- Home
- Find Gizmos
- Browse by Core Curriculum
- NWEA Textbooks
- Growth: Grades 6+ Math - Geometry (2017)

# Growth: Grades 6+ Math - Geometry (2017)

### 3: Geometry

3.1: 2-D and 3-D Identification and Classification

3.1.1: Identification and Classification of 2-D Shapes

3.1.1.1: [RIT 148 - 180] Identifies and names triangles, squares, rectangles, and circles

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 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

Classifying Triangles

Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview

3.1.1.3: [RIT 156 - 190] Identifies the number of sides or corners of 2-D shapes, given pictures

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

3.1.1.4: [RIT 160 - 181] Knows definitions of a triangle, a square, a rectangle, and a circle

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 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

Classifying Triangles

Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview

3.1.1.6: [RIT 171 - 180] Sorts shapes based on shared attributes

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

Classifying Triangles

Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview

3.1.1.7: [RIT 176 - 219] Identifies a polygon

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

3.1.1.9: [RIT 197 - 222] Identifies and names nonbasic shapes, such as trapezoids, hexagons, etc.

Classifying Quadrilaterals

Classifying Triangles

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

3.1.1.10: [RIT 201 - 235] Identifies and names special triangles, such as acute, right, scalene, etc., given pictures

Classifying Triangles

3.1.1.11: [RIT 201 - 224] Identifies properties of a 2-D shape, such as right angles, parallel sides, etc., given pictures

Classifying Quadrilaterals

Classifying Triangles

3.1.1.12: [RIT 203 - 221] Understands the relationships among categories of shapes

Classifying Quadrilaterals

Classifying Triangles

3.1.1.13: [RIT 204 - 236] Knows definitions of special triangles, such as acute, right, scalene, etc.

Classifying Triangles

3.1.1.14: [RIT 206 - 224] Classifies 2-D shapes by properties, given pictures

Classifying Quadrilaterals

Classifying Triangles

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

3.1.1.15: [RIT 207 - 207] Knows definitions of nonbasic shapes, such as trapezoids, hexagons, etc.

Classifying Quadrilaterals

Classifying Triangles

Polygon Angle Sum

3.1.1.16: [RIT 212 - 214] Identifies properties of a 2-D shape, such as right angles, parallel sides, etc., without pictures given

Classifying Quadrilaterals

Classifying Triangles

3.1.1.17: [RIT 213 - 245] Knows properties of special triangles, such as acute, right, scalene, etc.

Classifying Triangles

3.1.1.18: [RIT 213 - 260] Knows properties of parallelograms, including special parallelograms such as squares, rhombuses, etc.

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

3.1.2: Identification and Classification of 3-D Shapes

3.1.2.1: [RIT 154 - 195] Identifies and names cubes, cones, cylinders, and spheres

Measuring Volume

Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview

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

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

3.1.2.3: [RIT 179 - 186] Identifies and names rectangular prisms

Balancing Blocks (Volume)

This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. 5 Minute Preview

Measuring Volume

Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview

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

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

3.1.2.4: [RIT 179 - 199] Identifies the number of faces, edges, or vertices for a 3-D object, given pictures

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

3.1.2.5: [RIT 191 - 228] Identifies faces, bases, edges, or vertices of 3-D shapes

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

Surface and Lateral Areas of Prisms and Cylinders

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

3.1.2.6: [RIT 191 - 191] Describes polyhedrons based on the shapes of faces, and/or number of faces, edges, or vertices, given pictures

Prisms and Cylinders

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

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

3.1.2.7: [RIT 195 - 210] Describes cones, cylinders, and spheres based on the shape of surfaces and/or number of bases or vertices, without pictures given

Prisms and Cylinders

Pyramids and Cones

3.1.2.10: [RIT 241 - 241] Identifies and names polyhedrons

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

3.1.2.11: [RIT 254 - 254] Compares 3-D figures based on the shapes of faces and/or number of faces, edges, or vertices

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

3.2: Spatial Reasoning, Similarity, Congruence & Scale Factors

3.2.1: Congruence

3.2.1.1: [RIT 153 - 184] Identifies congruent shapes, given informal language

Rock Art (Transformations)

Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

3.2.1.2: [RIT 189 - 218] Identifies congruent shapes, given formal language

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

3.2.1.3: [RIT 194 - 206] Identifies corresponding sides and angles in congruent figures

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

3.2.1.7: [RIT 229 - 229] Uses formal notation to denote corresponding sides and angles in congruent triangles

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

3.2.1.9: [RIT 239 - 239] Describes a series of transformations that show two shapes are congruent on the coordinate plane

Rotations, Reflections, and Translations

Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview

3.2.1.10: [RIT 243 - 243] Describes a single transformation that shows two shapes are congruent on the coordinate plane

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

3.2.1.11: [RIT 251 - 255] Identifies congruent triangles using AAS, ASA, SAS, or SSS

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

3.2.1.12: [RIT 252 - 277] Identifies the congruence postulate that proves two triangles are congruent

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

3.2.1.15: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent

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

3.2.2: Similarity

3.2.2.1: [RIT 180 - 181] Identifies similar figures

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

3.2.2.2: [RIT 204 - 253] Applies scale factors to solve problems involving scale drawings, maps, and models

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

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

3.2.2.3: [RIT 212 - 212] Determines scale factors in problems involving scale drawings, maps, and models

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

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

3.2.2.4: [RIT 212 - 260] Determines lengths of corresponding sides in similar figures

Similar Figures

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

3.2.2.5: [RIT 213 - 226] Identifies corresponding sides and angles in similar figures

Similar Figures

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

3.2.2.6: [RIT 213 - 213] Knows the definition of similarity

Similar Figures

Similarity in Right Triangles

3.2.2.7: [RIT 215 - 249] Applies properties of similar triangles to solve real-world problems involving indirect measurements

Similar Figures

3.2.2.8: [RIT 223 - 239] Determines scale factors in problems involving scale drawings of geometric figures

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

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

3.2.2.10: [RIT 224 - 224] Determines the ratio between perimeters of similar figures

Perimeters and Areas of Similar Figures

3.2.2.11: [RIT 224 - 252] Applies scale factors to solve problems involving scale drawings of geometric figures

Dilations

Perimeters and Areas of Similar Figures

Similar Figures

3.2.2.13: [RIT 235 - 235] Applies properties of similar figures to determine an area

Perimeters and Areas of Similar Figures

3.2.2.14: [RIT 237 - 257] Applies properties of similar figures to determine a perimeter

Perimeters and Areas of Similar Figures

3.2.2.15: [RIT 239 - 239] Identifies the proportion of corresponding sides of similar figures

Similarity in Right Triangles

3.2.2.16: [RIT 243 - 263] Applies similarity postulates to solve for missing lengths and angles

Similarity in Right Triangles

3.2.2.17: [RIT 247 - 247] Applies similarity postulates to identify corresponding sides and angles

Similarity in Right Triangles

3.2.2.20: [RIT 256 - 256] Identifies similar triangles using AA

Proving Triangles Congruent

Similarity in Right Triangles

3.2.2.21: [RIT 260 - 276] Applies the geometric mean to solve for missing lengths and angles in triangles

Similarity in Right Triangles

3.2.2.22: [RIT 263 - 276] Determines the conditions necessary to prove two triangles are similar

Proving Triangles Congruent

3.2.2.23: [RIT 268 - 271] Identifies the similarity postulate that proves two triangles are similar

Proving Triangles Congruent

3.2.2.25: [RIT 283 - 283] Solves problems involving multiple theorems of similar triangles, including the Triangle Proportionality Theorem, segment proportionality property for parallel lines, and similarity postulates

Similarity in Right Triangles

3.2.2.27: [RIT 285 - 286] Determines the ratio between areas of similar figures

Perimeters and Areas of Similar Figures

3.2.3: Spatial Concepts and Symmetry

3.2.3.2: [RIT 162 - 180] Recognizes lines of symmetry in 2-D figures

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

Quilting Bee (Symmetry)

Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview

3.2.3.3: [RIT 170 - 217] Identifies the figure formed by folding and/or cutting a shape

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

3.2.3.4: [RIT 171 - 202] Composes or decomposes 2-D shapes to form new shapes

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

3.2.3.5: [RIT 175 - 208] Identifies multiple views of structures composed of cubes

