Operations and Algebraic Thinking

Write and interpret numerical expressions.

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Resource | Resource Type Grade Level | Rating |
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This Java applet allows the user to explore a variety of "spot" patterns. The tool generates an initial pattern and the learner must determine how many spots are contained in the next term and eventually a rule or expression to describe the growing pattern. A player can select the color of the spots as well as the level and type of pattern from a pull down menu. | Activity, Interactive Media Grade Level: 3, 4, 5, 6+ | |

This problem offers a simple context to begin an exploration of the properties of numbers and to make conjectures about those properties. Learners explore the sums of consecutive numbers and whether all positive numbers from 1-30 can be written as the sum of two or more consecutive numbers. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support. | Activity Grade Level: 3, 4, 5, 6+ | |

This lesson from Illuminations provides an introduction to the use of variables, and develops students' algebraic thinking. Students create variable machines to discover the value of words by assigning each letter of the alphabet a unique number value. Learning objectives, a materials list, a pdf file of the student worksheet, an instructional plan, questions for the students, assessment options, extensions, and teacher reflections are provided. | Lesson Plans Grade Level: 3, 4, 5 | |

Villainy, Inc. is a website devoted to helping upper elementary grade students build and use problem-solving skills to solve unique and complex mathematical problems. Students become undercover agents working to thwart the evil Dr. Wick, ID and his often-zany schemes to take over the world. Student activities include finding areas of rectangles, calculating with decimals and percents, finding averages, estimating and comparing whole numbers and decimals, all presented in the context of an animated and interactive cartoon story. Students complete one or both of the missions online. Teachers editions for each mission are provided, as well as additional tips, answer keys, printable worksheets and connections to standards. Note that it is not possible to save work online. | Activity, Interactive Media, Video Grade Level: 4, 5, 6+ | |

This problem provides an opportunity to introduce a visual way of representing operations on unknown numbers to help lead students to using a symbolic representation. Learners are asked to think of a number and then through an interactivity are given a sequence of operational instructions to follow which leads all students to the same final number. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support. | Activity, Interactive Media Grade Level: 5 | |

This problem provides an opportunity to introduce the concept of representing operations on unknown numbers algebraically and leads to work on inverse operations. Students are asked to think of a number, follow a sequence of computational instructions and finally to enter the result into the "machine." Students explore how the "machine" works out the starting number. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support. | Activity, Interactive Media Grade Level: 5, 6+ |

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