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TOPIC: Proportions and Percentages

GOAL OF LESSON: I want students to review how to set up proportions in order to find percents, parts, and wholes.

INSTRUCTIONAL OBJECTIVES: Students Will Be Able To (SWBAT):

• Recognize proportion problem.
• Understand which parts of the problem go in which spots on the proportion.
• Set up a proportion after reading a word problem.
• Solve their proportions to find the answers.

NY State Standards for Mathematics:

• 6.PS.3 Interpret information correctly, identify the problem, and generate possible strategies and solutions.
• 6.PS.7 Represent problem situations verbally, numerically, algebraically, and/or graphically.
• 6.PS.17 Determine what information is needed to solve problem.
• 6.RP.1 Recognize that mathematical ideas can be supported using a variety of strategies.
• 6.CM.3 Organize and accurately label work.
• 6.CN.1 Understand and make connections and conjectures in their everyday experiences to mathematical ideas.
• 6.CN.7 Apply mathematics to problem situations that develop outside of mathematics.
• 6.N.7 Express equivalent ratios as a proportion.
• 6.N.9 Solve proportions using equivalent fractions.
• 6.N.11 Read, write, and identify percents of a whole (0% to 100%).
• 6.N.12 Solve percent problems involving percent, rate, and base.
• 6.A.5 Solve simple proportions within context.

NCTM Standards:

• Standard 1: Mathematics as Problem Solving: In grades 5-8, the study of mathematics should emphasize problem solving so that students can:
• - formulate problems from everyday and mathematical situations.
• Standard 4: Mathematical Connections: In grades 5-8, the mathematics curriculum should include the investigation of mathematical connections so that students can:
• - value the role of mathematics in our culture and society.
• Standard 5: Number and Number Relationships: In grades 5-8, the mathematics curriculum should include the continued development of number and number relationships so that students can:
• - understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, and scientific notation) in real-world and mathematical problem situations.
• - understand and apply ratios, proportions, and percents in a wide variety of situations.
• Standard 7: Computation and Estimation: In grades 5-8, the mathematics curriculum should develop the concepts underlying computation and estimation in various contexts so that students can:
• - develop, analyze, and explain methods for solving proportions.
• - use computation, estimation, and proportions to solve problems.
• Standard 9: Algebra: In grades 5-8, the mathematics curriculum should include explorations of algebraic concepts and processes so that students can:
• - understand the concepts of variable, expression, and equation.
• - apply algebraic methods to solve a variety of real-world and mathematical problems.

ISTE NETS-S Standards:

• 1. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
• a. Apply existing knowledge to generate new ideas, products, or processes.

c. Use models and simulations to explore complex systems and issues.

• 3. Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
• a. Plan strategies to guide inquiry.

d. Process data and report results.

• 4. Critical Thinking, Problem Solving, and Decision Making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.
• a. Identify and define authentic problems and significant questions for investigation.

b. Plan and manage activities to develop a solution or complete a project.

c. Collect and analyze data to identify solutions and/or make informed decisions.

MATERIALS:

• Notebooks/Pens/Pencils
• Whiteboard w/markers and eraser (if no SMART Board).
• Computer with Internet access hooked up to an overhead projector/SMART board.

RATIONALE: The NYS Mathematics Standards state that students should use objects created using technology as representations. While doing their homework for this lesson, students will be using a game called Math at the Mall in order to practice their skills in solving proportions. Students will identify the problems represented in the game, represent the problems with proportions, determine the necessary pieces of information to solve each problem, and organize their work as they solve each problem. They will also see how math can be applied to everyday situations like depositing money in the bank or spending money on things like gym memberships. By setting up proportions to solve the problems, they will be using equivalent ratios/fractions. Students will be solving percent problems and simple proportions and identifying parts of a whole when they play this online game. The ISTE NETS-S state that students need to “apply existing knowledge to generate new processes.” Once students have learned the basic concepts and process of setting up proportions using information given in problems, they should be able to transfer that knowledge to the game.

PROCEDURES:

Introduction:

• 1. Tell students that we are going to review solving word problems with proportions briefly (we have been focusing on this topic for the past few days). Using the SMART Board or the projector onto the white board, display the following proportion word problems:

If you got 17 questions correct on a 20 question test, what was the percentage you got correct? (Answer: 85%)

%/100=part/(whole)

Jack’s truck had used 30 gallons of fuel from a 50 gallon tank. What percentage was used? (Answer: 60%)

%/100=part/(whole)

Fred’s sporting goods is giving a 6.25% discount on a bicycle that originally cost \$80.00. How much money will be taken off of the original price? How much will the bike cost after the discount has been taken off? (Answers: \$5.00, \$75.00)

%/100=part/(whole)

(Questions obtained from: http://www.tlsbooks.com/percentagepractice3.pdf)

Presentation:

• 2. Go through the steps of solving these problems on the SMART Board as the students follow along in their notebooks.

Application:

• Tell the students that they will be visiting a site called Math at the Mall to help them review percentage and proportion word problems for homework. Tell them to go to our site and go to the “Homework Assignments” page and read the directions under the “Homework Assignment 2” bullet. (http://www.mathplayground.com/mathatthemall2.html).

ASSESSMENT: I will check each student’s homework that they email me.

ASSIGNMENT: Students will play the Math at the Mall game and show all of their work in their notebooks. Then they will scan their work into their computers and email it to me as an attachment.

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