Joe Behnke 6 8 2008 Lesson Plan Title The Border Problem Activity 15 15 of Elementary and Middle School Mathematics by John A Van De Walle Key Concept s in this lesson finding functional relationships Grade Level 5 Section 1 WHAT YOU WANT STUDENTS TO KNOW BE ABLE TO DO OR FEEL UNDERSTAND Standards addressed EALRs GLEs EALR 5 The student understands how mathematical ideas connect within mathematics to other subject areas and to real world situations Component 5 1 Relate concepts and procedures within mathematics GLE 5 1 2 Use equivalent mathematical models to represent a mathematical idea Lesson Goals Use drawings words and number sentences to represent mathematical idea See and use functional relationships Specific Objectives Given a teacher demonstration of using number sentences to represent counting schemes of the tile border around a swimming pool SWBT invent counting schemes for the borders of swimming pools with different dimensions using functional relationships Primary Learning Targets Circle Appropriate Targets Be sure learning activities are congruent with targets chosen a Knowledge Skill d Create a Product e Dispositions b Reasoning Proficiency c Performance Section 2 HOW WILL YOU KNOW THAT THE LEARNING TARGETS WERE MET Preassessments Students respond to question on a half page of notebook paper Question Why do mathematicians need multiple ways of modeling a single mathematical idea Summative Assessment Students turn in their graph paper with swimming pool designs their number sentences and their universal formula for describing the number of tiles in all sized square swimming pool borders Section 3 HOW WILL YOU HELP YOUR STUDENTS MEET THE LEARNING TARGETS Materials Needed grid paper and markers or colored pencils Activities Label each step in the process Activating Prior Knowledge Disequilibration Elaboration Crystallization Time e g 5 min or 9 409 45 What Teacher Does What Students Do Introductory Activity Pass out the grid paper and markers Tell students to color in a square to represent a swimming pool They have choice of how big to make their swimming pool Also have them make a border around their swimming pool using a different colored marker Activating Prior Knowledge Tell them that the task is to find a way to count the border tiles without counting them one by one Walk them through one using Socratic dialogue What is a number sentence What s a way that we could write the solution to the border problem Tell them there are at least five methods of counting the border tiles other than counting them one at a time Disequilibration Time Time Time Students respond to teacher s questions and demonstration of writing a number sentence Let students work on developing number Students work alone or in pairs to figure out number sentences to represent their counting sentences to represent their counting schemes After schemes Direct them to create a they have come up with a few number sentences for different sized swimming pool and see if their first swimming pool they draw a different sized they can use similar number sentences to swimming pool and apply their new knowledge of find solutions to different sized swimming number sentences to the different sized swimming pool pools Crystalization Bring students back to teacher attention Students report out to teacher the different counting and ask for students to report on counting schemes they found schemes they discovered Write their answers on the board and discuss their mechanics relating to a visual of a swimming pool Elaboration Closure Plan consider including reinforcement of learning affirmations glimpse at tomorrow bridge Direct students to take out a blank piece Students attempt to apply a counting scheme universally of paper choose one of their counting to all sized square swimming pool borders schemes and write an equation or formula for applying the scheme universally to all sized square swimming pool borders Elaboration Evidence Task for Positive Impact on Student Learning Have students respond to the following question How do you think the ability to find and express functional relationships could serve you in the future Learning Goal GLE 5 1 2 Use equivalent mathematical models to represent a mathematical idea Beginning Student does not understand that number sentences can represent the number of tiles in the border of a square swimming pool Developing Student can writes number sentences that accurately describe the count of tiles in different sized swimming pools but cannot describe universal formulas and patterns they use Proficient Students write number sentences that accurately describe the count of tiles in different sized swimming pools and accurately describe universal formulas and patterns they use
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