Standards for Mathematical Practice

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In this series of three hands-on activities, students develop an understanding of the relationship between fractions, decimals, and percents based upon models of hundredths. Each activity requires students to display their one hundred pieces of candy in a different way: linear model, grid model (rectangular area), and region model (circle graph/pie chart). This lesson includes student worksheets, assessment questions, extension suggestions, and a link to a circle graph tool. | Activity, Lesson Plans Grade Level: 4, 5 | |

This 13-minute video shows Becky Pittard's class of 5th graders reasoning about multiplying fractions. This lesson is based on a real world problem and incorporates correct and incorrect models in order to get students to determine what a part of a part should look like. Included with this resource is a transcript of the video, a copy of the lesson plan, and the student's worksheet all in PDF form. | Lesson Plans, Video Grade Level: 4, 5, 6+ | |

This activity gives students a chance to visualize a two-dimensional net of a three-dimensional object. Students are shown three views of a decorated cube and a net of six plain squares. They must decorate the net so that it folds to a cube consistent with the views. An interactive applet is provided. Ideas for implementation, extension and support are included along with three printable sheets (pdf). | Activity, Interactive Media Grade Level: 4, 5 | |

This set of three interactive challenges from the Annenberg Teachers' Lab has learners develop spatial visualization skills. In "I Took a Trip on a Train," in "Plot Plans and Silhouettes" and in "Shadows" learners solve problems involving visual perspective. Background discussion and NCTM standards information is included. | Activity, Interactive Media Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This 440-page report explores how students in pre-K through grade 8 learn mathematics, with a focus on number and operations, and recommends how teaching, curricula, and teacher education should change to improve mathematics learning. (A 39-page summary, Helping Children Learn Mathematics, is catalogued separately.) The authors identify five interdependent components of mathematical proficiency and describe how students develop this proficiency. The report presents a portrait of mathematics learning: research findings on what children know about numbers before they arrive in pre-K and the implications for instruction; details on the processes by which students acquire mathematical proficiency; what is known from research about teaching for mathematics proficiency and developing proficiency in teaching. Visitors to this website may read the full text online, download a copy (pdf), or purchase a hard copy. | Reference Materials Grade Level: Pre-K, K, 1, 2, 3, 4, 5, 6+ | |

Teachers can use this interactive tool to help students build a conceptual understanding of adding fractions with common denominators by linking visual models to procedures. Students first add using models, and then progress to using numbers. This page includes a video demonstration of the tool and sample lessons from the Conceptua curriculum. Free registration is required to use the tool. A paid subscription is necessary to access full curriculum and allow full student use. | Activity, Demonstration, Interactive Media, Lesson Plans, Video Grade Level: 3, 4, 5, 6+ | |

This virtual manipulative allows a teacher or student to represent a linear equation and solve it through the use of a balance beam. Unit blocks (representing 1s) and x-boxes (representing the unknown), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, the learner can choose to perform any arithmetic operation to both sides of the equation keeping the beam balanced. The goal, of course, is to get a single X-box on one side, with however many unit blocks needed for balance thus giving the value of x. There is also the option of creating your own equations to solve. | Activity, Interactive Media Grade Level: 5, 6+ | |

This session, the first one in the Annenberg series "Patterns, Functions, and Algebra" enables the teacher to discover what it means to think algebraically, and to learn to use algebraic thinking skills to make sense of different situations. Topics covered include describing situations through pictures, charts, graphs, and words; interpreting and drawing conclusions from qualitative graphs; and creating graphs to match written descriptions of real-life situations. The session includes sequentially organized problems, video viewing, interactive activities, readings, and homework. The materials may be used on your own, in a study group, or as a facilitated online course for graduate credit, which is offered at a reasonable cost. | Course, Unit of Instruction Grade Level: 3, 4, 5, 6+ Resource is part of a PD collection | |

This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus. | Activity, Instructional Strategy, Lesson Plans, Unit of Instruction Grade Level: 3, 4, 5 | |

In this data analysis activity students investigate data in connection with recyclable materials and develop plans to help the environment. Students collect data about aluminum can usage and graph that data in a line plot. The lesson includes student worksheet and extension suggestions. | Activity, Lesson Plans Grade Level: 3, 4, 5 |