SETTING6th Grade Ratios and Proportional

Relationships; 6th grade Pre- algebra.Monroe Clark Middle School in the San Diego

community of City Heights, in California.One 60-minute math class, 1 day, beginning

of week 4.35 students/class

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LEARNING OBJECTIVES

Students will recall how to make the Least Common Denominator and how to add or subtract fractions.

Students will analyze proportional relationships and use them to solve real world and mathematical problems.

Students will understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

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STANDARDS6.RP.3: Use ratio and rate reasoning to solve real-world

and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6.RP.3a: Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.3b: Solve unit rate problems including those involving unit pricing and constant speed.

Mathematics Content Standards for CA Public Schools

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LEARNING MATERIALSTeacher will have the Smart Board in the

classroom which can connect to the teacher computer.

T-83 graphing Calculators.Students each will have a computer with

access to the internet. Each student already has an account with

the school district where they can save their practice tests and submit their work.

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RESOUCES ACCOMODATIONS

Low Tech-Students will use Paper and pencil.

Mid Tech-Teacher will use ELMO and Projector.

High Tech-Teacher and student will use TI-83 Calculators and computers with access to the internet. Online version of Xtranormal software so that students will learn how to make movies by typing text.

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CONTENT-BASED LIETRACY SKILLS

Text-based literacy: text bookCritical thinking: give reasons why believe

that is the answer.Collaborative and social dialogue related to a

subject, theme, or other component of content: Ask questions to teacher or talk in group to clarify the understandings.

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Nml skillsPlay —solve the problems and then evaluate to see if classmates

did the problems correctly.Simulations — understand how math relates and constructs to

dynamic models of real-world processes: look at pictures and determine the proportional relationships.

Multitasking — understand the example problems and the relationships of ratios, then know how to evaluate real life art works base on mathematics point of views.

Distributed Cognition — use online resources to search for pictures; use Xtranormal online software to create a project.

Collective Intelligence — understand the notes of each types of the proportional problem and then use the notes to solve similar problems.

Judgment — know how to evaluate the reliability and credibility of different information sources

Networking — know how to search on the internet and pick the information that relate to the content of the lesson.

(Jenkins, Clinton, Purushotma, Robison, & Weige, 2006, p. 4.)7

MOTIVATION ACTIVITY

Phase I: Motivation Activity (approximately 7 minutes.)Teacher will take roll for attendance.Teacher and students will review adding and subtracting fractions together.Teacher will introduce the link to the Xtranormal animated clip of ratios and proportional reasoning.http://www.xtranormal.com/watch/14200761/ratios-and-proportional-reasoning

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Input (teacher given)Teacher will show students the

picture of the pyramid, ask them to say what they think which one is the biggest, then second biggest, and the smallest. How much bigger the biggest and the smallest? State the answer in specific numbers i.e. the biggest pyramid is three times bigger than the smallest, etc.

Teacher will lecture the first part of the lesson: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Input(cont.)

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For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

→ Therefore we have the person walks with the speed two miles per hour.

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2 mile

1

4hour

= 1

2 *

4

1 =

4

2 =

2 miles

1 hour

OUTPUT(LEARNER GIVEN)

** Notes: Always keep the unit on the same position as original. For examples: mile on top and hour on the bottom.Students will be asked to come on the board to solve some practice problems: The problems already preloaded to the class website corresponding to each section.Teacher will explain the students’ work on the board. If they are correct, why; if they are incorrect, why? To assure students’ understanding.

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INPUT(CONT.)

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Teacher will lecture the second part of the lesson: Compare two different ratios with the same units:

For example: The distance from San Diego to Los Angeles is two hours of driving. The red car drove 65 miles for one hour. The yellow car drove 105 miles for 2 hours. Which car drove faster and will get to the destination first?

First write out the fractions:

Now compare two fractions: This will need the prior knowledge of comparing two fractions, the least common denominator.

the red car: 65 miles

1 hourthe yellow car:

105 miles

2 hours

INPUT(CONT.)

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The fractions will be come

Students will recognize and represent proportional relationships between quantities. Represent proportional relationships by fractions.

65 miles *2

1hour *2=

135 miles

2 hours (the red car) and

105 miles

2 hours (the yellow car)

the red car drove faster and will get to the destination first.

OUTPUT (CONT.)**Notes: Always make sure the top units are

the same and the bottom units are the same when comparing the proportional fractions.

Students will be asked to come on the board to solve some practice problems: The worksheet already preloaded to the class’ website corresponding to each section.

Teacher will explain the students’ work on the board. If they are correct, why; if they are incorrect, why? To assure students’ understanding.

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CULMINATION

A group with 3 students: Go to pictures link on the class website. Find the correspondent of the today section.

Discuss in your group: Identify the ratios or proportional relationships of given pictures/paintings. Explain your reasoning.

Do odd/even problems on homework from 4.1

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EXTENSIONSearch online to see any

pictures/paintings that you feel there are relationships in proportions.

Example of the project:1. The man, who is closer to us, looks a lot

bigger than the man that is further off. From a geometry point of view, the proportion between these two men is not correct when comparing the distance between them with their sizes.

2. The closest man’s size is almost three times bigger than the further man’s size; however, his fishing rod’s size is about two times that of the man further off. The angles look very good but the size proportion does not make sense in proportional perspectives.

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LEARNER ACCOMODATIONS

With the help of the teacher aide the student’s work will be modified according to the students IEP.

Individualized Education Plans for Special Education accommodations.Language Development needs: If students that need help in language, will provide them with the vocabulary worksheet so that they can fully understand the definition and meanings of the terms being used.Gifted and Talented needs: will provide them with advance problems so that they could gain deeper thinking and information of the lesson.

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ASSESSMENTUsing handout students are to be drilled on their

practices as an assessment.Students will understand the reasoning problems. After

students have mastered the ratios and proportions, they are shown the practice problems on their computer. Students will use calculators to check their answers to see if they got the correct comparisons.

Students can now compare the two proportions and given reason for their answers. Students are given a rubric for self-evaluation (Ormrod, 2011), as a second assessment.

Project: In group of three, students will find a problem, and then solve the problem. Students have to use the notes and strategies that have been learning to create an animated video clip by using Xtranormal software (like the one that introduced at the beginning of the lesson).

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LEARNING THEORY APPLICATIONS

“Construction: Mental process in which a learner takes many separate pieces of information and uses them to build an overall understanding or interpretation” (Ormrod, 2011, p. 218).

Sociocultural Theory, the Zone of Proximal Development aka the ZPD, Modeling, and scaffolding: show an example and then students will do one on their own.As the base stabilized, the scaffolding becomes less necessary and eventually being removed (Ormrod, 2011).

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STRENGS & WEEKNESSESThe strengths of this lesson are a lot of activities and

explanations for ratios and proportional reasoning. Also, the lesson introduced real pictures and projects to show students how math applied in real life.

Weaknesses of this learning plan are heavy reliance on students’ prior knowledge and their technology skills. Research of relevant pictures and painting emphasizing the proportional reasoning took a lot of times. The preparation of the lesson was not too heavy on the textbook in which teacher can create and give real life problems in giving examples. Elements of practice still need to change in order to improve student learning and participation with more hands-on activities. This lesson will contribute a lot to future lessons and sustain the application and development of skills sets such as geometry ratios, graphing and so on.

Moreover, this is using assessment formats in The Cognitive Process Dimension from Krathhwohl: checking tasks, where one is concerned with the consistence of the actual implementation. By encouraging them to speak out what they think, we will have a picture of what they have learned from observing their classmates and from the content so far (Anderson, L. W., & Krathwohl, D. R., 2001).

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