The Eight Mathematical Practices
Make sense of problems and persevere in solving them
This mathematical practice comes alive in the Connected Mathematics classroom as students and teachers interact around a sequence of rich problems, to conjecture, validate, generalize, extend, connect, and communicate.
Reason abstractly and quantitatively
As students observe, experiment with, analyze, induce, deduce, extend, generalize, relate and manipulate information from problems, they develop the disposition to inquire, investigate, conjecture and communicate with others around mathematical ideas.
Construct viable arguments and critique the reasoning of others
The student and teacher materials support a pedagogy that focuses on explaining thinking and understanding the reasoning of others.
Model with mathematics
The student materials provide opportunities to construct, make inferences from, and interpret concrete, symbolic, graphic, verbal, and algorithmic models of quantitative, statistical, probabilistic and algebraic relationships.
Use appropriate tools strategically
Problem settings encourage the selection and intelligent use of calculators, computers, drawing and measuring tools, and physical models to measure attributes, and represent, simulate and manipulate relationships.
Attend to precision
Students are encouraged to decide whether an estimate or an exact answer for a calculation is called for, to compare estimates to computed answers, and to choose an appropriate measure or scale depending on the degree of accuracy needed.
Look for and make use of structure
Problems are deliberately designed and sequenced to prompt students to look for interrelated ideas, and take advantage of patterns that show how data points, numbers, shapes or algebraic expressions are related to each other.
Look for and express regularity in repeated reasoning
Students are encouraged to observe and explain patterns in computations or symbolic reasoning that lead to further insights and fluency with efficient algorithms.