Appendix.

Sample Problems by Problem Type and by Position of Missing Information (A + B = C or A − B = C)

Problem	Problem type	Position of missing information
The art teacher had 82 pieces of colored paper. Some of the pieces of paper were blue, and 20 of the pieces were green. How many pieces of blue paper did she have?	Total	A (x + 20 = 82)
Donna and Natasha made 96 friendship bracelets. Donna made 25 bracelets. How many friendship bracelets did Natasha make?	Total	B (25 + x = 96)
There are 51 boys and 47 girls in the third grade at Baker Elementary School. How many third graders are there?	Total	C (51 + 47 = x)
Charles put 14 more roses than daisies in the vase. He put 25 daisies in the vase. How many roses did he put in the vase?	Difference	A (x − 25 = 14)
Maurice has 11 more comic books than Thomas. Maurice has 37 comic books. How many comic books does Thomas have?	Difference	B (37 − x= 11)
At the picnic, the kids ate 65 hot dogs. They ate 32 hamburgers. How many more hot dogs did they eat than hamburgers?	Difference	C (65 − 32 = x)
The temperature outside this morning was cool. By the afternoon, the temperature had gone up 35 degrees so it is now 87 degrees outside. What was the temperature in the morning?	Change	A (x + 35 = 87)
Jamarius baked 78 chocolate chip cookies. Then he gave some to his friends. Now Jamarius has 23 cookies. How many cookies did Jamarius give to his friends?	Change	B (78 − x = 23)
Mr. Luther had 26 pencils in his desk. Then he gave 12 pencils to his students. How many pencils does Mr. Luther have now?	Change	C (26 − 12 = x)

Note. Other problems included irrelevant information or incorporated relevant information in pictographs, scenes, or bar charts. Students only see the problem. They are taught to solve the problem by identifying the problem type; generating an algebraic sentence to represent that problem type; and solving for x within the algebraic equation.