Sneha TharayilProfessor LarrivaGED 650June 8, 2011

Robotics Unit

Stage 1—Desired ResultsEstablished Goals/Standards:Grade 6 MathAlgebra and Functions3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = d - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).3.2 Express in symbolic form simple relationships arising from geometry.

Measurement and Geometry1.3 Know and use the formulas for the volume of triangular prisms and cylinders (areaof base × height); compare these formulas and explain the similarity between themand the formula for the volume of a rectangular solid.2.1 Identify angles as vertical, adjacent, complementary, or supplementary and providedescriptions of these terms.2.2 Use the properties of complementary and supplementary angles and the sum of theangles of a triangle to solve problems involving an unknown angle.2.3 Draw quadrilaterals and triangles from given information about them (e.g., aquadrilateral having equal sides but no right angles, a right isosceles triangle).

Understandings:Students will understand that…

Geometric shapes are defined by their properties

Various disciplines in mathematics are entwined with each other

There are real-world and inter-disciplinary applications of the geometry concepts taught in this unit

Essential Questions: How are shapes defined? How do changes in properties/dimensions

affect the shape of a polygon or 3-dimensional figure?

How is geometry, specifically concepts of area, perimeter, angles, volume, etc. applied in the real world and in other disciplines?

How can we represent abstract (mathematical) concepts in a concrete way?

Students will know… Formulas for area, perimeter, volume for different polygons and three-dimensional figures Angle properties and rules (complementary, supplementary, adjacent, vertical, etc.) Types of various polygons (types of triangles, quadrilaterals, etc.) Properties of different polygons (total # of angles, number of sides, vertices, area, etc.)

Students will be able to… Write algebraic equations with missing variables Define properties of geometric shapes and figures Apply mathematical concepts (particularly geometry and algebraic equations) to real-world situations and

in other subject matter

Stage 2—Assessment EvidencePerformance Tasks:

Design a blue print of a house based on a customer’s desires and the specifications of land, space, and budgets available

Create a model bridge using knowledge of physics and geometric shapes that will best fulfill the purpose for the bridge

Invisible pathway challenge for LEGO MINDSTORMS Robot (The Robot must complete a sort-of reverse X-Bot challenge in which the pathway the robot must travel will be comprised of missing segments from various shapes. Students must determine what segment is missing from each shape to determine the path)

Create a cubism art piece using a LEGO MINDSTORMS robot (described below)

Other Evidence: Student journals/notebooks Student process papers Quizzes/Tests Worksheets Homework assignments Observation

Stage 3—Learning PlanLearning Activities:

Read from Math Textbook Exploration with shapes and prisms that are contrived, student-created, and within the environment Discussions on uses of geometry in the real-world (professions), and in other subjects Practice Problems/ worksheets Performance Learning Tasks (listed above in Stage 2)

1. Title: Roboto Picasso

2. Grade level: 6th grade (or Geometry and Algebra)

3. Goals and Objectives: Goals

Students will understand that geometric shapes have properties that define it Students will recognize that Mathematics is intertwined within itself and in

other areas of study or trades Students will be able to apply various mathematical concepts, especially:

algebraic formulas, proportions, area, volume, perimeter, etc. Students will develop an appreciation for different styles and genres in the

visual arts Students will recognize the value of technology in art Students will be able to masterfully use the LEGO Mindstorms Robotics kit in

a productive and unique way

Objectives

Students will use their knowledge about certain properties (such as area, angles, perimeter) of various polygons to draw certain polygons according to specifications given by the teacher

Students will program their robots to create a cubist drawing based on specific criteria for each geometric shape that will appear in their cubist drawing

Students will create a cubist drawing depicting the basic elements of cubism

4. California Content Standards:Algebra and Functions

1.1 Write and solve one-step linear equations in one variable.1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = d - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).3.2 Express in symbolic form simple relationships arising from geometry.

Measurement and Geometry2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).

Visual ArtsCreative Expression

2.4 Create increasingly complex original works of art reflecting personal choices and increased technical skill.2.6 Use technology to create original works of art.

Historical and Cultural Contexts3.2 View selected works of art from a culture and describe how they have changed or not changed in theme and content over a period of time.

5. Prior knowledge: Students will already be familiar with programming the LEGO Mindstorms

Robots Students will have had ample practice computing the perimeter and area of

basic two-dimensional polygons (rectangles, triangles, squares, parallelograms)

Students know the total degrees for each shape (180 degrees for Triangle, 360 for rectangles, etc.)

Students will have had practice with measuring the degree of an angle with a protractor and using one to draw a specific angle

Students will be familiar with using proportions for conversions of units

Students will be accustomed to writing simple equations and expressions with one to two missing variables based on whatever information is provided

6. Materials: LEGO Mindstorms Robotics Kit Computer access with LEGO Mindstorms software Pencil and/or Pen Markers, paint, or color pencils Graph Paper Large sheet of Butcher Paper or blank white Poster Board for each group Notebooks for each student

7. Time duration: For The Whole Lesson: 3-4 days Introduction and mini-lesson on Cubism: 20 minutes Explanation of Activity: 10-15 minutes Review of Mathematical concepts: 20 minutes Solving Clues: 30 minutes Drawing and mapping out cubism drawing: 60-75 minutes Programming Robots: 2-3 days

8. Activity: 1. The teacher will give students a mini lesson on cubism art. This lesson will discuss

the main elements of cubism art: geometric shapes, distortion of the image, bold and varied colors. Students will also be introduced to famous cubist artists, such as Pablo Picasso and Henry Matisse, and will be shown several examples of cubism pieces.

