For students to be successful with numbers, they need to be comfortable with them. How better than to use manipulatives as the first step towards developing numerical flexibility? The first step is to have students use manipulatives to model the process as you read the directions slowly, step by step. As students become more comfortable, begin to encourage them to visualize the amount and add to it.
For example, "I want you to visualize, or see, 6 counters in your head. Now, add two counters to those 6. (pause) Now, add 3 counters to those! How many counters do you have in all?"
The calling cards are scaffold, beginning with problems that equal 6 and proceed up to 20. You may wish to do this as a class and then branch off to small groups, pairs, or even individuals. When ever a child questions an answer, encourage them to use manipulatives to check the answer. My students enjoy taking turns reading a card to their partner who completes the problem using a dry erase board with marker. However, they do use counters to prove or disprove an answer.