• develop, select, apply, compare, and adapt a variety of problem-solving
strategies as they pose and solve problems and conduct investigations, to
help deepen their mathematical understanding;
• develop and apply reasoning skills (e.g., use of inductive reasoning, deductive
reasoning, and counter-examples; construction of proofs) to make mathematical
conjectures, assess conjectures, and justify conclusions, and plan and construct
organized mathematical arguments;
• demonstrate that they are reflecting on and monitoring their thinking to
help clarify their understanding as they complete an investigation or solve a
problem (e.g., by assessing the effectiveness of strategies and processes used,
by proposing alternative approaches, by judging the reasonableness of results,
by verifying solutions);
• select and use a variety of concrete, visual, and electronic learning tools and
appropriate computational strategies to investigate mathematical ideas and
to solve problems;
• make connections among mathematical concepts and procedures, and relate
mathematical ideas to situations or phenomena drawn from other contexts
(e.g., other curriculum areas, daily life, current events, art and culture, sports);
• create a variety of representations of mathematical ideas (e.g., numeric,
geometric, algebraic, graphical, pictorial representations; onscreen dynamic
representations), connect and compare them, and select and apply the
appropriate representations to solve problems;
• communicate mathematical thinking orally, visually, and in writing, using precise
mathematical vocabulary and a variety of appropriate representations, and
observing mathematical conventions.