Students create their own spinners and examine the outcomes given a specified ...

Students create their own spinners and examine the outcomes given a specified number of spins in this student interactive, from Illuminations. Students learn that experimental probabilities differ according to the characteristics of the model. Students can also discuss how does the experimental probability compare with the theoretical probability?

Using tiles to represent variables and constants, learn how to represent and ...

Using tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.

Students compare the relationships between radius, diameter, circumference, and area by manipulating ...

Students compare the relationships between radius, diameter, circumference, and area by manipulating a circle and increasing or decreasing its size in this interactive from Illuminations. It also provides a problems section where students determine the answer to each question using the applet, a calculator, or paper and pencil. They must also indicate the proper units!

This lesson from Illuminations illustrates how weather data can be collected and ...

This lesson from Illuminations illustrates how weather data can be collected and examined. In the first part, Collecting and Examining Weather Data, students organize and then examine data that has been collected over a period of time in a spreadsheet. In the second part, Representing and Interpreting Data, students use the graphing functions of a spreadsheet to help them interpret data.

The Greek mathematician Archimedes approximated pi by inscribing and circumscribing polygons about ...

The Greek mathematician Archimedes approximated pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. Similarly, the value of pi can be approximated by calculating the areas of inscribed and circumscribed polygons. This activity allows for the investigation and comparison of both methods.

This student interactive, from Illuminations, allows students to explore the conditions that ...

This student interactive, from Illuminations, allows students to explore the conditions that guarantee uniqueness of a triangle, quadrilateral, or pentagon regardless of location or orientation. Each set of conditions results in a new congruence theorem.

This three-part example from Illuminations highlights different aspects of students' understanding and ...

This three-part example from Illuminations highlights different aspects of students' understanding and use of patterns as they analyze relationships and make predictions, as discussed in the Algebra Standard. This first part, Making Patterns, includes an interactive figure for creating, comparing, and viewing multiple repetitions of patterns. The interactive figure illustrates how students can create pattern units of squares, then predict how patterns with different numbers of squares will appear when repeated in a grid, and check their predictions. In the second part, Describing Patterns, examples of various ways students might interpret the same sequence of cubes are given. This illustrates the importance of discussing and analyzing patterns in the classroom. The third part, Extending Pattern Understandings, demonstrates ways in which students begin to create a 'unit of units,' or a grouping that can be repeated, and begin to relate two patterns in a functional relationship. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

Students explore the volume of a box based on the amount of ...

Students explore the volume of a box based on the amount of unit cubes that can fit inside of it in this student interactive, from Illuminations. They are prompted to come up with a rule for determining the volume of a box when its width, depth, and height are known.

This applet contains four games (How Many?, Build, Fill, and Add) that ...

This applet contains four games (How Many?, Build, Fill, and Add) that utilize a frame with five slots for students to place objects, which helps students develop counting and addition skills.

Students see how well they understand function expressions by trying to match ...

Students see how well they understand function expressions by trying to match the function graph to a generated graph. They may choose from several function types or select random and let the computer choose.

Students to explore various geometric solids and their properties in this student ...

Students to explore various geometric solids and their properties in this student interactive, from Illuminations. Students can virtually manipulate and color each solid to investigate properties such as the number of faces, edges, and vertices. Students can explore tetrahedrons, cubes, octahedrons, dodecahedrons, icosahedrons, and irregular polyhedrons by toggling between solid and net to see different views of the selected shape.

Students are challenged with the following task: If two sheets of 8.5 ...

Students are challenged with the following task: If two sheets of 8.5 by 11 inch paper are rolled into a short cylinder and a tall cylinder, does one hold more than the other?

This resource describes activities using interactive geoboards to help students identify simple ...

This resource describes activities using interactive geoboards to help students identify simple geometric shapes, describe their properties, and develop spatial sense. The first part, Making Triangles, focuses attention on the concept of triangle, helping students understand the mathematical meaning of a triangle and the idea of congruence, or sameness, in geometry. In the next part, Creating Polygons, students make and compare a variety of polygons, describing the salient properties of the shapes they create.

Students can learn to visualize the effects of multiplying a fixed positive ...

Students can learn to visualize the effects of multiplying a fixed positive number by positive numbers greater than 1 and less than 1 with this tool. Using interactive figures, students can investigate how changing the height of a rectangle with a fixed width changes its area. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

Building on students' intuitive understandings of patterns and number relationships, teachers can ...

Building on students' intuitive understandings of patterns and number relationships, teachers can further the development of number concepts and logical reasoning as described in the Number and Operations and Reasoning and Proof Standards. In this two-part example from Illuminations, virtual hundred boards and calculators furnish a visual way of highlighting and displaying various patterns and relationships among numbers. Using calculators and hundred boards together, teachers can encourage students to communicate their thinking with others, as discussed in the Communication Standard. In this first part, Displaying Number Patterns, the same patterns are displayed on a calculator and on a hundred board simultaneously. In the second part, Patterns to 100 and Beyond, students examine number patterns, using a calculator to move beyond 100. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

In this two-part example from Illuminations, users can drag a slider on ...

In this two-part example from Illuminations, users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

Students to enter and compare numeric or algebraic expressions in this interactive ...

Students to enter and compare numeric or algebraic expressions in this interactive pan balance, from Illuminations, . They can "weigh" the expressions they want to compare by entering them on either side of the balance, allowing them to practice arithmetic and algebraic skills, as well as to investigate the concept of equivalence.

The interactive pan balance uses multiple shapes with different values, allowing students ...

The interactive pan balance uses multiple shapes with different values, allowing students to investigate what happens as different shapes are placed on the balance. This student interactive, from Illuminations, provides an interesting environment in which students can consider the concept of equivalence.

Students carry out an interactive, geometric "proof without words" for the algebraic ...

Students carry out an interactive, geometric "proof without words" for the algebraic technique of completing the square in this interactive. The page also includes directions and a link to the final solution.

Students use division skills to figure out how much each character gets. ...

Students use division skills to figure out how much each character gets. They also have the capability to design their own situation with dinosaurs dividing waffles, penguins sharing apples, or many other situations.

Students explore the relationship between theoretical and experimental probabilitiesin this student interactive, ...

Students explore the relationship between theoretical and experimental probabilitiesin this student interactive, from Illuminations. Students use this "box model" as a statistical device to simulate standard probability experiments such as flipping a coin or rolling a die.

Composing Transformations--This is part four of a four-part e-example from Illuminations that ...

Composing Transformations--This is part four of a four-part e-example from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Transformations, the users are challenged to compose equivalent transformations in two different ways. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.

This applet simulates two runners moving along a track and creates a ...

This applet simulates two runners moving along a track and creates a graph of the time-versus-distance relationship of their motion. Students then observe the simulated races as they happen and relate the changing positions of the two runners to dynamic representations that change as the events occur. Students can predict the effects on the graph of changing the starting position or the length of the stride of either runner. They can observe and analyze how a change in one variable, such as length of stride, relates to a change in speed. This computer simulation uses a familiar context that students understand from daily life, and the technology allows them to analyze the relationships in this context deeply because of the ease of manipulating the environment and observing the changes that occur.

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