Operations and Algebraic Thinking

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

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This narrative document describes the progression of Counting and Cardinality and Operations and Algebraic Thinking across the K-5 grade band. It is informed both by research on children's cognitive development and by the logical structure of mathematics. The document discusses the most important goals for elementary students that of understanding and using numbers. The focus is on the basic operations—the kinds of quantitative relationships they model and consequently the kinds of problems they can be used to solve as well as their mathematical properties and relationships. | Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5 | |

This interactive Flash applet includes single-step and multi-step whole number word problems at two levels: (1) addition and subtraction, and (2) multiplication and division. Students enter their answers to displayed problems and are either rewarded with a "home run" or given the option for a hint to help them correct an error. If, after asking for help, a student still answers incorrectly, the program provides a solution. The difficulty level gradually increases throughout any round of 15 (level 1) or 12 (level 2) problems. | Activity, Interactive Media Grade Level: 2, 3, 4, 5 | |

This problem from Figure This! helps students develop problem solving skills and algebraic thinking while practicing number operations. Students are challenged to use combinations of stamps of two different denominations to make a specific total. The "Try These" feature provides further challenges. The Answer page offers four different solution approaches. "Did You Know?" presents several related facts. The activity includes a page of print and Internet resources. Figure This! also provides information and support for families. | Activity Grade Level: 3, 4, 5, 6+ | |

This problem allows students to explore introductory multiplication and division concepts in the context of sharing cookies ("biscuits" in the UK). Cookies are displayed in two different arrays, and students are challenged to divide them equally among two, three, five, and six people and to deal with remainders. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable sheet (pdf). | Activity Grade Level: 1, 2, 3 | |

This iOS app presents a scramble style game which requires players to fill in the missing pieces of the equations using the numbers and operations given below each puzzle. These equations must match-up both horizontally and vertically. The game progresses through five levels of difficulty, with each level including twenty-five unique puzzles. | Activity, Interactive Media, Mobile App Grade Level: 3, 4, 5 | |

This document provides descriptions and examples of what each Mathematics Common Core standard means a Grade Three student will know, understand and be able to do. This "unpacking" of the standards provides instructional guidelines and was developed to assist North Carolina educators teach the Mathematics Common Core (Standard Course of Study). | Reference Materials Grade Level: 3 | |

In this PBS Mathline lesson plan, students investigate proportional reasoning through modeling, student sharing and questioning techniques. After reading "Oliver's Fruit Salad" to students, the teacher poses several problems about imaginary fruit salads that the students solve as a class. Using pieces of fruit shaped candy, students work in pairs and in small groups to solve other problems that build on the ones solved as a class. Finally, students share their solutions. | Lesson Plans Grade Level: 3, 4, 5 | |

This website for teachers offers tasks to integrate personal finance into the teaching of the CCSS in Mathematics. It provides teachers with Common Core aligned tasks that connect the Common Core to applications of the Big Ideas of Personal Finance. Tasks include teacher notes, printable student worksheets, and sample solutions. | Lesson Plans, Problem Set Grade Level: K, 1, 2, 3, 4, 5 | |

In this problem learners explore square numbers and the relationships between them while practicing basic number skills. By applying a systematic strategy they determine three numbers that satisfy the conditions of the scenario. There are links to hints and a solution page; Teachers' Resources include suggestions for implementation, reflection, and differentiation. | Activity, Instructional Strategy Grade Level: 3, 4, 5 | |

In this 5-minute video third grade teacher Jean Saul demonstrates how she uses problem solving tasks to create a classroom climate that fosters persistence, independence, responsibility, and risk-taking. Students are asked to find three different methods for solving each problem and to record them on a Choose Three Ways graphic organizer. Through collaboration and presentation of their work to peers, students develop math language and discourse skills. A side bar provides reflection questions. Supporting materials include a transcript of the video (doc), the graphic organizer (doc), and two samples of student work (pdf). | Instructional Strategy, Video Grade Level: 3, 4, 5 Resource is part of a PD collection |