Assign students an extremely complex mathematical problem or a research question with an obscure or ambiguous answer. Tell them that you will be circling the room to help them out. When they appear frustrated or start to ask for a lot of help, ask them questions, such as, What do you already know about the topic? Can the problem be restated in a different way? Who might be able to help? Asking students these questions helps show them what to do when they are stuck.
Encourage children to be resourceful in other ways. Demonstrate what you mean by collecting paper clips from old papers to be used again, or rinsing out used water cups for painting. Ask students to help establish a list of rules for the classroom. Whenever the student uses an item that can be used again, have them put it in a special box or cubby somewhere in the classroom. Award a small prize to the person who is the most resourceful by the end of the year.
Divide students up into pairs or small groups. Give each team a slip of paper with a scenario on it that would require them to be resourceful. For example, one scenario might be that they are driving a car that has broken down, or that they have to buy groceries for dinner with only $15. Have the students role play, in front of the class, the ways that they would use resourcefulness to go about solving these problems.
Sit down with individual students to plan personal goals or brainstorm ideas for some classroom goals with everyone. Make the goals reasonably high, so that there is some challenge. Encourage the children to pursue their goals. However, when an issue comes up that seems to block them from achieving them, suggest alternatives. For example, they might consult a research book, talk to an expert or decide to set a series of smaller goals to reach the big goal.