Assessment Photo Album

Subject: Geometry, Technology, and Family &Consumer Sciences

Grade: 9 – 10

By: Julie Owens

Unit: 2-Dimensional Objects

Polygons & Circles

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Polygons and CirclesInterdisciplinary Unit

This unit investigatesproperties, perimeter, andarea of 2-dimensionalobjects, as they related tothe real world, with theassistance of thePythagorean Theorem,technology and interiordesigns.

Students will know…

properties of 2-dimensional objects including triangles,quadrilaterals, regular polygons and circles

formulas for unknown values including side length, radius,perimeter, circumference, and area (literal equations)

calculators are tools to simplify formulas and verify exact andapproximate values

units of measure and conversions between units

optimization, maximization of area and perimeter using real-world materials (fence, carpet, tile) including waste

relationships of congruent 2-dimensional objects includingangles, side lengths and radii

application of the Pythagorean Theorem in right triangles andspecial right triangles

presentations are enhanced with computer software

Students will be able to…

calculate lengths, perimeter, and area of congruentobjects

apply Pythagorean Theorem to find unknown sidelengths of triangles

use properties of squares, equilateral triangles,and Pythagorean Theorem to discover the 45-45-90 and 30-60-90 triangles

discover formulas for perimeter, circumference and area usingproperties of triangles, squares and circles

calculate using literal equations and formulas to find the area ofpolygons and circles given the perimeter or circumference as exactvalues and approximate values with and without the aid of calculators

use appropriate units of measure to distinguish between perimeter,circumference and area

maximize area using properties of polygons, such as dimensions,optimizing perimeter using real world materials as carpet, fence and tile

Essential Questions

Does the same perimeter always give the samearea?

When does a mathematical value contradict alogical solution?

Why is reducing waste good for the environment?

How many diameters does it take to create thecircumference of a circle?

Why would an exact value be difficult to use in thereal world?

How can the Pythagorean Theorem be used inconstruction?

Are objects seen in nature accidental, or do theyhave an important role in the development of theirenvironment?

How can properties of polygons be used to designreal-life models?

How can using technology tell a math story?

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Learning Goal 1OK PASS 2.3a: Identify, describe, and analyzepolygons (for example, convex, concave, regular,pentagonal, hexagonal, n-gonal).

2-dimensional polygons are foundin real-world such as nature,

art, architecture, and

design models.

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Learning Goal 2OK PASS 2.3d: Use properties of 2-dimensionalfigures and side length, perimeter or circumference,and area to determine unknown values and correctlyidentify the appropriate unit of measure of each.

Changing a geometric shape inone or more dimension affectsarea.

Solutions can be written in decimalform and as an exact value,such as in terms of π.

Learning Goal 3OK PASS 2.5b: Use the relationships of congruency of2-dimensional figures to determine unknown values,such as angles, side lengths, perimeter orcircumference, and area.

Relationships between congruentobjects begin with determiningdimensions of objects.

Learning Goal 4OK PASS 3.1: Use the Pythagorean Theorem and theconverse to find missing side lengths.

Solutions can be written in decimal formand as an exact value.

PythagoreanTheorem is used insolving for missingside lengths avariety of situationsinvolving righttriangles.

Learning Goal 5OK PASS 3.2: Apply the 45-45-90 and 30-60-90right triangle relationships to solve problems

Special RightTriangles come fromproperties found insquares, equilateraltriangles, andpatterns within thePythagoreanTheorem.

Learning Goal 6:Family and Consumer Science 11.3.3 Applyhousing and interior design knowledge, skills andprocesses that include demonstrate measuring,estimating, ordering, purchasing, and pricingskills.

Logic plays animportant role in

solving problemsinvolving

geometric objects,including those

related to real worldsituations.

Learning Goal 7Technology 8.2 Apply reasoning, problem solving,imagining, creating and constructing design andtechnology tools.

Students will digital cameras to collect and createa presentation that represents geometry in thereal world.

Diagnostic Assessments

Diagnostic assessments are used to identifystudents’ readiness levels. A pre-test will begiven for each of the following:

Perimeter and area of triangles, squares, andrectangles.

Circumference and area of circles

Pythagorean Theorem

Student Survey: Using Technology and FamilyAssistance

Sample Pythagorean Theorem Pre-Assessment Questions

Solve for the missing side of the right triangleusing the Pythagorean Theorem: a2 + b2 = c2

c = _______b = _______

4cb 8

3 4

Student Survey:Technology and Family Assistance

Sample Questions:

I can download pictures from a digital camera or cell phone to thecomputer:

With assistance from family or friends

Without assistance

Can download and edit using computer software

Do not have a computer

I have created presentations:

Using PowerPoint

Using Internet program

Using Movie Maker

I have not made a presentation

I can get assistance using technology from:

Parents

Friends

Teachers

I do not need assistance using technology

Formative Assessments

Multiple Choice and Short Answer

Benchmark

Students will document individual results.

