1. Describe the process of counting on from first for the problem:
Mark has 3 Bionicles and 6 Hero Factory robots. How many robots does he have in all?
2. Describe the process of counting on from larger for the problem:
Mark has 3 Bionicles and 6 Hero Factory robots. How many robots does he have in all?
3. What CGI problem type is most closely associated with the counting on strategy?
4. For what addends is counting on an efficient computation strategy?
5. How can you get children who are in the habit of counting all to break that habit and start solving problems by counting on?
6. Which CGI word problem type is most closely associated with the counting back strategy?
7. For what sorts of numbers is counting back an efficient strategy? (Efficient means it can be reliably be used in a short amount of time--3 seconds of less).
8. Describe both ways of using counting back to solve the problem: 8-3
9. How can you use manipulatives to help children understand counting back as a strategy? And/or What sorts of manipulative use encourages children to develop counting strategies for subtraction instead of direct modeling?
10. Which CGI word problem type is most closely associated with the counting up to strategy?
11. For what sorts of numbers is "counting up to" an efficient strategy?
12. Rewrite the missing number addition problem as a subtraction problem: 8 + ? = 11
13. Describe how to use "counting up to" to solve 7 - 5
14. Why do we want children to learn to use "counting up to" to solve subtraction problems?
15. What would be a good problem type to compare counting back and counting up to?