has 5 red marbles and 8 blue marbles. How many marbles 
does she have? 

Part Unknown 

Connie has 13 marbles. 5 are red and the rest are blue. How many 
blue marbles does Connie have? 

COMPARE 


Difference Unknown 

Connie has 13 marbles. Juan has 5 marbles. 
How many more marbles does Connie have 
than Juan? 

 

Compared Quantity Unknown 

Juan has 5 marbles. Connie has 8 more than 
Juan. How many marbles does Connie have? 

Referent Set Unknown 

Connie has 13 marbles. She has 5 more 
marbles than Juan. How many marbles does 
Juan have? 

 

 

 

 

EQUAL 
GROUPS 


Multiplication 

Connie has 5 bags of cookies. There are 3 
cookies in each bag. How many cookies does 
Connie have altogether? 

 

 

 

Measurement Division 

Connie has 15 cookies. She puts 3 cookies in 
each bag. How many bags can she fill? 

Partitive Division 

Juan has 15 cookies. He put the cookies into 
5 bags with the same amount of cookies in 
each bag. How many cookies are in each 
bag? 



 

*From Children’s Mathematics (Carpenter, Fennema, Franke, Levi, & Empson, 1999)