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Accessing and Investigating Population Data
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In this activity, students investigate population projections from 1990-2100 using data from the U.S. Census Bureau Web. Using the five specific population pyramids, students investigate population projection data for the United States over a 110-year period. They examine how the population data is distributed over time and explain what factors might contribute to these trends. An activity sheet and thoughtful questions, included in the lesson plan, guide the class investigation.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Adding It All Up
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"In this lesson, students draw various polygons and investigate their interior angles. The investigation is done using both an applet and paper and pencil to foster an understanding of how different patterns can lead to the same solution. After comparing results with a partner, students develop a formula showing the relationship between the number of sides of a polygon and the sum of the interior angles." (from NCTM Illuminations)

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
National Council of Teacher's of Mathematics
Adjacent Circles (number of possible combinations)
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In this lesson, "students are encouraged to discover all of the combinations for a given situation. They use problem-solving skills (including elimination and collection of organized data) to draw conclusions. The use of higher-level thinking skills (synthesis, analysis, and evaluations) is the overall goal." (from NCTM's Illuminations)

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Alike and Different
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This lesson focuses on the observation of properties and the classification of objects to build ideas about variables. Learners compare buttons to identify similarities and differences. In addition, learners are introduced to Venn Diagrams by reading "The Elves and the Shoemaker" and sorting their shoes in a giant diagram.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Carol Midgett
Grace M. Burton
NCTM Illuminations
Thinkfinity/Verizon Foundation
All About Multiplication
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This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
All About Multiplication Exploring Equal Sets
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Students explore the set model for multiplication. They find products using equal sets and present their results in a table. Next students apply their knowledge about multiplication in the creation of pictographs (from NCTM's Illuminations website).

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Math
All About Multiplication: Hopping on the Number Line
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"Students generate products using the number line model. This model highlights the measurement aspect of multiplication and is a distinctly different representation of the operation. The order (commutative) property of multiplication is also introduced. Students are encouraged to predict products and to answer puzzles involving multiplication." from NCTM Illuminations.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Math
All About Multiplication: Modeling Multiplication with Rows and Columns
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"This lesson encourages students to explore the array model of multiplication. The lesson focuses on the factors 4 and 6. Students will also explore products with 0 or 1 as a factors. First students make arrays with counters, and then they create a second concrete example of the array model using toothpicks. They also write problems which involve multiplication." (from NCTM's Illuminations) This is lesson 3 in a 4-lesson unit.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Math
All in the Family
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This lesson from Illuminations asks students to use a geometry applet to analyze the characteristics of a square. Graphs are created to show relationships between characteristics (side length, diagonal length, perimeter, area). The lesson involves both algebra and geometry, is appropriate for grades 9-12 and should take one class period to complete.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Allow Me 2 Reiterate
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This lesson from Illuminations teaches students to use a computer algebra system to determine the square root of 2 to a given number of decimal places. Students will learn how utilizing technology makes an algorithm easy to use, as well as using different modes with an iterative algorithm. The lesson is intended for grades 9-12 and should take one class period to complete.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Aluminum Cans
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In this data analysis activity students investigate data in connection with recyclable materials and develop plans to help the environment. Students collect data about aluminum can usage and graph that data in a line plot. The lesson includes student worksheet and extension suggestions.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Amazing Attributes
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In this 5-lesson unit primary students identify attributes of buttons and other objects in their classrooms. Throughout the unit students learn to collect data about objects, display the data (Venn diagrams, pictographs, and bar graphs), and analyze the data to determine what this tells us about buttons and/or other objects. Each of the five lesson plans includes necessary student/class worksheets, questions for students, extension ideas, and assessment ideas. Lessons 2 and 3 reference stories that are an important part of the skill development: "The Button Box" by Margarette Reid and "The Elves and the Shoemaker" story.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton and Carol Midgett
Angle Sums
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"Examine the angles in a triangle, quadrilateral, pentagon, hexagon, heptagon or octagon and find a relationship between the number of sides and the sum of the interior angles." (Source: 2000-2012 National Council of Teachers of Mathematics)

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Angle Sums
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With this applet, students can examine the angles in a triangle, quadrilateral, pentagon, hexagon, heptagon or octagon. They can change the shape of the figure by dragging the vertices; the size of each angle is shown and the sum of the interior angles calculated. Students are challenged to find a relationship between the number of sides and the sum of the interior angles.

Subject:
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Apple Pi
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In this two-lesson unit, students will "use estimation and measurement skills to determine the ratio of circumference to diameter and explore the meaning of pi. Students will discover the circumference and area formulas based on their investigations." (from NCTM's Illuminations)

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
NCTM/Illuminations
Archimedes' Puzzle
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In this math activity, learners explore the history of the Stomachion (an ancient tangram-type puzzle), use the pieces to create other figures, learn about symmetry and transformations, and investigate the areas of the pieces. The Stomachion, believed to have been created by Archimedes, consists of 14 pieces cut from a square, which can be rearranged to form other interesting shapes.

