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As People Get Older, They Get Taller
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This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data ...

This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data analysis concepts and the major theme of analyzing change. In the first lesson, students measure the heights of classmates and older students and construct a table of height and age data to compare them. The second lesson's instructional goal is to understand how change in one variable, age, can relate to change in a second variable, height. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Elana Joram and Christina Hartman
Building a Box
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This lesson helps students develop spatial visualization skills and geometric understanding by ...

This lesson helps students develop spatial visualization skills and geometric understanding by exploring the different nets that can be folded into a cube. The lesson is placed in the context of a young woman who is trying to build a jewelry box. The lesson provides an activity sheet, a link to a helpful applet (Cube Nets, cataloged separately), questions for students and teachers, and ideas for assessment and extensions.

Subject:
Mathematics
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Dr. Bob Mann
Chairs
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This Java applet activity allows students to explore the various situations described ...

This Java applet activity allows students to explore the various situations described in "The Chairs Around the Table" lesson (cataloged separately). The user can select Exploration mode, in which the number of chairs needed for a particular arrangement of tables is displayed; or Guess, in which the user is able to construct an arrangement and then predict the number of chairs. There are two types of tables to choose from and two different table arrangements. Instructions and exploration question are provide.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Chairs Around The Table
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In this lesson from Illuminations, students explore and discover linear relationships. Linear ...

In this lesson from Illuminations, students explore and discover linear relationships. Linear patterns are identified, extended and described verbally, numerically and algebraically through three investigations. Using manipulatives and the linked applet, "Chairs", learners determine the number of chairs needed when the number of tables is known, and vice versa. Instructional plan, questions for the students, assessment options, extensions and teacher reflections are provided.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Samuel E. Zordak
Combinations
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This 2-lesson unit focuses on combinations, a subject related to probability. Students ...

This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Marcy Cook (adapted from "Ideas: Combinations", The Arithmetic Teacher Vol. 36, No. 1, September 1988)
Comparing Connecting Cubes
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In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, ...

In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lesson activities focus on the comparative mode of subtraction as children investigate the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts. The lessons include printable student activity sheets, a bibliography of children's counting books, questions for student discussion and teacher reflection, assessment options, extensions, and links to online applets (cataloged separately).

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Creating, Describing, and Analyzing Patterns
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This unit of four lessons highlights different aspects of students’ understanding and ...

This unit of four lessons highlights different aspects of students’ understanding and use of patterns as they analyze relationships and make predictions, as discussed in the Algebra Standard. In this cluster of activities, students use two interactive math applets (both catalogued separately) to learn about repeating and growing patterns. In the first part, students explore a two-square pattern unit and in the second part, students investigate repeating patterns with pattern units of three, four, and five squares. In Part 3, students analyze repeating patterns of colored cubes and lastly in Part 4, students create growing patterns of colored cubes and compare them to repeating patterns.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Dealing With Data In the Elementary School
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This project-based unit on statistics provides an opportunity for problem solving through ...

This project-based unit on statistics provides an opportunity for problem solving through real-world data collection and analysis. Students follow the seven- step "Elementary Mathematics Research Model" by identifying a research question, predicting the answer, and conducting research to test their hypothesis. Students use the mean, mode and median to analyze their data and use graphs to represent their findings so they can draw and justify conclusions. The lesson plan includes examples, questions for students, and possible assessment and extension ideas.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Do It with Dominoes
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In this 6-lesson unit, students use dominoes to explore four models of ...

In this 6-lesson unit, students use dominoes to explore four models of addition: counting, number line, sets, and balanced equations. They learn about the commutative property, the relation between addition and subtraction, the result of adding 0, and the concept of doubles. Students write story problems which involve the operation of addition and begin to memorize the addition facts. They represent addition in pictures. The various models of addition help students develop a rich conceptual schema for addition. Included are a Bibliography of Counting Books, student materials, questions for student and teacher reflection, assessment and extension ideas. [Suggestion: Use the alternate applet, Pan Balance - Numbers, listed as a Related Resource, rather than Pan Balance - Shapes, in Lesson 4.]

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Eat Your Veggies
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In this 7- lesson unit students use tallies, pictographs, bar graphs, line ...

In this 7- lesson unit students use tallies, pictographs, bar graphs, line plots, circle graphs, box-and-whisker plots, and glyphs to collect and display data about healthy eating. The unit includes lessons in which two sets of data are being compared and data sets are being analyzed for measures of central tendency (mean, median, mode). Learning objectives, materials, student questions, extensions, teacher reflections, and links to create graphs virtually are included.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
The Factor Game (i-Math Investigations)
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An online, interactive, multimedia math investigation. The Factor Game engages students in ...

