For example, if an instructional goal is to prepare students to solve a work-related problem involving ratio/proportion (indicated by the X in the matrix), some students may first need to review their understanding of the underlying concepts behind the operations involved (e.g., Why cross-multiply and divide?). Only then will they be able to estimate an answer, perform the computation, recognize inherent patterns, see relationships, and make connections to similar problems -- all of which lead to effective problem solving.

Teachers are strongly encouraged to select and sequence those aspects of instruction that are most relevant to the needs of their learners on an individualized and group basis. For initial assessment, an analysis of Tests of Adult Basic Education (TABE) or other testing instrument may provide a starting point for instruction by identifying learners' basic strengths/weaknesses. However, caution is advised in using only the results of these tests for instruction, since they may not identify gaps in understanding basic concepts of mathematics.

Research has shown that activities designed to facilitate recall of concepts and aid in the synthesis and application of reasoning skills are most effective if a team approach is used. A team approach can entail:

• embedding math topics and computation skills in problem-solving/decision-making processes.
• learner-centered activities as vehicles for instruction, since they aid in the synthesis and application of concepts through communication.
• students working in pairs/triads/teams, which allows opportunities for questioning and discussion, justification of thinking, and content integration.
• concrete hands-on materials, rather than pencil and paper alone.
• calculator use at all levels of teamwork.

The math curriculum that follows the matrix correlates goals and objectives with those of the National Council of Teachers of Mathematics (NCTM) and the recommendations of the Adult Numeracy Practitioners Network's A Framework for Adult Numeracy Standards. Note that there is an overlap of skills and examples in some cases.