Gamzebaykaldi.weebly.com



Date: 16.03.2015Teacher: Gamze Baykald?Number of Students: Grade 10 F Grade Level: 21Time Frame: 40 minutesTriangle Inequalities1. Goal(s)Students will be able to identify angle and side properties of triangles and prove the triangle inequality theorem.2A. Specific Objectives (measurable)Students will be able to recognize relationships between sides and angles in a triangle by constructing a triangle.Student will be able to use inequality for sides and angles in a triangle to solve problems involving triangles.Student will be able to describe the process in finding the range of the third side of a triangle when given the two other side lengths correctly.2B. Ministry of National Education (MoNE) Objectives9.4.1.3. Bir ü?gende daha uzun olan kenar?n kar??s?ndaki a??n?n ?l?üsünün daha büyük oldu?unu g?sterir.9.4.1.4. Uzunluklar? verilen ü? do?ru par?as?n?n hangi durumlarda ü?gen olu?turdu?unu belirler.?ki kenar uzunlu?u verilen bir ü?genin ü?üncü kenar uzunlu?unun hangi aral?kta de?erler alabilece?ini inceler.2C. NCTM-CCSS-IB or IGCSE Standards: NCTM Strand: Analyze characteristics and properties of two-dimensional and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. NCTM 6-8 Students develop and evaluate inferences and predictions that are based on data. 3. RationaleThe Triangle Inequality Theorem is a crucial concept to comprehend prior to continuing on to trigonometry. By creating a conceptual learning environment where students are physically involved with the mathematics, the teacher creates an anchor to which students can refer when they forget the technical definitely of the theorem. This lesson will lead up being able to solve problems that involve triangles that can come from real life situations such as architecture and geography.?SS includes one or two question in each year exam4. MaterialsBoard markersWorksheet ( There should be at least 10 copy because there are 21 students in the class and make a copy for each pair of them)Computer and projector5. Resources Geometry 10. S?n?fGeometry booklet 6. Getting Ready for the Lesson (Preparation Information)Make sure worksheets are ready and distributed after the rules are given outMake sure projector is connected the computer7. Prior Background Knowledge (Prerequisite Skills)Students will be expected to know that the difference between acute, isosceles and equilateral triangles as well as their properties and main properties of absolute value. The students should recognize and apply properties of inequalities to the measures of segments and angles.Lesson ProceduresTransition (2 min.): Good morning! I shall be teaching you today. Some of you would forget my name so I introduce myself. I am a Bilkent graduate student in mathematics education and you call me Gamze Han?m.( I will write my name on the board)( Also the objective of the lesson, date and agenda will be written on the board)Let’s get started, shall we?Today’s topic is triangle inequalities. Today, we will examine two of these relationships. The first relationship involves the lengths of the sides of a triangle in relation to the triangle's angles.8A. Engage (8 min.)Let's continue with a questionHow long must each side of this drawbridge be so that the bridge spans the river when both sides come down?How do the measures of the angles in the triangle relate to the lengths of the roads?Thanks to Euclidean geometry. Euclid is often referred to as the “Father of Geometry”, and he wrote perhaps the most important and successful mathematical textbook of all time. Triangle inequality is one of his theorem. Before starting the proof of the theorem, I will remind you something which you learnt the previous year. I mean, it is relationship of sides to interior angles in a triangle. (I will use the applet at this page . While I am using it, will ask some questions to remind the relation between sides and interior angles. What do you say about the shortest side/ the largest side? After that I solve an example and ask two more questions for students.(geometry booklet p:41 Q1, 4 (from the first column), Q4, 5 (from the second column))Transition: She explains what they will do before distributing the exploration sheet.B. Explore (5 min.)Teacher distributes the exploration worksheet and gives students 5 minutes to work with their pairs.Monitoring students and maintain silence during this time.Worksheet: Triangle InequalitiesMarch 16, 2015Q: The early Egyptians used to make triangles by using a rope with knots tied at equal intervals. Each vertex of the triangle had to occur at a knot. Suppose you had a rope with exactly 10 knots making 9 equal lengths as shown below. How many different triangles could you make? xyztriangle324yesTransition:C. Explain (15 min.)Triangle Inequality Theorem:One side of a triangle has a length less than the sum of the other two sides, but greater than the absolute value of difference of the other two sides.4095750115570 a-b<c<a+bb-c<a<b+ca-c<b<a+cProof: Example: (from booklet)Example: (from booklet)4686300495300Find the all possible values are for x.Find the integral values for x.733425571500(I am planning to solve p: 42 Q5,4, p:43 Q3, p:44 Q2,3,4 )58578752524125D. Extend (5 min.)Write special cases on the board and give time for students to find the properties.-If m∠ C=90°, what can you say about the relation between a2+b2 and c2-If m∠ C<90°, what can you say about the relation between a2+b2 and c2-If m∠ C>90°, what can you say about the relation between a2+b2 and c2Asked question from the booklet (p:43 Q4,6, p:46 Q17,15)E. Evaluate Evaluate each students performance in group work by using observer's noteTo make sure of the understandability of the solutions, teacher directs similar questions to students and want them to solve it.9. Closure & Relevance for Future Learning (2 min.)Teacher wants students to summarize what they learned from this lesson.HW: geometry booklet p:41,42, 43 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download