Formative Assessments

Perimeter, circumference, and area of polygons andcircles

Two assessments will be given over perimeter and area ofpolygons and circles.

1.Multiple choice and short answer using Student ResponseSystem, clickers.

2.Extended response and essay, allowing students to drawdiagrams, infer, and calculate based on progressiveknowledge.

Right triangle problems using Pythagorean Theorem

Two assessments will be given over Pythagorean Theorem.

1.Multiple choice and short answer using clickers.

2.Students will draw a diagram using a right triangle torepresent the information given in written situations.

Benchmark AssessmentStudents will individually track progress onstandards as related to EOI test

Sample End-of-Instruction question:

In radical form, what is the perimeter of this trapezoid?

A 30 + 6 √3 + 6 √2 in.

B 34 + 6 √ 3 + 6 √ 2 in.

C 30 + 8 √ 3 + 8 √ 2 in.

D 38 + 8 √ 3 + 6 √ 2 in.

Performance Assessments

Two performance assessments will begiven throughout this unit. Students willbe given choice of tasks, roles, andhave input on criteria used to createand evaluate slide show.

Performance Task #1Learning Goals 2 and 6

Student Choice:

Paint My Room

Carpet This House

Students will choose one of these tasks. Goal isto measure, calculate area, and determine costto either paint their bedroom or carpet the livingroom. Calculations must include waste.

Performance Task #2Learning Goals 1, 3, and 7

Digital Portfolio, Journal, and Slide Show

Students will work in cooperative groups to takepictures relating to geometric shapes as seen in art,architecture, and the community. They will documentobjects in the form of a journal, then organize theircollection into a digital presentation for their finalexam. Group members will be assigned variousroles based on survey results, interest levels, andlearning styles.

Co-constructed Checklist forDigital Portfolio

2-Dimensional Objects:

3 – 5 pictures of each:

Triangles ____________

Squares _____________

Rectangles ___________

Circles ______________

4 – 5 pictures combined:

Parallelogram _________

Pentagon __________

Hexagon __________

Octagon __________

Trapezoid _________

Other _____________

A variety of locations must be usedin collecting pictures.

Acceptable places to take pictures:

Home, School, School Events,

Community, Buildings, Art,

Architecture, Nature, Sculptures,

And Signs/Billboards

Minimum of 4 pictures must comefrom: art/architecture, nature,school and community

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Rubric for Digital Presentation

To view copy of how presentation will bescored, click on hyperlink.

Digital Portfolio rubric.pdf

Summative Assessments2 Paper/Pencil Exams

Stated Proposition:

Pythagorean Theorem, a2 + b2 = c2, isused to find unknown lengths, ordistances between two points, when aright triangle is used to represent thesituation.

Sample Questions:

True/False

True:

If a TV screen has dimensions of 80 x 60 cm, then thelength of the diagonal is 100 cm.

False:

If a TV screen has dimensions of 80 x 60 cm, then thelength of the diagonal is 140 cm.

Short Answer:

A TV screen has dimensions of 80 x 60 cm, what is thelength of the diagonal? Draw a diagram and, using thePythagorean Theorem, calculate the length of the diagonal.

Multiple Choice

A TV screen has dimensions of 80 x 60cm. Using the Pythagorean Theoremwhat is the length of the diagonal?

A.50 cm

B.70 cm

C.90 cm

D.100 cm

Essay

A TV screen has dimensions of 80 x 60 cm,what is the length of the diagonal? Explain,in writing, how a right triangle can be usedto represent the given situation. Draw adiagram that supports your response, andusing the Pythagorean Theorem, calculatethe length of the diagonal.

Contributions to Rubric

 Diagnostic Assessments: add family participation in eitherthe diagnostic assessment or performance assessment.

Performance assessment to include creativity.

Gives students options of performance tasks based onreadiness or interest levels.

Diagnostic Assessments

At least one assessmentincludes family/community asrelated to content orperformance task. (such assurvey or questionnaire)

Assessments

Variation within assessmentinclude: selected response,constructed response, productand/or performance..

Only two - threevariations are used

Only one - two variationsare used.

Options

Gives students options on type ofperformance task to completebased on readiness levels orinterests.

Evaluation

Comments….

Possible Revisions…..

Overall rubric score…