Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

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Resource | Resource Type Grade Level | Rating |
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This FAQ from the Teacher2Teacher service at The Math Forum @ Drexel contains many suggestions for learning multiplication facts. It includes ideas contributed by T2T Associates and teacher participants. There are links to Ask Dr. Math resources, children's literature connections, and outside websites with related recources. | Instructional Strategy, Reference Materials, Community Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

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 | |

In this problem students apply different strategies to solve a problem involving multiples and remainders. The problem provides clues about dividing a specific number of lollipops equally and asks solvers to determine possible totals. The problem presents three partial approaches and asks solvers to complete them. This resource includes hints for getting started, previously submitted solutions, and a teacher page with implementation suggestions, discussion questions, and differentiation strategies. | Activity, Instructional Strategy Grade Level: 3, 4, 5 | |

This packet of information for teachers is designed to be used with the Wooden Legs Problem of the Week from the Math Forum collection for grades 3 to 5. The sample problem provides an exemplar of the type of problem teachers can use to promote students' mathematical thinking and engage their interest. The key concepts in this problem include pattern identification and multiples. The packet contains the sample problem, standards alignment to the Common Core State Standards, possible solutions, teaching suggestions, a print-ready copy of the problem, and a problem-specific scoring rubric. | Assessment, Activity, Instructional Strategy, Instructor Guide/Manual Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This interactive Flash book, one in Greg Tang's series that combines math with poems and pictures, challenge learners to calculate how many objects are in each scene by thinking quickly in groups rather than counting. This more advanced book focuses on smart grouping strategies that make computations faster, easier and more accurate by looking for patterns, symmetries and rearrangements. | Activity, Interactive Media, Illustration, Video 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 | |

This one-page article describes and illustrates how arrays can be used to represent many number concepts, including building multiplication facts, commutativity, parity (odd/even), and exploring factors, prime numbers, and square numbers. | Instructional Strategy, Reference Materials, Article Grade Level: 1, 2, 3, 4, 5 Resource is part of a PD collection | |

This lesson helps students develop conceptual understanding of 2-digit multiplication. Students decompose 2-digit numbers, model area representations using the distributive property and partial product arrays, and carry out paper-and-pencil calculations from the arrays. Included are student activity sheets, a link to a supporting online applet, and extension suggestions. | Activity, Lesson Plans Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This problem provides an opportunity for students to practice counting and to represent and record findings in different ways: "Noah saw 12 legs walk by into the Ark. How many creatures did he see?" Multiple solution possibilities encourage students to be systematic in their strategies. The Teachers' Notes page offers suggestions for implementation, discussion questions, and an idea for extension. | Activity Grade Level: K, 1, 2, 3 | |

This interactive application helps students to learn visually about numbers from their possible arrangements and how those arrangements relate to division, multiplication, and factors. The web applet divides numbers and displays calculation to show the remainder as a number, fraction, or decimal value and allows demonstration of types of numbers such as prime, square, and triangular. The number explorer has automated tests for divisibility, factor pairs, or prime factors. Three different shapes can be used, the original fish swim around and obediently arrange themselves to show number properties. However balls or cards cards can be used instead, these animate faster and are better for displaying numbers. | Activity, Demonstration, Interactive Media, Video Grade Level: 3, 4, 5 |