Standards for Mathematical Practice

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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+ | |

This activity promotes algebraic thinking as a player must find the value of each of the three objects in a 3 by 3 or a 3 by 4 grid puzzle. The numbers given represent the sum of the objects in each row or column. | Activity, Interactive Media Grade Level: 4, 5, 6+ | |

This 1-minute video created by the UK Department of Education as an algebra lesson starter is based around how many friends can sit at a birthday party table. The video shows the birthday boy and girl sitting at opposite ends of the table with their guests sitting two on either side. As more tables are added and the number of children grow, a pattern starts to appear. Children are asked to predict how many children could come to the party if there were 100 tables. | Instructional Strategy, Video Grade Level: 3, 4, 5 | |

This interactive Java learning tool, which was constructed using the cross-platform open educational resource GeoGebra, allows a teacher to demonstrate and explore evaluating algebraic expressions with students. Choose from four algebraic expressions and use sliders to select the value of the variable (-10 to 10) and any parameters. Show or hide the algebraic expression, the expression with substitution, the notation shown for multiplication or division, and the result. Values range from -10 to 10 and can be integers or intervals of one tenth. | Demonstration, Interactive Media Grade Level: 4, 5, 6+ | |

This interactive Java learning tool allows a teacher to demonstrate and explore with students number line models for two simple variable expressions for multiplication. The first expression is a variable with an understood coefficient of one and the second is the multiplication of a variable by a coefficient. Sliders are used to select the value of the variable (-10 to 10) and the coefficient (0 to 10). Check boxes show or hide the algebraic expression, the expression with substitution, the notation shown for multiplication, the result, and a model for the multiplication, shown as jumps along a number line. | Demonstration, Interactive Media Grade Level: 5, 6+ | |

This Flash activity provides an opportunity for learners to develop their algebraic thinking skills. The activity uses objects in place of variables making this activity accessible to students in upper elementary grades. Learners are presented two or three weighing scales and must determine the weight of a specific object or group of objects. There are ten questions for each of the 3 levels of play and hints are provided for incorrect answers. | Activity, Interactive Media Grade Level: 4, 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 activity reinforces the concepts of area and perimeter and their independent relationship. Students analyze and compose shapes made from unit squares that satisfy area and perimeter specifications. Ideas for implementation, extension and support are included along with printable sheets and shape cards. | Activity Grade Level: 3, 4, 5 | |

This Sketchpad activity, which opens on Geometer's Sketchpad and on iOS with Sketchbook Explorer (cataloged separately), promotes logical reasoning skills and informally introduces the concept of sets. Student create Venn diagrams by arranging two or three different colored circles and placing given numbers in them to produce target sums. Sketchpad generates random challenges for the students, or they can create their own problems to share. The resource provides a movie with detailed instructions and downloadable PDFs: teacher notes and a student worksheet. | Activity, Game, Interactive Media, Video Grade Level: 3, 4, 5, 6+ | |

In this 2-minute video, teacher Andrew Crandall demonstrates and discusses a strategy for quick, informal assessment at the end of class for the purpose of planning future lessons. While the example shown involves patterns and multiplication, the practice can be applied to any content. The page provides questions for teacher discussion and a transcript of the video (doc). | Assessment, Instructional Strategy, Video Grade Level: 1, 2, 3, 4, 5 |