Unit Plan Template s12

Roselle School District Grade 8 Algebra Curriculum Unit 4: Geometry

Essential Question(s) Enduring Understanding(s) How can you understand congruency in physical models and Understand congruence and similarity using physical models, apply that understanding to solving for unknown angles and transparencies, or geometry software. variables? Understand and apply the Pythagorean Theorem. How can you apply the Pythagorean Theorem to right triangles and solve for unknown measures? Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. How can you use your understanding of volume, surface area and area to solve real world mathematical problems?

Common Core Standards, 2010

8.G.1. Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. Parallel lines are taken to parallel lines.

8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when

1 parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

8.G.6. Explain a proof of the Pythagorean Theorem and its converse.

8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Summative Assessment Task See attached document

Learning Expectations Activities/Instructional Student Formative Assessments Technology WAL To/That… Procedures Strategies/Modification/ Infusion/Resources Differentiation Verify experimentally Identify transformation Small Group Instruction Exit Ticket Smartboard the properties of as rotation, reflection, Roselle School District Grade 8 Algebra Curriculum Unit 4: Geometry rotations, reflections, and translation using Allow student who are Journal Entry Laptops and translations. line and line segments. having trouble to work with partner Do Now Interactive Games Understand and apply Transform the Formative Assessments transformations. coordinate point (-5, Rephrasing of information 6) 4 units down and 7 and questions Minute Papers  Finding the image, units to the right. Label Utilize textbook for those given the pre-image, the original point and the Homework and vice-versa transformed point with having trouble 2. Use iterative the correct coordinates. Stations procedures to generate geometric patterns. A rectangle has the Menus coordinate points A(1,4),  Fractals (e.g., the B(1,2), C(8,2), and Projects Koch Snowflake) D(8,4). Rotate the  Self-similarity figure 180° about the  Construction of origin and label the initial stages rotated figure with its Patterns in coordinates. successive stages (e.g., number of ^^^^^^^^^^^^^^^^^^^^ triangles in each stage of Sierpinski’s  1. Verify Triangle) experimentally the properties of rotations, reflections, and Verify experimentally translations the properties of o rotations, reflections, b. Angles are taken to and translations. angles of the same measure.

3 Verify experimentally ^^^^^^^^^^^^^^^^^^^^ the properties of rotations, reflections,  1. Verify and translations. experimentally the properties of rotations, Identify transformation reflections, and as rotation, reflection, translations and translation using  angles. c. Parallel lines are taken to parallel Identify transformation lines. as rotation, reflection, ^^^^^^^^^^^^^^^^^^^^^ and translation using  2. Understand parallel lines. that a two-dimensional figure is congruent to Determine if two figures another if the second can are congruent by using be obtained from the translations, rotations, first by a sequence of and reflections to place rotations, reflections, one figure to top of the and translations; given other matching two congruent figures, corresponding parts. describe a sequence that exhibits the congruence List series of between them. transformations that place one figure on the other to exhibit the congruence between them.

 Describe the Determine new Small Group Instruction Exit Ticket Smartboard effect of dilations, coordinates of two Roselle School District Grade 8 Algebra Curriculum Unit 4: Geometry translations, rotations, dimensional figures on a Allow student who are Journal Entry Laptops and reflections on two- coordinate plane created having trouble to work Do Now Interactive Games dimensional figures by dilations, translations, with partner using coordinates. 8.G.3 rotations, and Rephrasing of information Formative Assessments reflections. and questions Minute Papers Utilize textbook for those Homework having trouble Stations

Projects

 Understand that a Given two similar two- Small Group Instruction Exit Ticket Smartboard two-dimensional figure dimensional figures, is similar to another if describe a sequence of Allow student who are Journal Entry Laptops the second can be transformations that having trouble to work obtained from the first exhibits the similarity with partner Do Now Interactive Games by a sequence of between them. Formative Assessments rotations, reflections, Rephrasing of information and questions translations, and Minute Papers dilations; given two Utilize textbook for those similar two-dimensional Homework figures, describe a having trouble sequence that exhibits Stations the similarity between them. 8.G.4 Menus 

5 Projects

 Use informal Arrange three copies of Small Group Instruction Exit Ticket Smartboard arguments to establish the same triangle so that Allow student who are Journal Entry Laptops facts about the angle the sum of the three sum and exterior angle having trouble to work angles appears to form a of triangles, about the with partner Do Now Interactive Games angles created when line, and give an Formative Assessments parallel lines are cut by a argument in terms of Rephrasing of information transversals why this is and questions transversal, and the Minute Papers angle-angle criterion for so. Utilize textbook for those similarity of triangles. Homework For example, arrange having trouble three copies of the same Stations triangle so that the sum of the three angles Menus appears to form a line, and give an argument in Projects terms of transversals why this is so. 8.G.5   6. Explain a Use Pythagorean Small Group Instruction Exit Ticket Smartboard proof of the Pythagorean Theorem to identify Theorem and its triangles that are right Allow student who are Journal Entry Laptops converse. 8.G.6 triangles. having trouble to work  with partner Do Now Interactive Games

