Integrating+Digital+Literacy+Into+A+Geometry+Unit+Plan

Apply geometric concepts in modeling situations.
1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). 3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). MA.4. Use dimensional analysis for unit conversions to confirm that expressions and equations make sense.

Essential Understandings:
Geometry is all around us. Characteristics and properties of geometric shapes are used to solve real life problems. Geometric figures can be changed when their properties and relationships are changed.

Essential Questions
How do you apply formulas to real-world problems? How are the properties, relationships, and characteristics of geometric shapes used to solve everyday problems? When are the properties, relationships, and characteristics of geometric shapes changed?

Student Learning Outcomes:
__//STUDENTS WILL BE ABLE TO://__ -Analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships. -Specify locations and describe spatial relationships using coordinate geometry and other representational systems. -Apply transformations and use symmetry to analyze mathematical situations. -Use visualization, spatial reasoning and geometric modeling to solve problems. -Identify geometrical objects around us. __//STUDENTS WILL KNOW://__ -Common geometric shapes -Geometric figures are made up of lines, segments, and rays. -Angles are measured in degrees and you can use a protractor to measure angles. -Polygons can be classified according to the number of sides, size of their angles, or the length of their sides -Geometric figures can be changed through reflections, rotations, and translations. Some geometric figures has symmetry.

Student Needs:
This unit was designed for a class of 20 students all of varying academic levels in a high school inclusion geometry class. There are 9 boys and 11 girls in the class, five of which are on IEP's. The students who have English as a second language have all tested out of ELL support classes.

//Pre-Assessment Expectations:// Before specific sections of the unit, students will participate in pre-assessment activities. These activities are used to assess prior knowledge and guide instruction in order to better differentiate learning. For example, before learning about geometric shapes students will participate in the following activity: Using magazines to find examples of parallel and perpendicular lines and polygons (Please see assignment #7 below). The purpose of this pre-assessment activity is to determine what the students' prior knowledge regarding geometric shape recognition. Teacher's can't assume that students know basic geometric shapes and their properties. This assessment would tell you what shapes students recognize and understand the properties of that basic shape. For example, a rectangle has two (2) sets of parallel lines.

//Student Interests:// Students love math and fish in this particular class (8/20 students in the class have fish as pets). In addition to many of the students having fish as personal pets, there is a classroom fish that the students are responsible for taking care of. All students have a basic understanding of both fish and fish tanks. Because of this, our end of the unit assessment revolves around designing fish tanks in cooperative learning groups. Students will use their prior knowledge of fish tanks and combine it with the geometric concept of right rectangular prisms. See lesson below.

//Student Profile:// The matrix below describes the IEP accommodations of three of the students in the class. G has poor reading skills, low-average cognitive abilities, and a physical disability which has caused him to miss large amounts of school over the course of his academic career. G suffers from Brittle Bone Disease. Y has low-average cognitive abilities. In addition to fish, Y loves using the computer. However, Y loves using the computer for "non-academic" purposes. Y is very artistic and flourishes with art based activities. Y requires lots of staff prompting in order to complete academic tasks. J is diagnosed with ADHD and enjoys talking to both peers and staff members. J sometimes struggles with his self-esteem and requires lots of encouragement when completing academic tasks. In addition to bragging about his pet fish, J is a star on the athletic field.

Source

Possible Projects/Assessments:
1. Origami: paper folding to explore geometric patterns and use the language of geometry to tell others how to make them 2. Puzzle making: Tangrams – how shapes fit together 3. Frieze Pattern/ Pictures of Designs 4. Design Making – How civilizations used geometry to express themselves/Recognizing Geometry Around You 5. Logic Puzzles – logic in math and determining truths in math 6. Origami: lines, points, and segments. 7. Using magazines to find examples of parallel and perpendicular lines, polygons etc. 8. Clocks to classify angles: What type of angle if it is __ o’clock. 9. Measuring Angle game: Draw, measure, estimate. 10. Take apart angles from triangles to make straight lines. 11. Construct sides of a triangle using cardboard strips. 12. Using cut out shapes and alphabet to determine polygon symmetry and rotations. 13. Use pattern blocks to decide which shapes tessellate 14. Classify, identify, and construct points, lines, segments, rays, parallel lines, perpendicular lines and planes 15. Measure Angles and Segments using a protractor, ruler, and or algebra 1 concepts. 16. Define geometry related terms and use deductive reasoning to problem solve. 17. Classify polygons and quadrilaterals using geometric patterns 18. Identify polygons and quadrilaterals using geometric patterns 19. Construct polygons and quadrilaterals using geometric properties. 20. Graph reflection, rotations, translations, and dilations on a coordinate grid 21. Determine if shapes have a line of symmetry. 22. Use reasoning (if then statements) to solve problems 23. Compare relationships when given a variety of cut out triangles (congruent, similar, sides) 24. Classify lines and angles 25. Identify lines and angles 26. Construct lines and angles 27. Measure Angles and Segments using a protractor and ruler 28. Explore angles in a triangle and sides of a triangle 29. Classify triangles and angles 30. Construct various polygons based on their characteristics 31. Classify various polygons based on their characteristics 32. Identify various polygons based on their characteristics 33. Use SmartBoard to plot points to make geometric shapes on a coordinate grid 34. Making a net of a geometric solid 35. Constructing a geometric prism with a specified volume. 36. Calculate the surface area of a right rectangular prism. 37. Comparing and contrast various right rectangular prisms. 38. Illuminations.nctm.org - Exploring geometric solids (Design/Create a Fish Tank) 39. Illuminations.nctm.org - Exploring geometric solids (Evaluate a designed fish tank in the shape of a right rectangular prism). ** *Assignment numbers correspond to the numbers listed in the assignment matrix. ** = SSON =

Theme: Geometry Topic: Rectangular Prisms/ Volume/ Area
__Essential Understandings__ 1. Geometry is all around us. 2. Characteristics and properties of geometric shapes are used to solve real life problems. 3. Geometric figures can be changed when their properties and relationships are changed.

