Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

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This 46-page pdf document demonstrates the connections between the CCSS content standards and the mathematical practice standards. It is a compilation of research, standards from several states, instructional strategies, common misconceptions, and examples for each standard at the grade 1 level. It is intended to help teachers understand what each standard means in terms of what students must know and be able to do. Additional flip books are cataloged separately for grades K and 2-5. | Instructional Strategy, Reference Materials Grade Level: 1 | |

This web page provides links to resources aligned to the CCSS that guide and support first grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS) and Problems of the Month, (POM home page is cataloged separately) developed by the Noyce Foundation are included. The activities were designed to measure students' ability to solve non-routine problems, explain and justify their solutions, and promote high level thinking skills. Resources are listed for specific grade 1 standards and are also organized by progression for an alternate search route. | Instructional Strategy, Problem Set, Reference Materials Grade Level: 1 | |

This set of three challenges promote strategic thinking and offer opportunity for discussions about probability with young children. The player must attempt to complete each interactive activity in as few throws of the die as possible. With each challenge an additional rule is added to the play. Included in this resource are tips for getting started, possible solutions, a teacher resource page, and a printable version of the challenges. | Activity, Game Grade Level: 1, 2 | |

This problem, from the collection of Aunty Mathilda challenges, promotes algebraic thinking and problem solving strategies. Aunty Math must determine the individual weight of her two nephews and niece given clues about their combined weight. Included are links to an easier challenge and to a harder one, depending on the level of the solver, and a link to a page for parents and teachers with additional background support, alignment to the CCSS, explanations and extensions. | Activity Grade Level: 1, 2, 3 | |

In this lesson students use a rule of thumb about the weight of babies to practice doubling and halving numbers. They complete an organized table and compare data using vertical and horizontal double bar graphs. The lesson includes a student activity sheet and extension ideas. | Activity, Lesson Plans Grade Level: 1, 2 | |

This 8-page monograph explains bansho, a research-informed instructional strategy for mathematical communication and collective problem-solving. Following a brief overview, the article outlines how bansho can be used to plan and implement an effective three-part problem-solving lesson. Bansho can be incorporated into collaborative planning sessions, in which teachers work with partners or in groups within communities of practice to learn about mathematics for teaching. The author provides a sample grade 2 lesson on the development of multiplication concepts and a list of references. | Instructional Strategy, Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5 Resource is part of a PD collection | |

In this lesson plan students conduct a survey of ten students, collect data in a tally chart, and then display and analyze the results in a bar graph. In the analysis students must compare numbers, add, and subtract using the data in the bar graph to generate questions as well as answer them. The lesson plan includes a graph template, a link to an interactive graphing tool, extension questions, and a fact family sheet to show the related facts from their graph analysis. | Activity, Lesson Plans Grade Level: K, 1, 2 | |

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet. | Activity, Instructor Guide/Manual, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

In this Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf). | Activity, Lesson Plans Grade Level: K, 1, 2 | |

This formative assessment lesson is intended to help teachers assess how well students are able to use addition and subtraction in a problem solving situation. In particular, this lesson aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data, examining the data and looking for patterns and lastly describing and explaining findings clearly and effectively. | Activity, Lesson Plans Grade Level: K, 1, 2, 3 |