Inequalities in real life Proff. By ITIS GALVANI Giuseppe Chianese Maria Fioretti Raimondo Giangrande Elena Griffo Teresa Pianese Luigi Pianese 1ITIS GALVANI - GIUGLIANO - NA

LESSON PLAN We need to: identify content knowledge skills learners will be taught focus on the learner rather than the teacher We use learning outcomes: statements of what most learners should be able to know, be able to do and be aware of as a result of a learning experience 2ITIS GALVANI - GIUGLIANO - NA

LESSON PLAN Maths lesson: second year technical instruction Content : Inequalities graphic resolution. Stating problems using linear inequalities. First degree inequalities graphic resolution. Teaching aims : To enable learners to understand what an inequality is, how inequalities can be solved, how they could be applied in real life. 3ITIS GALVANI - GIUGLIANO - NA

Learning outcomes Know : Recognize linear inequalities; type of problems that can be solved with inequalities. Be able to : Find inequalities algebraic and graphic solution; be able to read a graph in relation to inequalities. Be aware : That many aspects of real life involve inequalities; of how to cooperate in a group. 4ITIS GALVANI - GIUGLIANO - NA

Assessment The learners should know how to: Set up an inequality to solve a specific problem and find out the solution. Be able to : Find inequalities algebraic and graphic solution; be able to read a graph in relation to inequalities. Be aware : That many aspects of real life involve inequalities; of how to cooperate in a group. 5ITIS GALVANI - GIUGLIANO - NA

Communication Vocabulary Revisited: previous learned terms: equality, numbers, sum, difference, funtions. New : Inequality Degree Greater > Smaller < limited interval unlimited interval 6ITIS GALVANI - GIUGLIANO - NA

Communication Structures : Describing a sequence of events. (First, then, next, finally). I have found out… What I thought would happen was … If I …, My graph shows than Present tense (Explain and affirmative, negative and questions sentences) Past Tense Future Tense (Predictions and hypothesis) Where, when, why, who, what, which, how? There is… and there are… Prepositions from, of,… If…(then)…+ if –clauses grammar Modal verb (instructions in the LAB) 7ITIS GALVANI - GIUGLIANO - NA

Communication Strategies : Strategies for reading and understanding a text. Strategies to improve classroom talk: Encourage student questioning Allow for student talk Survey the class Ask for summary to promote active listening and speaking. Poster with instructions Poster with discipline Poster with equipment and materials Frames to facilitate discussion. Tasks and demands. Mini presentations 8ITIS GALVANI - GIUGLIANO - NA

Communication Examples of communication: Showing examples where one think inequalities can be used. Your speed should not exceed 50 km per hour 9ITIS GALVANI - GIUGLIANO - NA

Cognition What thinking skills are learners demanded? Identifying: what’s an inequalities Classifying: when an inequalities is linear Reasoning: how can resolve an inequalities Generalizing: to apply the inequalities to resolution of a problem 10ITIS GALVANI - GIUGLIANO - NA

Resources Vocabulary extension Books Handouts Graphs Interactive whiteboard 11ITIS GALVANI - GIUGLIANO - NA

Whole class : Activate prior knowledge and previous vocabulary. Learners recall solution methods for equations, equation systems and function definitions. Vocabulary will be reminded with the exercise: Procedure 12ITIS GALVANI - GIUGLIANO - NA

Exercise Match the English words with the correct translation: Inequality Grado Degree Membro Unknown Incognita Interval Intervallo Side Variabile Variable Disuguaglianza 13ITIS GALVANI - GIUGLIANO - NA

Whole class : learn new vocabulary Procedure 14ITIS GALVANI - GIUGLIANO - NA

Whole class: Explanation starting from a real problem then general resolution methods. Procedure 15ITIS GALVANI - GIUGLIANO - NA

Problems of choice Two telephone companies offer the following rates in order to make calls: n. 1 Operator -Monthly fee subscription : € 5,00 -Conversation fee per minute : 10 cents n. 2 Operator -No fee subscription -Conversation cost per minute: 20 cents Which operator should be chosen? 16ITIS GALVANI - GIUGLIANO - NA

