CPM Professional Learning Portal

Also referred to as the LMS, is a software application system that monitors professional development for CPM users; keeps track of progress; allows interaction with others and CPM specialists.

A section in the Teacher tab of the Navigation Bar in the eBook that gives teachers strategies to support students struggling with the English language, specifically reading and writing; includes Introduction, Literacy Guide, Student Strategies, Team Strategies, and Reading Strategies.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x² + x + 1), and (x - 1)(x³ + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Mathematically proficient students look closely to discern a pattern or structure. Students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. 

Appearing routinely throughout the text, Math Notes consolidate core content ideas, provide definitions, explanations, examples, instructions about notation, formalizations of topics, and occasionally interesting extensions or applications of mathematical concepts. These boxes enable students to reference ideas that they missed or have forgotten.

Experience team-worthy math problems