Assessment Photo Album

Assessment Photo Album

Subject: Geometry, Technology, and Family & Consumer Sciences

Grade: 9 – 10By: Julie Owens

Unit: 2-Dimensional ObjectsPolygons & Circles

Polygons and CirclesInterdisciplinary Unit

This unit investigates properties, perimeter, and area of 2-dimensional objects, as they related to the real world, with the assistance of the Pythagorean Theorem, technology and interior designs.

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 and approximate values

unit 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 including

angles, side lengths and radii application of the Pythagorean Theorem in right triangles and

special right triangles computer software enhance presentations

Students will be able to…

calculate lengths, perimeter, and area of congruent objects

apply Pythagorean Theorem to find unknown side lengths 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 using properties of triangles, squares and circles

calculate using literal equations and formulas to find the area of polygons and circles given the perimeter or circumference as exact values 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 same area? When does a mathematical value contradict a logical

solution? Why is reducing waste good for the environment? How many diameters does it take to create the

circumference of a circle? Why would an exact value be difficult to use in the real

world? How can the Pythagorean Theorem be used in

construction? Are objects seen in nature accidental, or does it have

an important role in the development of their environment?

How can properties of polygons be used to design real-life models?

How can using technology tell a math story?

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

2-dimensional polygons are found in real-world such as nature,

art, architecture, and design models.

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

Changing a geometric shape in one or more dimension affects area.

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

Learning Goal 3OK PASS 2.5b: Use the relationships of congruency of 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

Relationships between congruent objects begin with determining dimensions of objects.

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

Solutions can be written in decimal form and as an exact value.

Pythagorean Theorem is used in solving for missing side lengths a variety of situations involving right triangles.

Learning Goal 5

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

Special Right Triangles come from properties found in squares, equilateral triangles, and patterns within the Pythagorean Theorem.

Learning Goal 6:Family and Consumer Science 11.3.3 Apply housing and interior design knowledge, skills and processes that include demonstrate measuring, estimating, ordering, purchasing, and pricing skills.

Logic plays an important role in

solving problems involving

geometric objects, including those

related to real world situations.

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

Students will digital cameras to collect and create a presentation that represents geometry in the real

world.

Not recorded as a grade

Diagnostic Assessments

Diagnostic assessments are used to identify students’ readiness levels. A pre-test will be given for each of

the following:

Perimeter and area of triangles, squares, and rectangles.Circumference and area of circlesPythagorean TheoremStudent Survey: Using Technology and Family

Assistance

Sample Pythagorean Theorem Pre-Assessment QuestionsSolve for the missing side of the right triangle

using the Pythagorean Theorem: a2 + b2 = c2

c = _______ b = _______ 

4 c b 8 

3 4

Student Survey:Technology and Family AssistanceSample Questions:

I can download pictures from a digital camera or cell phone to the computer: 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 and

circles Two assessments will be given over perimeter and area of

polygons and circles. 1. Multiple choice and short answer using Student Response

System, clickers. 2. Extended response and essay, allowing students to draw

diagrams, infer, and calculate based on progressive knowledge.

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 to represent

the information given in written situations.

Benchmark Assessment

Students will individually track progress on standards 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 be given throughout this unit. Students will

be given choice of tasks, roles, and have input on criteria used to create

and evaluate slide show.

Performance Task #1

Student Choice:

Paint My Room or

Carpet This House

Students will choose one of these tasks. Goal is to measure, calculate area, and determine cost to either paint their bedroom or carpet the living room. Calculations must include waste.

Performance Task #2

Digital Portfolio, Journal, and Slide Show

Students will work in cooperative groups to take pictures relating to geometric shapes as seen in art, architecture, and the community. They will document objects in the form of a journal, then organize their collection into a digital presentation for their final exam. Group members will be assigned various

roles based on survey results, interest levels, and learning styles.

Co-constructed Checklist for Digital 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 used in 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 come from: art/architecture, nature, school and community

Rubric for Digital Presentation

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

Digital Portfolio rubric.pdf

Summative Assessments2 Paper/Pencil Exams

Sample questions based on Stated Proposition:

Pythagorean Theorem, a2 + b2 = c2, is used to find unknown lengths, or distances between two points, when a right triangle is used to represent the situation.

True/False

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

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

Multiple Choice M/C: A TV screen has dimensions of 80

x 60 cm. Using the Pythagorean Theorem what is the length of the diagonal?

A. 50 cmB. 70 cmC. 90 cmD. 100 cm

Short Answer

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

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 used to represent the given situation. Draw a diagram that supports your response, and using the Pythagorean Theorem, calculate the length of the diagonal.

EvaluationComments….

Possible Revisions…..

Overall rubric score…