- Home
- Find Gizmos
- Browse by Core Curriculum
Geometry: A Common Core Edition (2014)
1: Preparing for Geometry
1.1: Changing Units of Measure Within Systems
Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
1.2: Changing Units of Measure Between Systems
Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
1.3: Simple Probability
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
1.4: Algebraic Expressions
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
Simplifying Algebraic Expressions I
Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview
Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
Using Algebraic Equations
Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview
Using Algebraic Expressions
Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview
1.5: Linear Equations
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
1.6: Linear Inequalities
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
1.7: Ordered Pairs
Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
1.8: Systems of Linear Equations
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
1.9: Square Roots and Simplifying Radicals
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
2: Tools of Geometry
2.1: Points, Lines and Planes
Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
Parallel, Intersecting, and Skew Lines
Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of these objects. 5 Minute Preview
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
2.4: Angle Measure
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
2.5: Angle Relationships
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
2.6: Two-Dimensional Figures
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
3: Reasoning and Proof
3.2: Logic
Biconditional Statements
Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
Conditional Statements
Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
3.3: Conditional Statements
Biconditional Statements
Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
Conditional Statements
Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
3.8: Proving Angle Relationships
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
4: Parallel and Perpendicular Lines
4.1: Parallel Lines and Transversals
Constructing Congruent Segments and Angles
Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
4.3: Slopes of Lines
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
4.4: Equations of Lines
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
4.5: Proving Lines Parallel
Constructing Congruent Segments and Angles
Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
Parallel, Intersecting, and Skew Lines
Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of these objects. 5 Minute Preview
5: Congruent Triangles
5.1: Classifying Triangles
Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
5.2: Angles of Triangles
Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview
Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
Triangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles. 5 Minute Preview
5.3: Congruent Triangles
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
Constructing Congruent Segments and Angles
Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
5.4: Proving Triangles Congruent – SSS, SAS
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
5.5: Proving Triangles Congruent – ASA, AAS
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
5.6: Isosceles and Equilateral Triangles
Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview
Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview
Triangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles. 5 Minute Preview
5.7: Congruence Transformations
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
6: Relationships in Triangles
6.1: Bisectors of Triangles
Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview
6.2: Medians and Altitudes of Triangles
Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
6.5: The Triangle Inequality
Triangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles. 5 Minute Preview
7: Quadrilaterals
7.1: Angles of Polygons
Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
7.2: Parallelograms
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
Parallelogram Conditions
Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram. 5 Minute Preview
Special Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition? 5 Minute Preview
7.3: Tests for Parallelograms
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
Parallelogram Conditions
Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram. 5 Minute Preview
Special Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition? 5 Minute Preview
7.4: Rectangles
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
Special Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition? 5 Minute Preview
7.5: Rhombi and Squares
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
Special Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition? 5 Minute Preview
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
7.6: Trapezoids and Kites
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
8: Proportions and Similarity
8.1: Rations and Proportions
Beam to Moon (Ratios and Proportions)
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
8.2: Similar Polygons
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
8.3: Similar Triangles
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
8.5: Parts of Similar Triangles
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
8.6: Similarity Transformations
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
8.7: Scale Drawings and Models
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
9: Right Triangles and Trigonometry
9.1: Geometric Mean
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
9.2: The Pythagorean Theorem and Its Converse
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
9.3: Special Right Triangles
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
9.4: Trigonometry
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
9.5: Angles of Elevation and Depression
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
9.7: Vectors
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
10: Transformations and Symmetry
10.1: Reflections
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
Holiday Snowflake Designer
Fold paper and cut in a certain way to make symmetrical snowflakes with six sides (similar to what can be found in nature) or with eight sides (an easier folding method). This simulation allows you to cut virtual paper on the computer screen with round dot or square dot "scissors" of various sizes before using physical paper. 5 Minute Preview
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
10.2: Translations
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
10.3: Rotations
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
10.5: Symmetry
Holiday Snowflake Designer
Fold paper and cut in a certain way to make symmetrical snowflakes with six sides (similar to what can be found in nature) or with eight sides (an easier folding method). This simulation allows you to cut virtual paper on the computer screen with round dot or square dot "scissors" of various sizes before using physical paper. 5 Minute Preview
10.6: Dilations
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
11: Circles
11.1: Circles and Circumference
Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
11.2: Measuring Angles and Arcs
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
11.3: Arcs and Chords
Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
11.4: Inscribed Angles
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
11.8: Equations of Circles
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
12: Areas of Polygons and Circles
12.1: Areas of Parallelograms and Triangles
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
12.3: Areas of Circles and Sectors
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
12.4: Areas of Regular Polygons and Composite Figures
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
12.5: Areas of Similar Figures
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
13: Extending Surface Area and Volume
13.1: Representations of Three-Dimensional Figures
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
13.2: Surface Areas of Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
13.3: Surface Areas of Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
13.4: Volumes of Prims and Cylinders
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
13.5: Volumes of Pyramids and Cones
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
14: Probability and Measurement
14.2: Probability with Permutations and Combinations
Binomial Probabilities
Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation. 5 Minute Preview
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
14.3: Geometric Probability
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
14.5: Probabilities of Independent and Dependent Events
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
14.6: Probabilities of Mutually Exclusive Events
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
How Free Gizmos Work
Start teaching with 20-40 Free Gizmos. See the full list.
Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.
Free Gizmos change each semester. The new collection will be available Jul 01, 2023.
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
STEM Cases take between 30-90 minutes for students to complete, depending on the case.
Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
Multiple grade-appropriate versions, or levels, exist for each STEM Case.
Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
Find Your Solution
Start playing, exploring and learning today with a free account. Or contact us for a quote or demo.
Sign Up For Free Get a Quote