Special | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | ALL
Learning Management System
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.
Mode of Instruction: Teamwork Purpose: Focus attention
Objective: To establish mathematics goals to focus learning, specific roles situated actions to move through a learning progression. Teacher monitors each team role through circulation.
In teams, two team members are mathematicians and two team members are observers. Team Member (1) and Team Member (2) problem solve, sharing explanations aloud. Team Member (3) listens to Team Members (1) and (2) and asks clarifying questions, as needed. Team Member (4) records observations about explanations and attitudes of participants, but Team Member (4) remains silent throughout the activity. After the assigned time—15 minutes—Team Member (4) shares notes and observations. Team Members (1), (2), and (3) may share their perspectives, as well. Variations of this activity include multiple rounds with the roles rotated to other members.
Look for and make use of structure
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.
Make sense of problems and persevere in solving them
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.
Mastery Over Time
CPM's Mixed, Spaced Practice provides students an opportunity to achieve conceptual understanding over time. Students must have the opportunity to engage meaningfully with and make sense of concepts before they are expected to have mastery.
Mode of Instruction: Independent/Teacher-led Purpose: Silent reflection
Objective: To establish mathematics goals to focus learning, students silently contemplate topics that generate ideas within learning progressions. Teacher observes to make instructional decisions.
Students participate in the silent activity to reflect, summarize ideas, generate ideas, assess learning, or solve problems. Display posters with one topic or concept on each poster. Students use a writing utensil and circulate to each poster. Student (1) adds one brief note or explanation to the poster. Time for activity varies depending on the topic. You may want to consider using a timer to help pace the time at each poster.
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.
Mathematical Content Outcome 1
Experience team-worthy math problems