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?
Say 3 (pause), 4 (raise 1 finger), 5 (raise a second finger), 6 (raise a third finger), 7 (raise a fourth finger), 8 (raise a fifth finger), 9 (raise a sixth finger). The answer is 9.
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?
Say 6 (pause), 7 (raise a finger), 8 (raise a second finger), 9 (raise a third finger). The answer is 9.
3. What CGI problem type is most closely associated with the counting on strategy?
Join, Result Unknown.
4. For what addends is counting on an efficient computation strategy?
Counting on is efficient for problems where one addend is small (1, 2, or 3)
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?
Ask problems where the first addend is large enough that counting all would be unreasonably difficult (above 20). It's also helpful to use visuals such as the Bears-in-a-cave activity, where one of the numbers (preferably the larger one) is hidden so that it's more difficult and less natural to count it from 1.
6. What is the place of rote counting in counting on?
Practicing counting on/counting up starting with a given number is good preparation for counting on and also for understanding number comparisons. Rote counting on is a Kindergarten standard.
7. Describe a teaching approach that is only minimally teacher directed for teaching counting on.
A teacher asks word problems that it would be easy to use counting on to solve. The children solve the problem, and the teacher invites children, including ones who used counting on, to share how they solved the problem. The teacher follows up with other problems appropriate for solving by counting on.
8. Describe a teaching approach that is more stongly teacher directed for counting on.
The teacher models how to solve a problem by counting on. Then the teacher gives the children problems so solve or a game to play where they should ues counting on to solve problems.
9. Describe a game or activity for teaching counting on.
A child hides some bear counters under a cup, and puts some bear counters outside of the cup. The child tells his or her partner how many bears are under the cup, and the partner figures out how many bears there are in all.
10. Describe a teaching idea that you found in the readings that wasn't in the lecture.
I hope you found one you like. I think my favorite that is in the readings but I didn't put in the lecture is probably the one from "How can you teach counting on for addition?" where you show how many are in the cup, and then children have to figure out how many after you add more by listening to you drop them into the cup. I suspect a really useful strategy that's in that same essay is the strategy of asking children after they solve the problem, how you could write the number sentence for what they just solved.