3D and Orthographic Views

Arrange blocks in a three-dimensional space so that the top view, front view, and side view match the target top view, front view, and side view. 5 Minute Preview

3.2.3.6: [RIT 177 - 177] Identifies 3-D shapes given multiple views

3D and Orthographic Views

Arrange blocks in a three-dimensional space so that the top view, front view, and side view match the target top view, front view, and side view. 5 Minute Preview

3.2.3.7: [RIT 180 - 202] Identifies 2-D figures which have line 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

Quilting Bee (Symmetry)

Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview

3.2.3.8: [RIT 181 - 220] Determines the number of lines of symmetry in 2-D figures

Holiday Snowflake Designer

Quilting Bee (Symmetry)

Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview

3.2.3.9: [RIT 185 - 234] Identifies and creates nets for prisms

Surface and Lateral Areas of Prisms and Cylinders

3.2.3.10: [RIT 186 - 202] Identifies and creates nets for pyramids

Surface and Lateral Areas of Pyramids and Cones

3.2.3.11: [RIT 195 - 222] Identifies and creates nets for cones

Surface and Lateral Areas of Pyramids and Cones

3.2.3.12: [RIT 206 - 206] Composes or decomposes 3-D shapes to form new shapes

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

3.2.3.13: [RIT 206 - 217] Identifies 2-D figures which have rotational symmetry

Quilting Bee (Symmetry)

3.2.3.14: [RIT 211 - 225] Identifies single views of 3-D shapes

3D and Orthographic Views

Arrange blocks in a three-dimensional space so that the top view, front view, and side view match the target top view, front view, and side view. 5 Minute Preview

3.2.3.15: [RIT 213 - 249] Identifies single views of structures composed of cubes

3D and Orthographic Views

3.2.3.16: [RIT 219 - 236] Identifies and creates nets for cylinders

Surface and Lateral Areas of Prisms and Cylinders

3.2.3.17: [RIT 244 - 270] Identifies the cross-sections of 3-D shapes

Pyramids and Cones

3.2.3.21: [RIT 260 - 260] Identifies the rotational or reflectional symmetry of a shape

Quilting Bee (Symmetry)

3.2.4: Geometric Proof/Logic/Inductive and Deductive Reasoning

3.2.4.1: [RIT 252 - 277] Identifies the congruence postulate that proves two triangles are congruent

Congruence in Right Triangles

Proving Triangles Congruent

3.2.4.2: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent

Congruence in Right Triangles

Proving Triangles Congruent

3.2.4.3: [RIT 263 - 276] Determines the conditions necessary to prove two triangles are similar

Proving Triangles Congruent

3.2.4.4: [RIT 268 - 271] Identifies the similarity postulate that proves two triangles are similar

Proving Triangles Congruent

3.3: Lines, Angles, Polygons, and Coordinate Geometry

3.3.1: Coordinate Geometry

3.3.1.1: [RIT 201 - 218] Counts to find the distance between points on the coordinate plane

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview

3.3.1.3: [RIT 205 - 237] Determines the distance between two points with the same first or second coordinate

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

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

3.3.1.4: [RIT 209 - 236] Determines the coordinates of points in all four quadrants of a coordinate graph

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

3.3.1.5: [RIT 214 - 236] Determines the coordinates of missing vertices of geometric figures in the first quadrant given the coordinates of the other vertices

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

3.3.1.9: [RIT 235 - 235] Determines a side length of a polygon given the coordinates of the vertices with the same first or second coordinate

Points in the Coordinate Plane

3.3.1.10: [RIT 242 - 266] Determines the distance between two points on the coordinate plane

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

3.3.1.13: [RIT 251 - 273] Identifies collinear points

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

3.3.1.24: [RIT 264 - 264] Determines the perimeter of a triangle given the coordinates of the vertices

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

3.3.2: Circles

3.3.2.1: [RIT 237 - 279] Writes the equation of a circle given the center and radius

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

3.3.2.2: [RIT 257 - 275] Writes the equation of a circle given a graph

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

3.3.2.3: [RIT 267 - 273] Graphs a circle given the equation

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

3.3.2.4: [RIT 272 - 272] Determines the center and radius given the standard form of the equation

