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.

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.

An applet for students to use in exploring the area and circumference of a circle in relation to its radius and diameter. When the radius is changed, the other measures automatically change and are shown on a board. Most importantly, the ratio between any pair of these measures can be shown.

This applet allows students to investigate the relationships between the area and circumference of a circle and its radius and diameter. There are three sections to the site: Intro, Investigation, and Problems. In the Intro section, students can manipulate the size of a circle and see how the radius, diameter, and circumference are affected. Students can also play movie clip to visually see how these measurements are related. The Investigation section allows students to collect data points by dragging the circle radius to various lengths, and adding and recording the data to a table which records the radius, diameter, circumference and area. Clicking on the x/y button allows students to examine the relationship between any two measures. Clicking on the graph button will take students to a graph of the data. They can plot any of the four measures on the x-axis against any of the four measures on the y-axis. The Problems section contains questions for students to solve and record their answers in the correct unit.

In this data collection and analysis activity students investigate data in connection with recyclable materials and develop plans to help the environment. This activity requires students to keep track of their own paper use for a week, graph the data with a line graph and then interpret their results with a partner. The lesson includes student worksheets and extension suggestions.

This lesson develops number skills, understanding of coin values, and the concept of equivalence. Students use coin blocks, concrete representations of the value of coins (pennies, nickels, dimes, and quarters), to compose and decompose values up to a dollar. The resource includes a 3-minute video for teachers on how to build the coin blocks prior to the lesson. An interactive game, Coin Box, provides additional practice for students and is cataloged separately.

In this Flash game, students may use a variety of activities to practice counting, collecting, exchanging, and making change for coins. Coin representations may show their amounts or not; coins may also be represented by coin tiles on a 10x10 grid, to help visualize their values. The five activities are: count, in which students determine the value of a given set of coins; collect, in which students choose coins to represent a given value; exchange, in which students use the smallest number of coins to represent a given value; change from coins, in which students are given a set of coins and asked how much change would be for a dollar (essentially counting up); and change from value, in which students are given a price owed (from a dollar) and asked to make change. There is a "bank" at the lower left side of the applet in which coins may be exchanged for other coins of the same value.

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.

In this lesson plan students learn to create bar graphs using unifix cubes, translate this representation to graph paper, and then compare the data that has been collected and displayed. Students are encouraged to make up their own questions about the data (favorite juice) and to practice with multiple sets of data. Sample questions for students and extension ideas are included. The lesson contains links to a PDF of graph paper and the Bar Grapher tool which is cataloged separately in this database.

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).

This familiar game can be played by one or two players taking turns. Players choose to match equivalent representations of numbers, shapes, fractions, or multiplication facts. The game can be played in clear pane mode, or for added challenge, with the windows closed.

This unit contains two lessons which help students develop number sense through activities involving collection, representation, and analysis of data. Students also practice reading and writing large numbers and develop estimation skills. In Lesson 1, Every Breath You Take, students estimate the number of breaths taken during a specified time, experiment, and display real-life data. In Lesson 2, Making Your First Millions, students develop the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition. They analyze situations and identify patterns that will enable them to develop the concept of large numbers. Each lesson includes student activity sheets, an instructional plan, and extensions.

This place value and problem solving lesson focuses on forming 3-digit address numbers to meet specific requirement. The lesson provides an opportunity for learners to use the problem-solving strategies of looking for patterns and establishing an organized list. Students also learn that careful reading of information and understanding of mathematical language are important to finding appropriate solutions.

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.

This interactive applet helps students develop spatial visualization skills and geometric understanding in both two and three dimensions. From an array of possible nets, students try to select the ones that actually fold to a cube. The applet supports the lesson Building a Box (cataloged separately). An animation that shows one net being folded is included.

In this lesson, students will use formulas they have explored for the volume of a cylinder and convert them into the same volume for rectangular prisms while trying to minimize the surface area. Various real world cylindrical objects will be measured and converted into a prism to hold the same volume. As an extension, students may design and create a rectangular prism container according to their dimensions to compare and contrast with the cylinder.

Students use this interactive tool to explore the connections between data sets and their representations in charts and graphs. Enter data in a table (1 to 6 columns, unlimited rows), and preview or print bar graphs, line graphs, pie charts, and pictographs. Students can select which set(s) of data to display in each graph, and compare the effects of different representations of the same data. Instructions and exploration questions are provided using the expandable "+" signs above the tool.

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.

Okta challenges you to a duel! That crazy octopus wants to play you in a game where the first person to choose cards with a specified sum wins. You can choose how many cards, what types of numbers, and Okta's level of strategy.

This lesson plan introduces the game Deep Sea Duel, which develops students' operation skills and strategic thinking, and can be played online or with cards. After playing several variations of the game, students attempt to identify a winning strategy and compare the game to other familiar games. Variations include whole numbers, decimals, fractions, exponents, and words. The lesson includes printable cards and a student worksheet, questions for student discussion and teacher reflection, assessment options, and extensions. The online game and the cited article are cataloged separately.