Rephrasing of information Formative Assessments and questions Minute Papers Utilize textbook for those Homework having trouble Roselle School District Grade 8 Algebra Curriculum Unit 4: Geometry

Stations

Projects

 Apply the Two joggers run 8 miles Small Group Instruction Exit Ticket Smartboard Pythagorean Theorem to north and then 5 miles determine unknown side west. What is the Allow student who are Journal Entry Laptops lengths in right triangles shortest distance, to the having trouble to work in real-world and nearest tenth of a mile, with partner Do Now Interactive Games mathematical problems they must travel to Formative Assessments in two and three return to their starting Rephrasing of information and questions dimensions. 8.G.7 point? Minute Papers Utilize textbook for those Solve for the red Homework Apply the Pythagorean diagonal for this having trouble Theorem to find the 9inx9inx9in cube: Stations distance between two points in a coordinate Menus system 8.G.8 Projects

 Know the Apply formulas to solve Small Group Instruction Exit Ticket Smartboard formulas for the real-world problems. volumes of cones, Quaker Oats uses Allow student who are Journal Entry Laptops cylinders, and spheres cylindrical boxes to having trouble to work and use them to solve package their oatmeal with partner Do Now Interactive Games real-world and products. The cylinder Formative Assessments mathematical problems. has a radius of 8 inches Rephrasing of information

7 8.G.9 and a height of 12 and questions Minute Papers inches. -Find the amount of oats Utilize textbook for those Homework 4.2.8A that can fit into this type having trouble 1. Understand and of package. Stations apply concepts involving -Calculate the surface Menus lines, angles, and planes. area of the cylinder so that the Quaker  Complementary and Projects company can create supplementary angles labels for the product.  Bisectors and perpendicular bisectors  Parallel, ^^^^^^^^^^^^^^^^^^^ perpendicular, and intersecting planes Identify the name of the  Intersection of plane with cube, cylinder, quadrilateral and find cone, and sphere any missing angles. 3. Understand and 2. Are there any line apply properties of segments parallel to polygons. each other?  Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi  Regular polygons  Sum of measures of interior angles of a polygon Find any missing angle  Which polygons can of regular octagon be used alone to generate a ^^^^^^^^^^^^^^^^^^^ tessellation and why Convert 15 miles into 4. Understand and Roselle School District Grade 8 Algebra Curriculum Unit 4: Geometry

apply the concept of yards. similarity. Convert 10 miles into  Using proportions to kilometers. find missing measures Order from least to  Scale drawings greatest:  Models of 3D 10 feet, 0.5 miles, 1000 objects centimeters, and 300 Use logic and reasoning inches to make and support conjectures about Name 3 objects that you geometric objects would measure using each of these units: -Meters -Inches 4.2.8D -Grams 1. Solve problems -Tons requiring calculations that A person is driving 60 involve different miles per hour on the units of measurement Garden State Parkway. within a About how many miles measurement system does the person drive in (e.g., 4’3” plus 7’10” 38 minutes? equals 12’1”). 2. Use approximate ^^^^^^^^^^^^^^^^^^^ equivalents between Find the area and standard and metric perimeter of the figure systems to estimate below: measurements (e.g., 5 kilometers is about

9 3 miles). 3. Recognize that the degree of precision needed in calculations depends on how the results will be used and the instruments used to Calculate the area of this generate the composite figure: measurements. 4. Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular Calculate the surface problem-solving area of this triangular situation. prism: 5. Recognize that all measurements of continuous quantities are approximations. 6. Solve problems that involve compound measurement units, such as speed (miles per hour), air pressure (pounds per square inch), and population density (persons per square mile). Roselle School District Grade 8 Algebra Curriculum Unit 4: Geometry

4.2.8E 1. Develop and apply strategies for finding perimeter and area.

 Geometric figures made by combining triangles, rectangles and circles or parts of circles  Estimation of area using grids of various sizes  Impact of a dilation on the perimeter and area of a 2dimensional figure

3. Develop and apply strategies and formulas for finding the surface area and volume of a three- dimensional figure.

 Surface area - prism (triangular or rectangular base),

11 pyramid (triangular or rectangular base)  Impact of a dilation on the surface area and volume of a three-dimensional figure

4. Use formulas to find the surface area of a sphere.