The problem will be resolved according to the three steps: STEP 1 : from problem to inequality Let m be the minutes of conversation. The n.1 operator offer is € 5.00 for the monthly subscription plus 10 cents per minute for the conversation fee and it can be written as: cost n. 1 operator = cost + conversation fee= m The n.2 operator offer can be written as: cost n.2 operator = conversation fee =0.2 m To ensure that the n. 1 operator is more convenient than of the n. 2 operator, it shall happen that: 17ITIS GALVANI - GIUGLIANO - NA

so you get the following equivalent inequality. STEP 2: resolution of the inequality Sum of similar terms According to the principle of equivalence Transportation rule 18 ITIS GALVANI - GIUGLIANO - NA

STEP 3 : graphic representation of the solutions ITIS GALVANI - GIUGLIANO - NA n.1 operator convenience interval n.2 operator convenience interval

The result shows that the n. 1 operator choice is convenient only if we make over 50 minutes of telephone calls per month. Remark: the problem can also be solved graphically, particularly the step 2 and step 3. 20ITIS GALVANI - GIUGLIANO - NA

Graphical problem solution In order to graphically interpret the inequality STEP 1 : resolution of the inequality The left hand side of the inequality can be considered as linear function: y = 0,1 x +5 ( cost operator 1) The function graph of the y = 0.1 x + 5 is a straight line. 21ITIS GALVANI - GIUGLIANO - NA

The right hand side of the inequality can be considered as linear function: y = o,2x ( cost operator n.2) The function graph of y = o,2x is a line through the origin of the coordinate system. 22ITIS GALVANI - GIUGLIANO - NA

STEP 2: The graph of the function y = 0.1 x + 5 is a line and can be represented in the Cartesian plane using the table x y The graph of the function y = 0.2 x is a line through the origin of the coordinate system. 23ITIS GALVANI - GIUGLIANO - NA

You can determine the intersection point of the lines by solving the two variables system using the comparison method : y = 0,1x + 5 y = 10 y = 0,2x 0,1x + 5 = 0,2 x = 50 We can represent the lines in the coordinate system. 24ITIS GALVANI - GIUGLIANO - NA

STEP 3: We can represent the lines in the coordinate system. minutes The result shows that the choice of the operator n. 1 is convenient only if we make over 50 minutes of telephone calls per month. 25ITIS GALVANI - GIUGLIANO - NA n.2 operator convenience interval n.1 operator convenience interval

Linear Inequalities scheme solution (read in L2) Algebraic solution Graphical representation on a straight line a > 0 x > b/a ax >b a < 0 x < b/a a = 0 b < 0 ( S = R) 0 > b b > 0 ( S = O ) x x 26ITIS GALVANI - GIUGLIANO - NA

Linear Inequalities scheme solution (read in L2 ) Algebraic solution Graphical representation on a straight line a > 0 x ≤ b/a ax ≤ b a < 0 x ≥ b/a a = 0 0 ≤ b b < 0 b > 0 x x 27ITIS GALVANI - GIUGLIANO - NA

Individually : learning record observations on worksheets Whole class: group exercises Procedure 28ITIS GALVANI - GIUGLIANO - NA

A graph and its reading 29ITIS GALVANI - GIUGLIANO - NA

 Look at the graph: 1) How is the turtle headstart? 2) After 4 sec Achilles ran for 20m, while the turtle ran for… m 3) How many seconds does it take Achilles to reach the turtle? 4) How many seconds are needed to Achilles to travel twice the meters of the turtle? a) 25 sec b) 40 sec c) 30 sec d) do not know 5) The equation representing the movement of the turtle is: a) s = 5t b) s = t c) s = t d) t = 2.5 s 6)In which time interval is the distance traveled by the turtle less than the distance covered by Achilles? 7)In which time interval is the distance traveled by Achilles less than the distance traveled by the turtle? 30ITIS GALVANI - GIUGLIANO - NA

Whole class : Final plenary Follow-up : Correction of the exercises Procedure 31ITIS GALVANI - GIUGLIANO - NA