Circles

3.3.2.5: [RIT 275 - 275] Writes the equation of a circle given the center and a point on the circle

Circles

3.3.2.6: [RIT 278 - 286] Determines the center and radius of a circle given the general form of the equation

Circles

3.3.3: Conic Sections

3.3.3.1: [RIT 237 - 279] Writes the equation of a circle given the center and radius

Circles

3.3.3.2: [RIT 247 - 271] Identifies the conic section from the equation

Circles

Ellipses

Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview

Parabolas

Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview

3.3.3.3: [RIT 257 - 275] Writes the equation of a circle given a graph

Circles

3.3.3.4: [RIT 267 - 273] Graphs a circle given the equation

Circles

3.3.3.5: [RIT 268 - 268] Writes the equation of an ellipse given the center and vertices

Ellipses

Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview

3.3.3.6: [RIT 268 - 268] Graphs a parabola with an axis of symmetry parallel to the x-axis

Parabolas

Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview

3.3.3.7: [RIT 272 - 272] Determines the center and radius given the standard form of the equation

Circles

3.3.3.8: [RIT 275 - 275] Writes the equation of a circle given the center and a point on the circle

Circles

3.3.3.9: [RIT 278 - 286] Determines the center and radius of a circle given the general form of the equation

Circles

3.3.4: Geometric Constructions

3.3.4.1: [RIT 257 - 257] Identifies the geometric construction of an angle bisector

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

3.3.4.2: [RIT 263 - 263] Identifies the geometric construction of a line segment bisector or the midpoint of a line segment

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

3.3.5: Points, Lines, Segments, Rays, and Angles

3.3.5.1: [RIT 181 - 203] Identifies parallel lines involving real-world objects

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

3.3.5.2: [RIT 185 - 198] Identifies intersecting lines

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

3.3.5.3: [RIT 186 - 213] Identifies right angles

Classifying Triangles

3.3.5.4: [RIT 193 - 210] Identifies parallel lines

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

3.3.5.5: [RIT 201 - 229] Identifies acute or obtuse angles

Classifying Triangles

3.3.5.6: [RIT 202 - 229] Identifies points, lines, rays, line segments, and angles

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

3.3.5.7: [RIT 203 - 203] Knows the definition of an acute angle

Classifying Triangles

3.3.5.8: [RIT 205 - 205] Recognizes precise definitions of parallel and perpendicular lines

Constructing Parallel and Perpendicular Lines

Parallel, Intersecting, and Skew Lines

3.3.5.9: [RIT 213 - 239] Identifies perpendicular lines involving real-world objects

Constructing Parallel and Perpendicular Lines

3.3.5.10: [RIT 222 - 228] Understands what the measure of an angle represents

Investigating Angle Theorems

Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

3.3.5.11: [RIT 227 - 243] Identifies perpendicular lines

Constructing Parallel and Perpendicular Lines

3.3.5.12: [RIT 248 - 248] Defines midpoints of line segments

Segment and Angle Bisectors

Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true. 5 Minute Preview

3.3.5.13: [RIT 275 - 275] Defines bisectors of line segments

Segment and Angle Bisectors

Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true. 5 Minute Preview

3.3.6: Angle Measurement

3.3.6.1: [RIT 203 - 203] Knows the definition of an acute angle

Classifying Triangles

3.3.6.2: [RIT 222 - 228] Understands what the measure of an angle represents

Investigating Angle Theorems

Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

3.3.6.3: [RIT 226 - 235] Knows the definition of an angle

Investigating Angle Theorems

Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

3.3.7: Relationships involving Lines, Angles, and Polygons

3.3.7.1: [RIT 194 - 194] Identifies diagonals of polygons

Polygon Angle Sum

3.3.7.2: [RIT 215 - 258] Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles

Investigating Angle Theorems

3.3.7.3: [RIT 220 - 250] Applies the formula for the sum of the interior angles of a polygon

Polygon Angle Sum

3.3.7.4: [RIT 223 - 241] Recognizes that the sum of the interior angles of a triangle is 180 degrees

Polygon Angle Sum

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

3.3.7.5: [RIT 226 - 246] Applies the Triangle Angle-Sum Theorem to determine the measure of an unknown angle

