Title III Technology Literacy Challenge Grant s2

Title III Technology Literacy Challenge Grant

Learning Unit

LU Title: Ratio, Proportions, Scale / Author(s): Denise M. Parmon
Grade Level: 6th / School : West Canada Valley CS
Topic/Subject Area: Math / Address: POB 360 Newport, N.Y.113416
Email: / Phone/Fax: 315-845- 8074/ 8652

OVERVIEW

This is a 6th grade math unit that is designed for all ability groups. It should take three to four weeks. During this unit the students will participate in various activities to reinforce the concepts of ratio, proportion, scale and how they are connected. Activities will be structured so that the students discover the connection.

CONTENT KNOWLEDGE

Declarative / Procedural
¨ Know what scale is. / ¨ The students will learn how to set up a ratio.
¨ Know what ratio is. / ¨ The students will learn how to simplify ratios.
¨ Know what a proportion is. / ¨ The students will learn how to set up a proportion.
¨ Know the connection between ratio, proportion, and scale. / ¨ The students will learn how to use scale.

ESSENTIAL QUESTIONS

What are ratio, proportion, and scale?

What is the connection between ratio, proportion, and scale?

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

Standard 3 - Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Intermediate - Mathematical Reasoning

1. Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

Students:

· apply a variety of reasoning strategies.

· make and evaluate conjectures and arguments using appropriate language.

· make conclusions based on inductive reasoning.

Intermediate - Number and Numeration

1. 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.

Students:

· understand and apply ratios, proportions, and percents through a wide variety of hands-on explorations.

Intermediate - Modeling / Multiple Representation

1. Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

Students:

· use maps and scale drawings to represent real objects or places.

Intermediate - Measurement

1. Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world ion order to describe and compare objects and data.

Students:

· estimate, make, and use measurements in real-world situations.

· select appropriate standard and nonstandard measurement units and tools to measure to a desired degree of accuracy.

· develop measurement skills and informally derive and apply formulas in direct measurement activities.

Standard 1: Language for Information and Understanding Students will listen, speak, read, and write for information and understanding. As listeners and readers, students will collect data, facts, and ideas; discover relationships, concepts, and generalizations; and use knowledge generated from oral, written, and electronically produced texts. As speakers and writers, they will use oral and written language that follows the accepted conventions of the English language to acquire, interpret, apply, and transmit information.

Standard 1 - Language for Information and Understanding

Students will read, write, listen, and speak for information and understanding.

Intermediate - Listening and Reading

1. Listening and reading to acquire information and understanding involves collecting data, facts, and ideas, discovering relationships, concepts, and generalizations; and using knowledge from oral, written, and electronic sources.

Students:

· interpret and analyze information from textbooks and nonfiction books for young adults, as well as reference materials, audio and media presentations, oral interviews, graphs, charts, diagrams, and electronic data bases intended for a general audience

· compare and synthesize information from different sources

· relate new information to prior knowledge and experience

Intermediate - Speaking and Writing

1. Speaking and writing for critical analysis and evaluation requires presenting opinions and judgments on experiences, ideas, information, and issues clearly, logically, and persuasively with reference to specific criteria on which the opinion or judgment is based.

Students:

· use standard English, precise vocabulary, and presentational strategies effectively to influence an audience.

INITIATING ACTIVITY

What's in the box?

As a hook into the unit each student will be given a box. When the students are told they will open their box. Inside they will find an object with a letter on it or just a letter. They will then go find the person that has the same letter. (This is a way to pair the students.) Together with their partner, they will make observations about their object. Through guided discussion they will become familiar with the term scale. Using a Five- Words, Three- Words (attachment 1) brainstorm ideas that come to mind when they think of scale and how it is used. i.e.: souvenirs, maps, models, blueprints, etc. After class discussion, the students will take guided notes on what was discussed in class.