__Content Objectives:__ 1. Analyze characteristics and properties of geometric shapes and geometric relationships to solve problems. 2. Describe objects using geometric shapes and their properties. 3. Determine the area, surface, area, and volume of a rectangular prism. 4. Apply geometric methods to design a fish tank. 5. Convert units of measure when calculating the area, volume, and surface area of rectangular prisms.

__Developmental Objectives:__ 1. Work cooperatively in a small group setting to create a final product.

__Affective Objectives:__ 1. After viewing the design of each fish tank designed by the various groups in the class, students will share his or her opinions of which fish tank is the best designed tank.

__Connection to the Frameworks:__ G-MG.1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). G-MG. 2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). G-MG. MA.4. Use dimensional analysis for unit conversions to confirm that expressions and equations make sense.

__Materials:__ Computer with internet Worksheet Plastic blocks that interlock/ paper nets Pencil Reference Sheets with formulas

__Vocabulary:__ Right Rectangular Prism, Net, Area, Surface Area, Volume, Cubic Units, Square Units, Faces, Vertices, Edges, Formula, Length, Width, Height

__Procedure:__ //Introduction (10 minutes):// 1. Show students a right rectangular prism made out of blocks. 2. Brainstorm with students the different types of objects they see that look like a right rectangular prism (e.g. – fish tanks, dice, box, etc.) 3. Ask students how rectangular prism is formed – go over nets. 4. Assess prior knowledge by asking how many faces, vertices, and edges a right rectangular prism has. – Go through an example with them. 5. Have students explore rectangular prisms and nets using the following website: http://www.learner.org/interactives/geometry/3d_prisms.html

//Student/Teacher/Materials Interaction (50 minutes):// 1. Give each student a cut out of a net that will make a right rectangular prism. 2. Make the right rectangular prism together. Then ask students if they think there is only one type of net that can be made. 3. Have students explore different nets on the website: [] 4. Introduction to the activity. Students will be told that they will design their own fish tanks and get into groups of three to complete the activity. 5. Pass out the following worksheet for students to use for their design: http://illuminations.nctm.org/Lessons/PrismFishing/PrismFishing-AS-FishTank.pdf Numbers 1-9 only 6. In groups, students will use 1x1 blocks to make rectangular prisms with a volume of 8 cubic units. Each group will come up with three designs. 7. Students will draw the net of their design. 8. Students will practice finding the surface area of a net using the website: [] 9. Student will calculate the surface area of their net. 10. Students will manipulate the fish tank by rotating it to see if the surface area of the tank changed. 11. Students will then calculate the price of glass needed to build their design. 12. Students will then go back compare the volume and surface area of all three original designs and determine which design is the most effective.

//Conclusion (10 minutes):// 1. Students will then compare their designs to other groups’ designs to determine which group had the best design and why. 2. Students will then determine how many fish can fit into the top three fish tanks using no more than 2 inches of fish for one gallon of water. 3. Using the information from number two students will then write a 3-4 sentence summary of why the number one fish tank is the best. Modifications for special needs/ELL learners:

__Differentiation by Levels__ Extension for the students at the highest level – Look up dimensions of various fish tanks that are marketed as being the best and compare different designs. Then answer the following- What guidelines would you provide a company to create a container with a set volume and minimum surface area? Include mathematical reasoning to convince the company. Differentiating the activity for students at the lower levels – Students will be given a pre-determined net to use with the dimensions. Students will be placed in a group of various abilities. Struggling students will also be given a formula sheet with examples to use when completing the assignment.

__Differentiation by Learner__ Posters of the various shapes such as a right rectangular prism and their properties will be posted in the room. Posters of how to calculate surface area and volume will also be posted. The kinesthetic learners will benefit from building models of fish tanks and using rulers to measure dimensions.

__Differentiation (Other)__ All students will be pre-taught vocabulary. ELL students will be able to look up their language equivalent to better understand new vocabulary. ELL Students will also be given reference sheets with examples under each new vocabulary word. Students will be given the opportunity for 1:1 instruction as needed as well as the opportunity to work in groups. However, all students will have a final product. Other accommodations based on the students IEP will also be taken into account when completing this lesson.

__Measurement of learning:__ Rubric (see below) Accurately answering problem one on practice page 1-9 when the activity is done.

MY SCORE= _ out of 24 = _ %
= References: = "Class Profile Matrix." Johns Hopkins University Center for Technology in Education. N.p., 2006. Web. Document retrieved from  on June 21, 2012.