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

3.3.7.6: [RIT 228 - 250] Applies properties of isosceles triangles to determine the measure of an unknown angle

Isosceles and Equilateral Triangles

Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

3.3.7.7: [RIT 230 - 255] Solves problems involving parallel lines cut by a transversal

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

3.3.7.8: [RIT 230 - 230] Determines the number of diagonals that can be drawn from one vertex in a polygon

Polygon Angle Sum

3.3.7.10: [RIT 237 - 268] Solves problems by applying multiple properties of angles, including interior and exterior angles of triangles; complementary, supplementary, and vertical angles; and angles created by perpendicular lines or parallel lines cut by a transversal

Investigating Angle Theorems

Triangle Angle Sum

3.3.7.12: [RIT 240 - 240] Defines complementary and supplementary angles

Investigating Angle Theorems

3.3.7.13: [RIT 241 - 276] Applies the Triangle Inequality Theorem

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

3.3.7.14: [RIT 242 - 243] Applies the Triangle Exterior Angle Theorem to determine the measure of an unknown angle

Triangle Angle Sum

3.3.7.15: [RIT 245 - 249] Identifies corresponding, alternate interior, and alternate exterior angles

Triangle Angle Sum

3.3.7.16: [RIT 248 - 258] Identifies complementary and supplementary angles

Investigating Angle Theorems

3.3.7.17: [RIT 253 - 260] Determines the conditions necessary to show that two lines are parallel

Constructing Parallel and Perpendicular Lines

3.3.7.18: [RIT 256 - 258] Applies the formula for the measure of each exterior angle of a regular polygon

Polygon Angle Sum

3.3.7.19: [RIT 258 - 258] Applies the formula for the measure of each interior angle of a regular polygon

Polygon Angle Sum

3.3.7.21: [RIT 280 - 280] Identifies vertical angles

Investigating Angle Theorems

3.3.8: Geometric Proof/Logic/Inductive and Deductive Reasoning

3.3.8.1: [RIT 253 - 260] Determines the conditions necessary to show that two lines are parallel

Constructing Parallel and Perpendicular Lines

3.3.8.2: [RIT 275 - 275] Proves theorems involving the properties of parallelograms

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

3.4: Transformations

3.4.1: Transformations

3.4.1.1: [RIT 177 - 226] Performs a slide, flip, or turn without using a grid

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

3.4.1.2: [RIT 199 - 220] Identifies a slide, flip, or turn that will carry a given figure onto another, without a grid

Rock Art (Transformations)

Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

3.4.1.3: [RIT 202 - 225] Performs a translation, reflection, or rotation, without the coordinate plane

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

3.4.1.4: [RIT 208 - 208] Knows the definition of a slide, a flip, or a turn

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

Rock Art (Transformations)

Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

Rotations, Reflections, and Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview

3.4.1.5: [RIT 214 - 221] Identifies the degree of rotation that will map one figure onto another, without the coordinate plane

Rock Art (Transformations)

3.4.1.6: [RIT 214 - 214] Identifies the degree of rotation that shows that two given figures are congruent, without a coordinate plane

Rock Art (Transformations)

3.4.1.7: [RIT 218 - 232] Describes a single transformation that will map one figure onto another, without the coordinate plane

Reflections

Rotations, Reflections, and Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview

3.4.1.8: [RIT 221 - 254] Determines the image of a polygon on a coordinate plane after a reflection or a series of reflections

Rotations, Reflections, and Translations

3.4.1.9: [RIT 223 - 260] Determines the coordinates of the vertices of a polygon after a dilation or a series of dilations, with center at the origin

Dilations

3.4.1.11: [RIT 224 - 232] Understands that rigid transformations preserve congruency

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

3.4.1.12: [RIT 226 - 230] Determines the coordinates of the vertices of a polygon after a translation or a series of translations

Translations

3.4.1.13: [RIT 226 - 226] Determines the image of a polygon on a coordinate plane after a rotation or a series of rotations

Rotations, Reflections, and Translations

3.4.1.15: [RIT 231 - 259] Determines the coordinates of the vertices of a polygon after a reflection or a series of reflections

Rotations, Reflections, and Translations

3.4.1.16: [RIT 231 - 242] Describes the effects of dilation on lengths and angle measures

Dilations

3.4.1.17: [RIT 232 - 272] Describes a single transformation that will map one figure onto itself, without the coordinate plane

Rock Art (Transformations)

3.4.1.18: [RIT 236 - 244] Determines the coordinates of the vertices of a polygon after a rotation or a series of rotations

Rotations, Reflections, and Translations

3.4.1.19: [RIT 239 - 239] Performs a series of translations, reflections, and rotations, without the coordinate plane

Rotations, Reflections, and Translations

3.4.1.20: [RIT 240 - 240] Determines the image of a translation represented in coordinate notation

Translations

3.4.1.22: [RIT 249 - 263] Describes a translation using coordinate notation

Translations

3.4.1.23: [RIT 250 - 250] Determines the image of a polygon on a coordinate plane after a series of translations, reflections, or rotations

Rotations, Reflections, and Translations

3.4.1.24: [RIT 251 - 251] Determines the image of a dilation represented in coordinate notation

Dilations

3.4.1.25: [RIT 252 - 252] Identifies the center and scale factor used in a dilation represented in the coordinate plane

Dilations

3.4.1.26: [RIT 253 - 253] Applies the scale factor in a dilation to solve for unknown lengths

Dilations

3.4.1.27: [RIT 264 - 264] Determines the image of a reflection represented in coordinate notation

Rotations, Reflections, and Translations

3.4.1.29: [RIT 285 - 285] Describes the effects of dilation on areas

Dilations

3.5: Pythagorean Theorem, Trigonometry & Special Right Triangles

3.5.1: Pythagorean Theorem

3.5.1.1: [RIT 240 - 266] Uses the Pythagorean Theorem to calculate the length of a missing side of a right triangle

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

3.5.1.2: [RIT 241 - 275] Uses the Pythagorean Theorem to solve real-world or mathematical problems

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

3.5.1.3: [RIT 253 - 268] Applies the converse of the Pythagorean Theorem to identify right triangles

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

3.5.2: Trigonometry

3.5.2.2: [RIT 240 - 267] Represents the tangent of an angle as a ratio of sides in a right triangle

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

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

3.5.2.3: [RIT 241 - 263] Represents the sine of an angle as a ratio of sides in a right triangle

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

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

3.5.2.4: [RIT 247 - 267] Represents the cosine of an angle as a ratio of sides in a right triangle

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, 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

3.5.2.5: [RIT 250 - 270] Uses sine, cosine, or tangent to determine the length of a side in a right triangle

Sine, Cosine, and Tangent Ratios

3.5.2.7: [RIT 263 - 266] Uses sine, cosine, and tangent to determine lengths to solve real-world and mathematical problems

Sine, Cosine, and Tangent Ratios

3.5.3: Relationships involving Lines, Angles, and Polygons

3.5.3.1: [RIT 258 - 279] Uses the 45-45-90 and 30-60-90 right triangle relationships to calculate the length of a missing side of a right triangle

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

3.5.3.2: [RIT 259 - 275] Uses the 45-45-90 and 30-60-90 right triangle relationships to solve real-world and mathematical problems

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

3.6: Circles

3.6.1: Circles

3.6.1.1: [RIT 236 - 236] Recognizes the relationship between the diameter and the radius of a circle

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 5 Minute Preview

3.6.1.2: [RIT 238 - 263] Understands that the ratio between the circumference and the diameter of a circle is equal to pi

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 5 Minute Preview

3.6.1.3: [RIT 242 - 286] Uses properties of central and inscribed angles to solve problems involving circles

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

3.6.1.4: [RIT 243 - 271] Solves problems involving inscribed angles on a diameter

Inscribed Angles

Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview

3.6.1.5: [RIT 256 - 271] Uses properties of chords to solve problems involving circles

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

3.6.1.8: [RIT 263 - 263] Recognizes a precise definition of circles

Circles

3.6.1.9: [RIT 263 - 274] Calculates arc lengths

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

3.6.1.11: [RIT 266 - 266] Solves problems involving arc measures of a circle

Chords and Arcs

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 January 1 and July 1.

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