2. Students will be divided into groups of 3-4.3. Each group of 3-4 students will receive an envelope of clues for various polygons that

their cubist piece will be comprised. For example: “This shape has an area of 6ft squared and a perimeter of 10ft.

All angles are 90 degrees” Each envelope will contain 3 clues for 3 polygons. Students MUST only use

these shapes for their cubist piece. All angles for any polygon will be limited to 30, 45, 60, 90 (and possibly 150,

120 degrees if parallelograms are being used) degree angles.4. In their notebooks, students must show how they solved each clue and they must

show use of algebraic expressions and variables. They will also draw each polygon individually in their notebooks. This will be checked by the teacher before students can proceed to the next step.

5. Each group will then make a scale drawing of their cubist piece on graph paper and have it approved by the teacher. They may use each polygon more than once. (It is recommended that the scale for the scale drawing be that the length of 1 side of 1 square on the graph paper represent 1 foot. For example, the scale would be 1cm:1ft, on graph paper where each square is 1cm X 1cm)

6. Students will also map out the robot’s pathway to create the drawing. The robot will have to draw at least 3 of the polygons on the poster board. The other shapes may be hand-drawn on the final piece afterwards.

7. Students will then need to design a robot that has a drawing apparatus attached to it (something that will hold a writing tool).

-If necessary, the teacher will provide some groups who need it with a basic design for a robot with a drawing apparatus

8. Students will then program their robots to create the drawing in one continuous pathway on a large poster.

The teacher will provide the approximate number of rotations required for each degree of turns the robot must make

Extraneous lines between each shape will be permitted9. Students may then color/paint their piece and add in a picture of something (ex:

someone’s face, an animal, etc.)10. Students will then write a brief write-up explaining their process.11. At the completion of the project, all work will be evaluated using the rubric found in

the assessment section.

*Below is a sample showing how students will map out their cubism pieces*

9. Scaffolding: The teacher will model each phase of the process, especially for Step #4,

when students will have to solve each clue. Heavy emphasis will be placed on modeling the identification of key words/phrases and variables when writing algebraic expressions/equations from word problems. [Modeling].

The teacher will have students recall past activities that involved the same mathematics concept. For example, showing how the same concepts of area were applied in an activity done earlier in the unit. This will be done in the review component of the lesson. [Bridging, Schema Building].

A set of pictures of familiar objects/images will be displayed for students to see at the very beginning of class. Each image will have two versions: one version will depict the image in its normal, ordinary form; the other version will depict the image in a distorted, cubist fashion. This will be used during the mini lesson on cubism. The teacher will first show the cubist version and then the normal version so students can see how cubist pieces come about. (See Below) [Bridging].

The teacher will also give ELL students a sort of “Cheat Sheet” with definitions of important academic vocabulary and terms with illustrations to help enhance the definitions. Students may use these while solving their polygon clues. [Contextualization, Re-Presenting Text].

Students will be paired with other group members that can best help each other, especially in scaffolding each other’s understandings and skills in the concepts at hand, as well as linguistically. [Cooperative Learning, ZPD]

The notebooks and graph paper maps/rough drafts are also a mechanism of scaffolding because not only will students be able to monitor and check their own learning but so will their peers as well as the teacher. [Metacognition]

10. Assessment: Formative Assessment

o Observation The teacher will look to see how students solve the clues and

how they construct their scaled drawings

o Student Notebooks

The student notebooks will help the teacher determine whether students have developed the following competencies:

Writing algebraic expressions/equations to represent word problems with missing quantities

Calculating the perimeter and area of different polygons Distinguishing the different properties of various shapes Applying knowledge of geometric shapes to determine

geometric shapeso Graph Paper scaled maps/rough drafts of cubist drawing

This student work will allow the teacher to determine the following competencies:

Drawing geometric shapes accurately given specific information about the shape

Alignment with elements of cubism Feasible planning for Robot’s pathway

Summative Assessmento The following rubric will be used to assess student work throughout

the project (this includes notebooks, graph paper maps, final robot drawing/cubist piece, and write-up):

o This rubric assesses mastery of all the same competencies listed above in the Formative Assessment

Anticipated Student Responseso Students may not immediately attempt to formulate an equation in order to

solve each clue. They may draw a diagram, and may use guess-and-check methods first in order to solve each clue. While this is permissible, students will still be required to construct an equation and/or expression to express the geometric quantities and relationships

o Students may able to correctly solve the clues but may not be able to accurately draw the figures. In this case, these students will be re-taught how to use various measurement tools (rulers, protractors) accurately in order to achieve the desired results

o Students may have difficulty understanding the clues. In this case, the clues will be edited for clarity. For students with really struggling linguistic capabilities, perhaps clues may revised so that there is a minimal written language they must manipulate in order to solve the clue

o Students may have some challenges in planning their robot’s pathway. To prevent this, students will be given some helpful guidelines in order to best achieve a feasible pathway

o There may be discrepancies in how precisely the robot follows the intended pathway. Because this could be due to different environmental factors, students will be given numerous chances to test their programming until they can get it as close as possible to the intended pathway/drawing. If even after numerous attempts the robot is still not able to produce an accurate drawing, then student’s will be graded on the robot’s run, but most importantly all the group’s work prior.