Subject:
Mathematics
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
NCTM Illuminations
Samuel E. Zordak
Thinkfinity/Verizon Foundation
Area Contractor
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"This lesson gives students the opportunity to explore surface area in the same way that a contractor might when providing an estimate to a potential customer. Once the customer accepts the estimate, a more detailed measurement is taken and a quote prepared. In this lesson, students use estimation to determine the surface area of the walls and floor of their classroom. They check the reasonableness of their estimates, and then measure the classroom for accuracy." (from Illuminations, NCTM)

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Arithme-Tic-Toc
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These activities introduce modular arithmetic in real-world scenarios. Students begin by investigating patterns and relationships that exist in 12-hour addition and multiplication clock tables. All student handouts are included, plus ideas for assessment and class discussion.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
As People Get Older, They Get Taller
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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
Averages and The Phantom Tollbooth Book
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This worksheet uses The Phantom Tollbooth as a literature basis for problem-solving tasks that challenge students to explore the concept of averages.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Baby Weight
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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.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Marcy Cook
Balancing Act
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"Problems such as those in this activity help develop what students already know in preparation for writing equations and learning ways to solve for variables. Students use mathematical models to explore quantitative relationships. When presented with pictures of pan balances with one or more objects in each pan, they communicate relationships between the weights of the objects by comparing the balanced and unbalanced pans." (from NCTM's Illuminations)

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Math
Balancing Algebraic Understanding
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"Using a balance in the classroom is a first step to algebraic understanding. Use this pan balance (numbers) applet to practice the order of operations in simplifying numerical expressions and to demonstrate the conventions of using algebraic logic in simplifying expressions" (from NCTM's Illuminations). Lesson 2 of a three lesson unit.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Balancing Shapes
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"Students will balance shapes on the pan balance applet to study equality, essential to understanding algebra. Equivalent relationships will be recognized when the pans balance, demonstrating the properties of equality." (from NCTM's Illuminations)

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Bar Graph Investigations
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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.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Barbie Bungee
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In this lesson, students model a bungee jump for a Barbie doll. They collect data in a table (number of rubber bands and jump distance), then create a scatterplot of the data, find its line of best fit, and write an equation of that line. Students go on to analyze the equation, noting its slope in relation to the data collected, and the meaning of the y-intercept. Since the distance to which the doll will fall is directly proportional to the number of rubber bands, the lesson provides a scenario for examining linear functions.

Subject:
Mathematics
Algebra
Functions
Numbers and Operations
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Zordak, Samuel E.
Barbie Bungee (linear functions)
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The consideration of cord length is very important in a bungee jump‰ŰÓtoo short, and the jumper doesn't get much of a thrill; too long, and ouch! In this lesson, students model a bungee jump using a Barbieĺ¨ doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
NCTM Illuminations
Samuel E. Zordak
Thinkfinity/Verizon Foundation
Bean Counting and Ratios - NCTM Illuminations
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In this lesson, students apply their knowledge of unit rate and proportions to develop and test a probability model for sampling marked beans from a larger collection of marked and unmarked beans.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Bears in a Boat
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In this math activity, learners are challenged to create aluminum foil boats that will hold plastic bears until the boats sink. The lesson serves as a fun, hands-on way to collect data. Data from two attempts is collected and used to make two class box-and-whisker plots with some surprising results. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

Subject:
Mathematics
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Jim Rubillo
NCTM Illuminations
Thinkfinity/Verizon Foundation
Begin With Buttons
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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.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Begin With Buttons
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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.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Birthday Paradox - NCTM Illuminations
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This activity demonstrates the Birthday Paradox, using it as a springboard into a unit on probability. Students use a graphing calculator to run a Monte Carlo simulation with the Birthday Paradox and perform a graphical analysis of the birthday-problem function.This lesson was adapted from an article, written by Matthew Whitney, which appeared in the April 2001 edition of Mathematics Teacher.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
National Council of Teachers of Mathematics
Block Pounds
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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).

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Block Pounds
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In this lesson,''students explore the use of variables as they solve for the weights of objects using information presented in pictures. They model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols." (from NCTM's Illuminations)

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Math
Bobbie Bear
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This interactive applet introduces students to the topic of combinations, a basic concept in probability. Users create combinations of shirts and pants to determine the total number of possible outfits. They may simply explore by placing the clothes on Bobbie, or make a guess and then test it. The number of shirt and pants choices is customizable. An optional voice provides prompts and feedback.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Bobbie Bear
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Using a virtual manipulative, children construct combinations of different colored shirts and pants to help Bobbie Bear, who is planning a vacation and wants to know how many different outfits he will be able to make from these combinations.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Bouncing Tennis Balls - NCTM Illuminations
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In this lesson students develop their skills in collecting and recording data using the real-world situation of a bouncing tennis ball. They use the data collected to graph and formulate the relationship between the dependent and independent variable in their experiment.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Illuminations National Council of Teachers of Mathematics
Box Plotter
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This Flash tool allows students to make a box plot of their data, using up to four categories of their own choosing, or using one of the data sets provided. The tool will plot all the data together, or break it out by category. Students can set a multiple of the Interquartile Range to be the Extreme Range, and exclude that data from the graph if they wish. Associated lessons (free) and a Mathematics Assessment Sampler (for purchase) are linked at the right side of the page.

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