An online, interactive, multimedia math investigation. The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers.

Subject:
Mathematics
Algebra
Numbers and Operations
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Fair and Square: Using Concrete-Pictorial-Abstract Activities to Maximize Area
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Through this four part lesson students develop an understanding of the relationship ...

Through this four part lesson students develop an understanding of the relationship between area and perimeter. The lesson involves students making human rectangles, exploring geoboard connections, playing perimeter war, and playing Square Off from Calculation Nation. The lesson plan includes all data collection worksheets, games pieces, link to Calculation Nation, extension and assessment ideas.

Subject:
Mathematics
Algebra
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
S. Rosen
Fractional Clothesline
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This lesson fosters a student's conceptual fraction sense with proper fractions, improper ...

This lesson fosters a student's conceptual fraction sense with proper fractions, improper fractions, and mixed numbers by placing thirty fraction cards in order between given whole numbers on a number line clothesline. Users will visually identify that all proper fractions are grouped between zero and one, and that improper fractions or mixed numbers are all grouped above one. Users also play an estimation game with groups using the same principle. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Corey Heitschmidt
Fun with Fractions
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In this five lesson unit with overview from Illuminations, student activities explore ...

In this five lesson unit with overview from Illuminations, student activities explore relationships among fractions through work with the length model. Students construct fraction strips and use fraction bars throughout the unit to make sense of basic fraction concepts, to compare fractions and order fractions and to work with equivalency in fractions. Specific learning objectives, a material list, an instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given for each lesson.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Tracy Y. Hargrove
Fun with Pattern Block Fractions
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This unit from Illuminations consists of five lessons designed to help students ...

This unit from Illuminations consists of five lessons designed to help students understand fractions when they are represented as a part of a region. Learners investigate relationships between parts and wholes, the relative value of the fraction based on the pattern block shape and equivalency while working with physical and/or virtual pattern blocks. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given for each lesson.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Tracy Y. Hargrove
Geometry and Quantum Field Theory, Fall 2002
Conditions of Use:
Remix and Share
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A rigorous introduction designed for mathematicians into perturbative quantum field theory, using ...

A rigorous introduction designed for mathematicians into perturbative quantum field theory, using the language of functional integrals. Basics of classical field theory. Free quantum theories. Feynman diagrams. Renormalization theory. Local operators. Operator product expansion. Renormalization group equation. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and string theory.

Subject:
Calculus
Geometry
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Etingof, Pavel I.
Get the Turtle to the Pond
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This interactive lesson encourages young students to solve problems by estimating angles ...

This interactive lesson encourages young students to solve problems by estimating angles and distances. They use an applet to give LOGO-like commands, e.g. forward (length), turn (right or left) to make a path that moves a turtle to a pond. Students can create a Path 1 and Path 2 and try to minimize the total path length. There is a newer applet (Turtle Pond, cataloged separately) that allows for adding or editing the commands and a choice of right angles only, or angles in multiples of 15 degrees. The lesson provides suggestions for implementation and discussion questions.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
L.O.Cannon, et.al. (Univ. of Utah)
How Many More Fish?
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The activities in this 6-lesson unit use fish-shaped crackers to help students ...

The activities in this 6-lesson unit use fish-shaped crackers to help students develop their understanding of comparative subtraction by exploring five meanings of subtraction (counting, sets, number line, balance, and inverse of addition). Students investigate properties of subtraction, represent subtraction with objects and pictures, record subtraction with vertical notation and equations, create and solve problems, and carry out missing addend activities. Lessons include questions for student discussion and teacher reflection, extensions, printable student sheets, assessment options, and links to online applets.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Illuminations: Combinations
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This 2-lesson unit focuses on combinations, a subject related to probability. Students ...

This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Marcy Cook
Interactive Geometry Dictionary: Areas in Geometry
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The applets in this Interactive Geometry Dictionary (IGD) will allow students an ...

The applets in this Interactive Geometry Dictionary (IGD) will allow students an opportunity to explore finding the area of some common shapes. The applets demonstrate how to find the area of a triangle using the area of a parallelogram, which in turn can be found using the area of a rectangle. This tool also supports the lesson "What's My Area" cataloged separately.

Subject:
Mathematics
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations