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- Growth: Geometry International (2017)

# Growth: Geometry International (2017)

### 1: Properties of Geometric Shapes

1.1: Points, Lines, Planes, and Angles

1.1.1: Geometric Constructions

1.1.1.1: [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

1.1.1.2: [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

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

1.1.2.1: [RIT 186 - 207] Identifies right angles

Classifying Triangles

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

1.1.2.2: [RIT 193 - 196] 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

1.1.2.3: [RIT 202 - 215] 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

1.1.2.4: [RIT 202 - 209] Identifies acute or obtuse angles

Classifying Triangles

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

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

Classifying Triangles

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

1.1.2.6: [RIT 213 - 239] Identifies perpendicular 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

1.1.2.7: [RIT 226 - 240] 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

1.1.2.8: [RIT 236 - 237] Identifies perpendicular lines

Constructing Parallel and Perpendicular Lines

1.1.2.9: [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

1.1.2.10: [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

1.1.3: Angle Measurement

1.1.3.1: [RIT 187 - 239] Calculates unknown angle measures using the additive property of angles

Investigating Angle Theorems

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

1.1.3.2: [RIT 211 - 222] Measures non-right angles using a protractor

Investigating Angle Theorems

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

1.1.4: Relationships involving Lines, Angles, and Polygons

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

Investigating Angle Theorems

1.1.4.2: [RIT 226 - 257] 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

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

Investigating Angle Theorems

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

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

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

Investigating Angle Theorems

1.1.4.6: [RIT 253 - 267] Determines the conditions necessary to show that two lines are parallel

Constructing Parallel and Perpendicular Lines

1.1.4.7: [RIT 269 - 269] Identifies vertical angles

Investigating Angle Theorems

1.2: Polygons and Circles

1.2.1: Circles

1.2.1.1: [RIT 208 - 208] Knows the number of degrees in a circle

Radians

As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the beltâ€™s wheel. How do you set these to get the distance right? See how this relates to arc length, and discover how radians help make this task easier. 5 Minute Preview

1.2.1.2: [RIT 218 - 231] Identifies radii and diameters of circles

Circumference and Area of Circles

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

1.2.1.3: [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

1.2.1.5: [RIT 242 - 292] 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

1.2.1.6: [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

1.2.1.7: [RIT 250 - 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

1.2.1.8: [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

1.2.1.11: [RIT 263 - 263] Recognizes a precise definition 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

1.2.1.12: [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

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

Chords and Arcs

1.2.2: Identification and Classification of 2-D Shapes

1.2.2.1: [RIT 210 - 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

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

Classifying Triangles

1.2.3: Perimeter/Circumference

1.2.3.1: [RIT 250 - 250] 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

1.2.4: Relationships involving Lines, Angles, and Polygons

1.2.4.1: [RIT 194 - 194] Identifies diagonals 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

1.2.4.2: [RIT 220 - 250] Applies the formula for the sum of the interior angles of 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

1.2.4.3: [RIT 221 - 233] 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

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

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

Triangle Angle Sum

1.2.4.5: [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

1.2.4.7: [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

1.2.4.9: [RIT 240 - 240] Determines the number of diagonals that can be drawn from one vertex in a polygon

Polygon Angle Sum

1.2.4.10: [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

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

Triangle Angle Sum

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

Polygon Angle Sum

1.2.4.14: [RIT 269 - 269] Applies the formula for the measure of each interior angle of a regular polygon

Polygon Angle Sum

1.3: Three-Dimensional Figures

1.3.1: Identification and Classification of 3-D Shapes

1.3.1.1: [RIT 191 - 223] 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

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

1.3.1.2: [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

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

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

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

1.3.2: Spatial Concepts and Symmetry

1.3.2.1: [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

1.3.2.2: [RIT 184 - 229] Identifies and creates nets for prisms

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

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

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

1.3.2.4: [RIT 190 - 241] Identifies and creates nets for cones

Surface and Lateral Areas of Pyramids and Cones

1.3.2.5: [RIT 209 - 249] Identifies single 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

1.3.2.6: [RIT 212 - 236] Identifies and creates nets for cylinders

Surface and Lateral Areas of Prisms and Cylinders

1.3.2.7: [RIT 216 - 216] 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

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

Pyramids and Cones

### 2: Measurement of Geometric Shapes

2.1: Perimeter and Circumference

2.1.1: Perimeter/Circumference

2.1.1.1: [RIT 200 - 245] Solves problems involving perimeters of rectangles within a real-world or mathematical context

Fido's Flower Bed (Perimeter and Area)

Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas. 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

2.1.1.2: [RIT 209 - 230] Determines side lengths given the perimeter of rectangles

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

2.1.1.3: [RIT 213 - 239] Determines the circumference of circles, given the formula

Circumference and Area of Circles

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

2.1.1.4: [RIT 220 - 238] Solves problems involving decimals and perimeters of rectangles within a real-world or mathematical context

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

2.1.1.5: [RIT 222 - 251] Determines the circumference of circles, formula not provided

Circumference and Area of Circles

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

2.1.1.7: [RIT 231 - 231] Determines the ratio between perimeters of scaled 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

2.1.1.8: [RIT 232 - 240] Describes the effect on perimeter when dimensions of a non-rectangular polygon are changed

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

2.1.1.9: [RIT 233 - 244] Identifies the formula for the perimeter of a polygon

Perimeter and Area of Rectangles

2.1.1.10: [RIT 248 - 248] Solves problems involving perimeters of non-rectangular polygons within a real-world or mathematical context

Fido's Flower Bed (Perimeter and Area)

Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas. 5 Minute Preview

2.2: Area and Surface Area

2.2.1: Area

2.2.1.1: [RIT 200 - 222] Determines the area of rectangles with whole-number sides, given the formula

Multiplying Decimals (Area Model)

Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview

Perimeter and Area of Rectangles

2.2.1.2: [RIT 201 - 224] Determines the area of rectangles with whole-number sides, formula not provided

Multiplying Decimals (Area Model)

Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview

Perimeter and Area of Rectangles

2.2.1.3: [RIT 206 - 224] Determines side lengths given the area of rectangles

Perimeter and Area of Rectangles

2.2.1.4: [RIT 206 - 226] Determines the area of figures composed of whole and partial unit squares

Multiplying Decimals (Area Model)

Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview

Multiplying with Decimals

Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview

2.2.1.5: [RIT 209 - 238] Solves problems involving areas of rectangles within a real-world or mathematical context

Chocomatic (Multiplication, Arrays, and Area)

Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview

Multiplying Decimals (Area Model)

Multiplying with Decimals

Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview

Perimeter and Area of Rectangles

2.2.1.6: [RIT 213 - 250] Determines the area of parallelograms, formula not provided

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

2.2.1.8: [RIT 223 - 245] Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context

Fido's Flower Bed (Perimeter and Area)

Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas. 5 Minute Preview

Perimeter and Area of Rectangles

2.2.1.9: [RIT 223 - 242] Determines the area of rectangles with decimal sides, formula not provided

Perimeter and Area of Rectangles

2.2.1.10: [RIT 224 - 257] Describes the effect on area when dimensions of a rectangle are changed

Perimeter and Area of Rectangles

2.2.1.11: [RIT 224 - 224] Determines the base or height given the area of a parallelogram

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

2.2.1.12: [RIT 224 - 252] Describes the effect on area when dimensions of a triangle are changed

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

2.2.1.14: [RIT 228 - 267] Solves problems involving areas of figures composed of polygons within a real-world or mathematical context

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

Chocomatic (Multiplication, Arrays, and Area)

Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview

Fido's Flower Bed (Perimeter and Area)

Perimeter and Area of Rectangles

2.2.1.16: [RIT 230 - 235] Determines the area of triangles,Â given the formula

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

2.2.1.18: [RIT 232 - 232] Identifies the formula for the area of a circle

Circumference and Area of Circles

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

2.2.1.19: [RIT 234 - 239] Determines the area of circles,Â given the formula

Circumference and Area of Circles

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

2.2.1.20: [RIT 235 - 260] Determines the perimeter of rectangles given the area

Fido's Flower Bed (Perimeter and Area)

2.2.1.21: [RIT 236 - 254] Determines the area of triangles, formula not provided

Area of Triangles

2.2.1.22: [RIT 236 - 260] Determines the area of figures composed of polygons

Area of Parallelograms

Area of Triangles

Chocomatic (Multiplication, Arrays, and Area)

Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview

Fido's Flower Bed (Perimeter and Area)

2.2.1.23: [RIT 237 - 250] Determines the area of rectangles given the perimeter

Perimeter and Area of Rectangles

2.2.1.24: [RIT 240 - 269] Determines the ratio between areas of scaled 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

2.2.1.27: [RIT 244 - 260] Determines the circumference given the area of a circle

Circumference and Area of Circles

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

2.2.1.29: [RIT 247 - 247] Determines the radius or diameter given the area of a circle

Circumference and Area of Circles

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

2.2.1.30: [RIT 249 - 257] Determines the area of circles, formula not provided

Circumference and Area of Circles

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

2.2.1.31: [RIT 251 - 251] Determines the area of figures composed of polygons and circles

Circumference and Area of Circles

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

2.2.1.34: [RIT 260 - 270] Describes the effect on area when the radius or diameter of a circle is changed

Circumference and Area of Circles

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

2.2.1.35: [RIT 261 - 261] Describes the effect on area when the circumference of a circle is changed

Circumference and Area of Circles

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

2.2.1.36: [RIT 265 - 265] Solves problems involving areas of circles within a real-world or mathematical context

Circumference and Area of Circles

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

2.2.3: Surface Area

2.2.3.1: [RIT 236 - 248] Uses the net of a prism to solve surface area problems within a real-world or mathematical context

Surface and Lateral Areas of Prisms and Cylinders

2.2.3.2: [RIT 238 - 261] Determines the surface area of rectangular prisms or cubes, formula not provided

Surface and Lateral Areas of Prisms and Cylinders

2.2.3.4: [RIT 241 - 241] Determines the surface area of cylinders, given the formula

Surface and Lateral Areas of Prisms and Cylinders

2.2.3.5: [RIT 241 - 248] Determines the surface area of a prism given a net

Surface and Lateral Areas of Prisms and Cylinders

2.2.3.6: [RIT 246 - 246] Determines the surface area of cones, given the formula

Surface and Lateral Areas of Pyramids and Cones

2.2.3.7: [RIT 251 - 252] Determines the surface area of pyramids, given the formula

Surface and Lateral Areas of Pyramids and Cones

2.2.3.8: [RIT 252 - 252] Determines the surface area of triangular prisms, formula not provided

Surface and Lateral Areas of Prisms and Cylinders

2.2.3.9: [RIT 252 - 256] Determines the surface area of pyramids, formula not provided

Surface and Lateral Areas of Pyramids and Cones

2.2.3.10: [RIT 255 - 263] Describes the effect on surface area when dimensions of a rectangular prism are changed

Surface and Lateral Areas of Prisms and Cylinders

2.2.3.12: [RIT 260 - 263] Solves problems involving surface areas of prisms within a real-world or mathematical context

Surface and Lateral Areas of Prisms and Cylinders

2.2.3.13: [RIT 266 - 269] Determines the surface area of cylinders, formula not provided

Surface and Lateral Areas of Prisms and Cylinders

2.2.4: Perimeter/Circumference

2.2.4.1: [RIT 244 - 244] Determines the circumference given the area of a circle

Circumference and Area of Circles

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

2.2.5: Problem Solving with Units

2.2.5.1: [RIT 265 - 265] Solves problems involving areas of circles within a real-world or mathematical context

Circumference and Area of Circles

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

2.3: Volume

2.3.1: Conversion of Units

2.3.1.1: [RIT 282 - 282] Converts units of volume within the same measurement system

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

Unit Conversions 2 - Scientific Notation and Significant Digits

Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview

2.3.2: Volume

2.3.2.1: [RIT 206 - 229] Determines the volume of rectangular prisms, given the formula

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

2.3.2.2: [RIT 206 - 225] Determines the volume of figures by counting unit cubes

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

2.3.2.3: [RIT 207 - 241] Determines the volume of rectangular prisms, formula not provided

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

2.3.2.4: [RIT 218 - 218] Solves problems involving rectangular prisms composed of unit cubes

Balancing Blocks (Volume)

Measuring Volume

2.3.2.5: [RIT 220 - 264] Solves problems involving volumes of rectangular prisms within a real-world or mathematical context

Balancing Blocks (Volume)

Measuring Volume

Prisms and Cylinders

2.3.2.6: [RIT 226 - 226] Identifies the formula for the volume of a rectangular prism

Balancing Blocks (Volume)

Measuring Volume

Prisms and Cylinders

2.3.2.7: [RIT 227 - 244] Identifies units for measuring volume

Measuring Volume

Prisms and Cylinders

Pyramids and Cones

2.3.2.9: [RIT 231 - 253] Determines the volume of figures composed of rectangular prisms

Balancing Blocks (Volume)

Measuring Volume

Prisms and Cylinders

2.3.2.11: [RIT 235 - 268] Determines the volume of pyramids, given the formula

Pyramids and Cones

2.3.2.12: [RIT 237 - 240] Determines the volume of cylinders, given the formula

Prisms and Cylinders

2.3.2.13: [RIT 239 - 273] Describes the effect on volume when dimensions of a rectangular prism are changed

Prisms and Cylinders

2.3.2.15: [RIT 245 - 245] Determines the volume of spheres, given the formula

Measuring Volume

2.3.2.16: [RIT 250 - 275] Determines the volume of cylinders, formula not provided

Prisms and Cylinders

2.3.2.19: [RIT 254 - 274] Determines the volume of pyramids, formula not provided

Pyramids and Cones

2.3.2.21: [RIT 258 - 258] Determines the radius or diameter of a cylinder given the volume and height

Prisms and Cylinders

2.3.2.26: [RIT 266 - 266] Solves problems involving volumes of 3-D figures composed of cones, cylinders, and spheres within a real-world or mathematical context

Measuring Volume

Prisms and Cylinders

Pyramids and Cones

2.3.2.27: [RIT 266 - 266] Determines the volume of figures composed of rectangular and triangular prisms

Balancing Blocks (Volume)

Measuring Volume

Prisms and Cylinders

2.3.2.29: [RIT 269 - 281] Understands that the volume of a cone is one-third the volume of a cylinder with the same base area and height

Pyramids and Cones

2.3.2.30: [RIT 270 - 270] Determines the volume of spheres, formula not provided

Measuring Volume

2.3.2.31: [RIT 273 - 273] Determines the volume of cones, formula not provided

Pyramids and Cones

2.3.2.32: [RIT 276 - 276] Solves problems involving volumes of cones within a real-world or mathematical context

Pyramids and Cones

2.3.2.33: [RIT 278 - 278] Solves problems involving volumes of cylinders within a real-world or mathematical context

Prisms and Cylinders

### 3: Geometric Relationships

3.1: Congruence and Similarity

3.1.1: Congruence

3.1.1.1: [RIT 184 - 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

3.1.1.2: [RIT 186 - 230] 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

3.1.1.3: [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

3.1.1.8: [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

3.1.1.9: [RIT 252 - 284] 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

Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview

3.1.1.11: [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

3.1.2: Identification and Classification of 2-D Shapes

3.1.2.1: [RIT 230 - 230] Identifies congruent shapes, given formal language

Proving Triangles Congruent

3.1.3: Similarity

3.1.3.1: [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

3.1.3.2: [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

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

3.1.3.3: [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

Similar Figures

3.1.3.4: [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

3.1.3.5: [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

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

Similar Figures

3.1.3.7: [RIT 220 - 220] Knows the definition of similarity

Similar Figures

Similarity in Right Triangles

3.1.3.8: [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

Similar Figures

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

Perimeters and Areas of Similar Figures

3.1.3.11: [RIT 225 - 252] Applies scale factors to solve problems involving scale drawings of geometric figures

Dilations

Perimeters and Areas of Similar Figures

Similar Figures

3.1.3.12: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar

Proving Triangles Congruent

3.1.3.13: [RIT 232 - 257] Applies properties of similar figures to determine a perimeter

Perimeters and Areas of Similar Figures

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

Perimeters and Areas of Similar Figures

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

Similarity in Right Triangles

3.1.3.17: [RIT 244 - 263] Applies similarity postulates to solve for missing lengths and angles

Similarity in Right Triangles

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

Similarity in Right Triangles

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

Proving Triangles Congruent

Similarity in Right Triangles

3.1.3.22: [RIT 260 - 279] Applies the geometric mean to solve for missing lengths and angles in triangles

Similarity in Right Triangles

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

Proving Triangles Congruent

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

Perimeters and Areas of Similar Figures

3.1.3.27: [RIT 288 - 288] 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

3.1.4: Geometric Proof/Logic/Inductive and Deductive Reasoning

3.1.4.1: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar

Proving Triangles Congruent

3.1.4.2: [RIT 252 - 284] Identifies the congruence postulate that proves two triangles are congruent

Congruence in Right Triangles

Proving Triangles Congruent

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

Congruence in Right Triangles

Proving Triangles Congruent

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

Proving Triangles Congruent

3.2: Pythagorean Theorem, Right Triangle Trig

3.2.1: Pythagorean Theorem

3.2.1.1: [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

3.2.1.2: [RIT 242 - 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

3.2.1.3: [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

3.2.2: Trigonometry

3.2.2.1: [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

3.2.2.2: [RIT 246 - 266] 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

3.2.2.3: [RIT 247 - 263] 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

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

Sine, Cosine, and Tangent Ratios

3.2.2.6: [RIT 263 - 273] Uses sine, cosine, and tangent to determine lengths to solve real-world and mathematical problems

Sine, Cosine, and Tangent Ratios

3.2.3: Relationships involving Lines, Angles, and Polygons

3.2.3.1: [RIT 255 - 279] 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

3.2.3.2: [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

3.3: Transformations and Symmetry

3.3.2: Spatial Concepts and Symmetry

3.3.2.1: [RIT 165 - 228] Determines the number of 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

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

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

3.3.2.4: [RIT 275 - 284] Identifies the rotational or reflectional symmetry of a shape

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

3.3.3: Transformations

3.3.3.1: [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

3.3.3.2: [RIT 197 - 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

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

3.3.3.3: [RIT 198 - 227] Describes a single transformation that will map one figure onto another, 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

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

3.3.3.4: [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

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

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

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

Rock Art (Transformations)

3.3.3.8: [RIT 219 - 232] Understands that rigid transformations preserve congruency

Reflections

Rock Art (Transformations)

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

3.3.3.9: [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

3.3.3.10: [RIT 223 - 254] Determines the coordinates of the vertices of a polygon after a dilation or a series of dilations, with center at the origin

Dilations

3.3.3.11: [RIT 225 - 228] Determines the coordinates of the vertices of a polygon after a translation or a series of translations

Translations

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

3.3.3.12: [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

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

Rotations, Reflections, and Translations

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

Dilations

3.3.3.16: [RIT 232 - 255] Describes a single transformation that will map one figure onto itself, without the coordinate plane

Rock Art (Transformations)

3.3.3.17: [RIT 233 - 239] Performs a series of translations, reflections, and rotations, without the coordinate plane

Rotations, Reflections, and Translations

3.3.3.18: [RIT 235 - 271] Determines the coordinates of the vertices of a polygon after a rotation or a series of rotations

Rotations, Reflections, and Translations

3.3.3.19: [RIT 237 - 239] Describes a series of transformations that show two shapes are congruent on the coordinate plane

Rotations, Reflections, and Translations

3.3.3.20: [RIT 239 - 239] Represents translations in the plane using matrices

Translations

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

Translations

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

Rotations, Reflections, and Translations

Translations

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

Translations

3.3.3.26: [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

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

Dilations

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

Dilations

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

Dilations

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

Rotations, Reflections, and Translations

3.4: Coordinate Graphing and Distance

3.4.1: Coordinate Geometry

3.4.1.1: [RIT 181 - 229] 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

3.4.1.2: [RIT 187 - 208] Interprets points with whole number coordinates in the first quadrant within the given context

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

Elevator Operator (Line Graphs)

Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 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

3.4.1.3: [RIT 198 - 221] Determines the coordinates of points in the first quadrant of a 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

Elevator Operator (Line Graphs)

Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 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

3.4.1.4: [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

3.4.1.6: [RIT 203 - 215] Plots the coordinates of points in the first quadrant of a coordinate plane

City Tour (Coordinates)

Points in the Coordinate Plane

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

3.4.1.7: [RIT 205 - 232] 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

3.4.1.8: [RIT 214 - 235] 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

3.4.1.9: [RIT 215 - 236] Plots points in all four quadrants of a coordinate plane

Points in the Coordinate Plane

3.4.1.12: [RIT 242 - 268] 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

3.4.1.15: [RIT 251 - 280] Identifies collinear points

Points, Lines, and Equations