Standards for Mathematical Practice

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Resource | Resource Type Grade Level | Rating |
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This applet provides students with tools to investigate the relationships among the measures of a circle. Students can resize a circle and record measurements to discover the circumference to diameter ratio, for example. A video clip, assignments, and a set of application problems is provided. For upper level students, lessons are provided for formally measuring and calculating circumference and area with pi. | Activity, Interactive Media Grade Level: 4, 5, 6+ | |

This Sketchpad activity, which opens on Geometer's Sketchpad and on iOS with Sketchbook Explorer (cataloged separately), allows players to learn about the use of symbols and variables as a way to represent numbers as students solve puzzles involving two unknowns using algebraic thinking. The sketch displays eight rows of symbols and each row presents a different combination of squares and circles. When students drag a row of symbols across the vertical divider line, the sketch displays the sum of the symbols. By dragging two or more rows, students gather information and determine the value of the circle and the square. Overview instructions and teacher notes are available as downloadable PDF. | Activity, Game, Interactive Media Grade Level: 4, 5 | |

In this blog entry Michelle Flaming describes what the implementation of MP 8 looks like in the classroom. She lists student actions, teacher actions, and open-ended questions that teachers can ask students to elicit the kind of reasoning called for in MP 8. | Reference Materials, Community Grade Level: K, 1, 2, 3, 4, 5 Resource is part of a PD collection | |

This brief article relates the legend of young Gauss and the summing of consecutive numbers. Readers are asked to apply the method and they are shown a general solution. A link to a printable page is provided as well as links to related topics. | Reference Materials, Article Grade Level: 3, 4, 5, 6+ | |

This activity and Java applet allows a student to explore modular arithmetic. It is also a tool for finding remainders where all the possible numbers (the numbers less than the divisor) are put in a circle or clock. The learner uses the scroll bar to modify the size of the clock from 2 to 26 hours, sets a starting value and then moves the "clock" forward a number of specified hours to see the resulting sum. Support pages for the learner and the instructor are included. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This interactive Java applet helps students analyze and extend patterns. The applet displays a pattern of beads and the user selects colors in the correct sequence to continue the pattern. The applet acknowledges each correct solution and encourages the user to fix any incorrect ones. | Activity, Interactive Media Grade Level: Pre-K, K, 1 | |

This series of nine articles interprets and illustrates each of the eight Mathematical Practices of the Common Core State Standards as they might be exemplified in grades K-5. The final article sheds light on how curriculum needs to connect the Practices with the Content Standards. | Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5 Resource is part of a PD collection | |

This lesson provides practice in converting common fractions (tenths, fifths and halves) to decimal equivalents and expressing decimals (tenths) as equivalent fractions in reduced form. It includes instructions and a link to an interactive Java applet. Students get feedback for each of the 18 examples in a round. A downloadable student worksheet with warm-up and follow-up exercises is included in Word and pdf formats. | Activity, Interactive Media, Lesson Plans Grade Level: 4, 5 | |

These 5 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce learners to making conjectures and using counterexamples in proofs. Investigations into the theory of numbers provide the content. Supporting documents, and progress indicators are included. | Activity, Instructor Guide/Manual, Illustration Grade Level: 4, 5, 6+ | |

In this investigation students explore the concept of ratios and their relationship with factors and multiples. Given an assortment of cogs (gears) with different numbers of teeth, solvers are asked to find which pairs allow for each tooth of one to fit into every gap of the other, and to form conjectures regarding which pairs would work generally. The problem is well-suited for group work. The Teachers' Notes page offers suggestions for implementation, key questions, student sheets, and links to articles, videos, and an interactive Cog Environment (cataloged separately). | Activity, Interactive Media, Video Grade Level: 3, 4, 5, 6+ |