Is it Really that BIG?
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This lesson provided by:
Author: YVETTE AKRIDGE
Organization: ENTERPRISE STATE COMMUNITY COLLEGE

General Lesson Information
Lesson Plan ID:
32212
Title:

Is it Really that BIG?
Overview/Annotation:

Just how tall is that object? In this lesson, students will participate in an outdoor group activity using shadows to extend their knowledge of proportions to solve problems dealing with similarity. The cooperative learning groups will measure the heights and shadows of familiar objects (like themselves!) and use indirect measurement to find the heights of things that are much bigger in size, such as a tree, a school building, or a flagpole.

Associated Standards and Objectives
Content Standard(s):
TC2 (6-8) 2. Publish digital products that communicate curriculum concepts.

Examples: Web pages, videos, podcasts, multimedia presentations

MA2015 (7) 2. Recognize and represent proportional relationships between quantities. [7-RP2]

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [7-RP2a]

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [7-RP2b]

c. Represent proportional relationships by equations. [7-RP2c]

Example: If total cost t is proportional to the number n of items purchased at a constant price p , the relationship between the total cost and the number of items can be expressed as t = pn .

d. Explain what a point (x, y ) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r ) where r is the unit rate. [7-RP2d]

MA2015 (7) 3. Use proportional relationships to solve multistep ratio and percent problems. [7-RP3]

Examples: Sample problems may involve simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.

Local/National Standards:

NCTM Standards and Objectives:

Geometry 6-8

Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Measurement 6-8

Solve problems involving scale factors, using ratio and proportion.

Understand both metric and customary systems of measurement.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

Primary Learning Objective(s):

This lesson will allow students to find the heights of objects they normally could not measure with everyday measuring utensils (e.g. rulers, yard sticks, or measuring tapes). They will do so, by measuring shorter objects (like themselves!) and their shadows, then use similarity and indirect measurement to set up and solve proportions.

Additional Learning Objective(s):

Students will compute unit rates associated with ratios of lengths, areas, and other quantities measured in like or different units.

Preparation Information
Total Duration:

61 to 90 Minutes

Materials and Resources:

Scissors

Calculators (Optional)

"Is it Really that Big?" Worksheet

Large Objects (Tree, School Buildings, Flagpole, etc.)

String

Yard Stick or Measuring Tape

Technology Resources Needed:

Document Camera (Optional)

Digital Projector

Computer with Internet Access for Teacher and Students

Multimedia Presentation Software - Glogster (Choose create your own GLOG now, for free, if the students do not already have an account.)

Digital Cameras (Enough for each group of 4 to have one.)

Interactive Whiteboard (Optional)

Background/Preparation:

Teacher will need:

Print and Copy "Is it Really that BIG?" Worksheet (Attachment)

Teacher should visit Glogster prior to the lesson to become familiar with the site.

Teacher should visit Proportions Review prior to the lesson.

Teacher should predetermine groupings of students, in sets of 4, with careful consideration of student strengths and weaknesses in solving proportions. (It would be best to consider peer tutoring for this activity.)

Student will need:

Students should have prior knowledge of solving proportions.

Students will need to be taught how to use Glogster , if they are unfamiliar with the multimedia presentation website.

Procedures/Activities:
The Lesson (This Lesson Should Be Done on a Sunny Day):

As the students enter the room, inform them know that they will be participating in a group activity named "Is it Really that BIG?". Once the predetermined groupings have been assigned, have the groups sit together, it makes for an easier outside transition.
Engage the students by asking if anyone remembers how to solve proportions? If someone can answer the question, reward them with positive feedback. Continue reviewing by allowing students to answer questions from the Proportions Review website. This ice-breaker should take 5-10 minutes.
Introduce the lesson, by asking students how they might find the height of a tall object just by knowing the length of its shadow? Discuss what the word "similar" means. Next, help the students see how to use proportions to determine the heights of tall objects that they cannot physically measure. Measure the height and shadow of an object in your classroom and the height of another object to set a proportion of similar objects. Give the students a visual picture of what this activity is going to teach them. Work with the students on setting up proportions to solve for missing measures.
Give each group two yard sticks or a measuring tape, string, scissors, a digital camera, worksheet and a calculator. Explain to them that they will be going outside to apply what they have learned about proportions.
Instructions :
Working in their cooperative learning groups, the students will measure each others' heights and the shadows their bodies produce with the string. They are to cut the string to match the measurements and use the yard stick or measuring tape to measure the lengths of the strings for both their height and their shadow (they should have two strings per individual group member).
Each member of the group, should record their individual data on the "Is it Really that Big?" worksheet (Attachment). Remind the students that their measurements should be consistent, using either all metric measurements or all customary measurements.
Next, instruct the students to measure the shadows of two "large" objects outside (e.g. flagpole, school building, or a tree) and record that data on the worksheet as well.
Instruct the students to work quickly when measuring each others' shadows and the shadows of the "large" objects. Remind them of the Earth's rotation and what happens due to the rotation (if they take 5 minutes between measuring a person's shadow and the "large" objects shadow, it could skew, distort the results, the answers to their worksheets).
Once the data has been collected, have the groups return to the classroom and begin to working on their multi-media presentations.
While the data is being collected, group members should take turns taking pictures of each other, with the digital camera, being measured, as well as, pictures of the objects being measured. The pictures, along with the calculations and answers to the worksheet, should be used to make a multi-media group presentation using Glogster .

Attachments: **Some files will display in a new window. Others will prompt you to download.

Assessment
Assessment Strategies

Assessment :

Students will be given a cooperative group grade for the multi-media presentation and the "Is it Really that BIG?" worksheet. (The grade should be based on the following: the group listed each of their names, their heights, their shadow lengths, the "large" objects' names, the "large" objects' shadow length, verification of the correct outcome and correct information on Glogster presentation.)

Acceleration:

Extension :

To determine whether the students are able to use indirect measurement, have them use the measurements gathered earlier (their own heights and shadows) to figure out the measures of the shadows of classroom objects (filing cabinets, Interactive Whiteboards, bulletin board, classroom door, etc.). This activity will be the reverse of the previous process because the actual heights of the objects will be known. This allows for assessment of whether the students can apply indirect measurement in multiple settings.

Intervention:

Remediation :

Grouping students would help those who may have trouble comprehending and solving proportions individually. Consider technology strengths and weaknesses when forming groupings.

During the time frame of this lesson, peer tutoring could help a student who needs extra preparation for solving proportions.

Each area below is a direct link to general teaching strategies/classroom
accommodations
for students with identified learning and/or behavior problems such as: reading
or math performance below grade level; test or classroom assignments/quizzes at
a failing level; failure to complete assignments independently; difficulty with
short-term memory, abstract concepts, staying on task, or following directions;
poor peer interaction or temper tantrums, and other learning or behavior problems.

Be sure to check the student's IEP for specific accommodations.