TitleIII Technology Literacy Challenge Grant

Learning Unit

Overview | Content Knowledge | Essential Questions | Connection To Standards | Initiating Activity | Learning Experiences | Culminating Performance | Pre-Requisite Skills | Modifications | Schedule/Time Plan | Technology Use

OVERVIEW

One need not look far to see that percent applications surround us. Like our students, we have all experienced occasions when we overlook what stares us in the face. This unit is intended to first direct attention to the prevalence of percents, and then to develop a working understanding of them. As outlined in Understanding by Design teachers must establish curricular priorities. The premise for this learning unit is that percents are both "enduring" and "at the heart" of the grade 7 mathematics curriculum. Although this unit includes a significant amount of skill development, the main thrust will be to establish a base for meaningful and long-lasting understanding for the application of percents.

(It should be noted that this unit requires integration with an ELA instructor.)

(www.askjeves.com and www.dogpile.com are excellent search engines to find both dining and shopping locations.)

CONTENT KNOWLEDGE

ESSENTIAL QUESTIONS

1. What are the advantages of using percents as a standardized means of making comparisons?
2. Mental math lends itself to "solutions at the ready." What benefit might this provide for one when dealing with percents in a store, restaurant, bank, or school?
3. How does understanding percents make one a "smart consumer"?

CONNECTIONS TO NYS LEARNING STANDARDS
List Standard # and Key Idea #: Write out related Performance Indicator(s) or Benchmark(s)

MST 1:

Key Idea 1- Mathematical Analysis: Abstraction and symbolic representation are used to communicate mathematically.

Performance Indicator: Students extend mathematical notation and symbolism to include variables and algebraic expressions in order to describe and compare quantities and express mathematical relationships. This is evident when students create an equation to solve real life problems involving percents.

Key Idea 2- Mathematical Analysis: Critical thinking skills are used in the solution of mathematical problems.

Performance Indicator: Students apply mathematical knowledge to solve real-world problems and problems that arise from the investigation of mathematical ideas, using representations such as pictures, charts, and tables. This is evident when students compare the sum of multiple percents off vs. the equivalent total. E.g. 50% off plus and additional 25% off compared to 75% off

MST 3:

Key Idea 1- Mathematical Reasoning: Students use mathematical reasoning to analyze mathematical situations, making conjectures, gather evidence, and construct an argument.

Performance Indicator: Students will apply a variety of reasoning strategies. This is evident when students use multiple means for solving percent related word problems, such as 25% of 80 is __ = .25 (80) = X or 25/100 = X/80

Key Idea 2 - Number and Numeration: Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.

Performance Indicator 1: Students understand, represent, and use numbers in a variety of equivalent forms. This is evident when students understand and demonstrate the concept that a number can be symbolized by many different numerals as in: 3/12=1/4=25/100=.25=25%.

Performance Indicator 2: Students understand and apply ratios, proportions, and percents through a variety of hands on exploration. This is evident when students are able to identify and solve real world problems involving percents.

Performance Indicator 3: Students develop an understanding of number theory (primes, factors and multiples). This is evident when student are able to simplify expressions.

Key Idea 3 - Operations: Students use mathematical operations and relationships among them to understand mathematics.

Performance Indicator: Students apply concepts of ratio and proportion to solve problems. This is evident when students find the missing number in a proportion in which three of the numbers are known, and letters are used as placeholders.

Key Idea 4 - Uncertainty: Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with every situation.

Performance Indicator 1: Students use estimation to check the reasonableness of results obtained by computation, algorithms, or the use of technology. This is evident when students are able to use "reference percents" to make mental calculations.

Performance Indicator 2: Students use estimation to solve problems for which exact answers are inappropriate. This is evident when students estimate a reasonable "tip" when dining out.

Key Idea 5 - Patterns/Functions: Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

Performance Indicator: Students develop an understanding of functions and functional relationships: that a change in one quantity (variable) results in change in another. This is evident when students solve real life problems involving percents.

ELA 1

Key Idea 1 - Speaking an Writing: Speaking and writing to acquire and transmit information requires asking probing and clarifying questions, interpreting information in one's own words, applying information from one context to another, and presenting the information and interpretation clearly, concisely, and comprehensibly.

Performance Indicator: Students produce an oral and written reports on topics related to all school subjects. This is evident when students orally present to their classmates and write an essay that contains information from a variety of sources.

INITIATING ACTIVITY

Students will be required to collect five to eight examples of "real world" percents. An essay must be written indicating where the application of percent is used and conclude with a persuasive statement supporting the value of them. The following resources may be referenced: newspaper, magazines, Internet (hard copy), or a television advertisement (drawing). Students will be placed in cooperative triads. Each member will be required to discuss his/her contribution and the team will then create a collage. These will be graded and displayed in the classroom.

LEARNING EXPERIENCES
In chronological order including acquisition experiences and extending/refining
experiences for all stated declarative and procedural knowledge.

CULMINATING PERFORMANCE
Include rubric(s)

Students will have a choice of either "Dining Out, " or having a "Sports Related Shopping Spree" on the Internet.

Dinner

Five dinners representing at least three different cultures

The following items must be listed for each dinner - Drink, entrée, and dessert

Calculations must be determined for meal, tax, tip, and total expenditure for each of the five days.

One dinner must be selected for an oral presentation. Part of this presentation must include a "walk through solution."

Sports Shopping Spree

Shop on the web to purchase clothing and equipment for two sports

Must include at least two sale items for each sport

Percent of savings and amount of savings must be determined for each

Total bill must be calculated, including shipping and handling

Shipping and handling must also be expressed as a percent

If no tax is charged, 8% is to be used to determine the approximate amount of savings due to no tax.

An oral presentation must be reflect why a sale item was purchased. Part of this presentation must be a "walk through solution.."

PRE-REQUISITE SKILLS

Percents are first introduced to students in grade 5 . This important concept continues to be spiraled through intermediate and commencement levels. Although all students will recognize and be able to perform some skill functions, they will need to be broadened and refined.

MODIFICATIONS

• Abbreviated Assignments
• Extended Time
• Individual Help (Lab and/or After School)
• Calculators Allowed For All

TECHNOLOGY USE

1. Student essays must be completed using word processing software.

2. The worldwide web will be utilized to gather necessary data to complete the culminating performance. An introductory level of Internet sophistication will be necessary to satisfactorily complete this requirement.

Culminating Performance Self-evaluating and Teacher Rubric