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

Day / (D)Declarative (P)Procedural Acquisition Experiences
1 / Each student will be given a different shape. The students will then be asked to find all students in the room that have a similar shape. The students will then be asked to measure the width/diameter of their objects. Each object will be labeled A, B, C, or D; on the teacher made worksheet write down the corresponding measurement. (see attachment 2 )
(P) Through guided discussion the students will talk about their observations. The teacher will then construct a model to find the ratio between two objects and show the different ways a ratio can be written.
(D) Using the same shapes the students will practice ratios. Example: find two shapes that show a 2:1, a 1:1, etc.
The students will then take guided notes on ratio in their math notes.
They will then be given an assignment to reinforce the concept of ratio. These assignments are graded for completion and understanding of concept taught.
2 / (P) Ratio isn't just related to size, it can be group components. Using concrete examples the teacher will model group ratios. Example: boys in the class to girls in the class, left- handed students to right-handed students. Etc.
(D) The teacher will set up 10 stations around the room with questions related to ratio. In pairs the students will be given a teacher made worksheet and assigned a station to begin. The students will complete all ten stations. (attachment 3)
Examples: red cubes: green cubes; pens: pencils; large cubes: small cubes.
Once stations are completed the students will return to their seats and discuss their findings. The students will then take notes on ratio in their math notes.
3 / (P) Simplifying Ratios: Through teacher modeling the students will be introduced to simplifying ratios. After modeling the students will practice simplifying ratios using their worksheets from yesterday’s activity.
(D) Each pair will then be given a different sized American flag. They will measure its length and width. They will then simplify the ratio by dividing the length by the width (length: width). Federal law says that the ratio of length to width of an official American flag is 1.9:1. They will then decide if their flag is an official flag.
The students will then take guided notes on simplifying ratios.
The students will be given an assignment, chosen by the teacher, to practice simplifying ratios. This assignment will be graded.
4 / Rates are special kinds of ratio in which the two things being compared have different units of measure. One example is miles per gallon of gas.
Vocabulary: rate, unit rate
Students will be shown a cartoon. (attachment 4) What is being compared? (Dollars: cords of wood) The teacher will then explain that this is a special kind of ratio called rate. The students will then be asked to compute the cost of a cord of wood cost. We then can calculate how much 2 cord cost, 3 cord, etc. Using the overhead, the students, together with the teacher, can complete a table of cost per cord of wood.
(D) Using the EBD Carousel model,* the students will be put into four groups by the teacher. The four questions they will be asked are: What kind of things get sold by weight? ; What kinds of things get sold by usage? ; Where do you see rate posted/advertised? ; What people use rates in their everyday life?
The class will then post the questions in the front of the room and discuss what they have written.
The students will then take guided notes on rate in their math notes.
The students will then be given an assignment on rate. The assignment will be graded.
5 / Proportion: comparison of two ratios. Use cross products to find out if the two ratios are a proportion. In a proportion the two products are equal.
Note: For this activity I would give each student a 12 by 18 sheet of white drawing paper and have them fold it into four sections. This will allow them to use the front for drawing and the back for indirect measurement.
(P) The teacher will model what a proportion is and show them how to cross-multiply to see if the ratios are a proportion. The teacher can use any examples that they choose. Examples can be from the math text or any other available resources.
(D) The students will then work with a partner under teacher direction and set up proportions. The following things can be used.
¨ Circles: diameter to circumference. The teacher will have the students draw two circles, then measure the diameter and figure out the circumference of each. After which they can set up a ratio for each and then a proportion. They can compare with another person, depending on time.
¨ Squares: length of the side to its diagonal. On the same sheet of paper the students can draw two squares and then measure the length of the side and the diagonal. They will then set up a ratio each square and then compare both ratios and see if they are in proportion. They can then compare with another person, again depending on time.
¨ Proportions can also be used for indirect measurement. Examples from any math text can be used.
Journal: How are proportions useful to us? (attachment 5)
Graded: Plus- completely understood the usefulness of proportions.
Check- somewhat understood the usefulness of proportions.
Minus- unable to see their usefulness/purpose.
6 / Extend/Refine: Deduction
The students will discuss the salaries of different careers today. After a short discussion the students will be given the deductive graphic organizer with the statement about job salaries. (attachment 6) The students will then find a computer and go to the internet and look up the salaries of four different professions both men and women. (teaching, engineering, doctor, etc.)
Website: http://stats.bls.gov/blswage.htm
They will then set up a ratio of average salary of men and women in each profession. They will then set up ratios comparing men's salary to women's salary and see if they are in proportion.
The students will then discuss their findings.
The students can then discuss the salaries of professional athletes. The students can read any material on athletes' salaries. (Time for Kids; March 30, 2001; Vol.6, No. 22) Guided discussion will focus on whether they are in proportion.
7 / Scale: is a ratio showing a comparison of the actual to the model.
Scaling: to make use of a scale.
Scale drawings: dimensions of a scale drawing may be smaller than, equal to, or larger than the dimensions of the object.
Using the overhead the students will be shown several pictures of a grasshopper (attachment 7). The class will discuss which they think is the actual size of the grasshopper. They will discuss the different size scales that are used and what it means. The students will then take guided notes on scale in their math notes.
(D) The students will be given a scale model of a child's toy or a souvenir. They will then measure the length of the model. Using any resource available (internet, encyclopedia, etc.) the students will find the actual measurement of the object. The student will then set up a ratio and find the scale used.
The students will be given an assignment to reinforce scale. The assignment will be graded.
8 / The students will be given a map and discuss how scale is used on the map. Look for the scale that is used.
(P) Practice Scale: using maps the students will use scales to determine distance.
The students will be given a worksheet related to maps and scale to reinforce this concept for homework. This assignment will then be graded.
9 / The students will review the vocabulary for the unit: rate, proportion, scale, equal ratio, ratio, unit rate. This can be done playing concentration with the words and definitions or similar activities.
(D) Ratio, Proportion, Scale: What is the connection?
Using the FWL (Fifty Words or Less) strategy (attachment 8) the students will explain the connection between ratio, proportion, and scale. The class will then discuss what they think the connections are.
FWL is graded on a +, Ö, - scale.
Plus: completely understood the connection between the three.
Check: had some understanding of the connection.
Minus: was unable to make a connection.

CULMINATING PERFORMANCE
Include rubric(s)

Problem Solving: The students need to make a scale drawing of themselves to fit on an 8.5 by 11 grid graph paper. Using partners assigned by teacher, the students will measure each other (head, trunk, arms, hands, legs, feet) and then decide on the appropriate scale to use that will allow their whole body to fit on the paper.