5. There was a white board, which seemed to be better than a blackboard in terms of health and convenience.

6. The native speaker threw a pack of sentence cards to each group so they started to do the group activity.

7. The use of power point was appropriate. She showed pictures from an easy one to a difficult one so that students could guess the country's name step by step.

8. The native speaker gave them a project, so students worked in pairs. By doing the pair work, they made a dialogue and encouraged to memorize the dialogue. Later some pairs stood up and did the dialogue.
----------------------------------------
[5-8] I have written down what we can think of after co-teaching. Would you correct the sentences, please?

#5 - looks fine

#6 - I'd put a comma after the first use of the word "group" and change "so" to "and."

#7 - "PowerPoint" is a brand name (Microsoft's) and should be spelled and capitalized correctly. I'd also put a comma after "country's name."

#8 - The native speaker gave them a project, so students worked in pairs. Working together, each pair wrote a dialogue and encouraged each other to memorize it. Later<~~add comma some pairs stood up and did<~~There has to be a better word than "did" -- performed? the dialogue.

Certainly! Here are the corrections for the sentences you provided:

5. There was a whiteboard, which seemed to be better than a blackboard in terms of health and convenience.
Explanation: This sentence is grammatically correct. It talks about a whiteboard being better than a blackboard in terms of health and convenience.

6. The native speaker threw a pack of sentence cards to each group, so they started to do the group activity.
Explanation: This sentence is grammatically correct. It describes the action of the native speaker throwing sentence cards to each group, which then started their group activity.

7. The use of PowerPoint was appropriate. She showed pictures from an easy one to a difficult one so that students could guess the country's name step by step.
Explanation: This sentence is grammatically correct. It mentions the appropriate use of PowerPoint where pictures were shown gradually from easy to difficult, allowing students to guess the country's name step by step.

8. The native speaker gave them a project, so students worked in pairs. By doing the pair work, they made a dialogue and were encouraged to memorize it. Later, some pairs stood up and performed the dialogue.
Explanation: This sentence is grammatically correct. It describes how the students were given a project and they worked in pairs. Through pair work, they created a dialogue and were encouraged to memorize it. Finally, some pairs stood up and performed the dialogue.

Overall, all the sentences are grammatically correct, but I have provided some clarification and minor adjustments for better understanding.