Cognitive Guided Instruction Classification of Word Problems
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Problem Type |
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Join |
Result Unknown Connie had 5 marbles. Juan gave her 8 more marbles. How many 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? |
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Separate |
Result Unknown Connie had 13 marbles. She gave 5 to Juan. How many marbles does Connie 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? |
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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? |
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Compare |
Difference unknown Connie has 13 marbles. Juan has 5 marbles. How many more marbles does Connie have than Juan? |
Compare quantity unknown Juan has 5 marbles. Connie has I more than Juan. How many marbles does Connie have? |
Referent unknown Connie has 13 marbles. She has 5 more marbles than Juan. How many marbles does Juan have? |
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Multiplication |
Megan has 5 bags of cookies. There are 3 cookies in each bag. How many cookies does Megan have altogether? |
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Measurement Division |
Megan has 15 cookies. She puts 3 cookies in each bag. How many bags can she fill? |
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Partitive Division |
Megan has 15 cookies. She put the cookies into 5 bags with the same number of cookies in each bag. How many cookies are in each bag? |
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Instructor Comments: Problems with action tend to be easier. For example, although the "join with result unknown" and the "part- part whole with the whole unknown" may appear to be similar, children find the join with result easier to direct model than the part part whole. Problems with "result unknown" tend to be easier to direct model than problems with "change unknown" and problems with "start unknown" tend to be the most difficult. A high percent of first graders were able to do the multiplication and division problems by direct modeling.