Maximum area for a given perimeter

Unit 5: Day 4: Maximizing Area for a Given Perimeter Learning Goal: Materials Minds On: 15 Students will . BLM 5.4.1 Explore optimization of two-dimensional figures . BLM 5.4.2 . GSP Sketch 35 Solve problems to maximize area for a given perimeter Action: . Chart Paper . Markers Consolidate:25 Total=75 min Assessment Opportunities Minds On... |Placemat -> Brainstorm and Discussion For more information Arrange students in groups of 4 and have them complete a placemat activity on on placemats, refer to the "Think Literacy different types of triangles and calculating the perimeter and area of triangles. - Mathematics This activity should be done on chart paper. The centre of the placemat should Grades 10-12" read "Different Types of Triangles & Perimeter and Area". Give students 5 document, p. 66. minutes to write individually and 5 minutes to summarize as a group in the centre of the placemat. Summarize the entire activity as a class on the board. Include Pythagorean Theorem in the class discussion. Mathematical Process Focus: Reflecting - Students will reflect upon their prior learning. Action! Pairs -> Exploration If you do not have Distribute BLM 5.4.1 and direct students to the GSP file on the computers access to a computer (MAP_USL4GSP1) to aid them in completing the investigation. Circulate to lab, the activity could ensure students are maintaining a perimeter of 15 cm for their triangles. be done as a demonstration using Learning Skills(Teamwork/Initiative)/Observation/Anecdotal comments:. a projector Observe students and make anecdotal comments. Mathematical Process Focus: Representing - Students will represent the problem with diagrams to solve the problem. Consolidate Whole Group > Guided Instruction Debrief Have students describe the triangle they created that had the maximum area (and conclude that it was a right-isosceles triangle). Ask students to help you determine the approx dimensions, using any method, of a garden with a 34' perimeter. Keep prompting students for 'another way' to solve this. Lead students through a general algebraic solution (refer to BLM 5.4.2) by asking about formulae that can be considered to make the 'guess and check' easier. Have students check to see if the general solution applies to the 34' perimeter as well as another given perimeter. Home Activity or Further Classroom Consolidation For each of the given perimeters, find the lengths of the sides of the right triangle that will maximize the area. Be sure to show all of your work and provide a labelled sketch of each solution. Find the dimensions of 1 other triangle and show that your original triangle's area is maximized. Application P = 32 inches P = 151.3 cm 3. P =5 yards Content Expectations/Investigation/Rating Scale: Collect the completed questions and assess for correctness. MAP4C : Unit 5 - Geometry (Draft - August 2007) Last saved 20/08/2007 at 1:16 PM