Unit Planner IGCSE Mesuration and Trigonometry

Unit Planner

Teacher NameGauri Pathak                                       Grade & Section:10 C                        Subject: Mathematics

Unit Name: (Mesuration ,Trigonometry)

Duration and Dates for completion of Unit: 6 January to 9^th February

About the Unit:  In this unit students will cover topics based on Extended Mathematics which comes under IGCSE Level such as Mesuration and Trigonometry . In Mensuration Students will learn about 2D and 3D figures. In trigonometry students will learn how to find the sine, cosine, and tangent of angles of right triangles, given the measures of at least two sides.

Where the Unit fits in: This unit will help students to Develop their mathematical skills in learning Geometry in a way which encourages confidence in solving IGCSE problems. Mensuration is necessary part of geometry and in Trigonometry students will explore the importance of triangles, particularly right angled triangles, in the real world. Students will use practical measuring skills and calculations to find a pattern linking the ratio of the sides of a triangle with the angles. Introducing trigonometry using scale diagrams improves understanding of the concepts in the context of everyday situations and of other subjects they may be studying .

Prior Learning: It is helpful if the students have the knowledge of algebraic skills for solving equations and rounding before .A quick review of basics will be done using “Class Brainstrom”  for 10 minutes on first day.

Future Learning: Future learning will be discussed before starting a topic For Mensuartion  ppt will be shown https://prezi.com/3o46jmdxh3aq/application-of-mensuration-in-daily-life/ Trigonometry : Trigonometry is commonly used in finding the height of towers and mountains.  It is used in finding the distance between celestial bodies. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves. Architects use trigonometry  to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles

Expectations: At the end of this unit:(Based on CIE Requirements) Most students will be able to Carry out calculations involving the volume of a cuboid, prism and cylinder and the surface area of a cuboid and a cylinder. Carry out calculations involving the surface area and volume of a sphere, pyramid and cone. Carry out calculations involving the circumference and area of a circle. Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right-angled triangle. Some students will not have made so much will be able to Carry out calculations involving the circumference and area of a circle. Solve problems using the sine and cosine rules for any triangle. Some students will progress further can Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.  Solve problems involving the arc length and sector area as fractions of the circumference and area of a circle. Interpret and use three-figure bearings. Solve simple trigonometric problems in three dimensions including angle between a line and a plane.

Language for Learning: Through the activities in this unit students will be able to understand, use and spell correctly academic/ new vocabulary words: Studnets  can keep a record of new vocabulary words in a diary or at the end of notebook . Reading-Students will learn close reading of the text-comprehend what is read and then Carry out a transformation from the words of the problem to the selection of an appropriate mathematical strategy. Writing –Students will learn how to Encode the answer in an acceptable written form. Listening and Speaking- students will learn to prepare for and participate effectively in a range of conversations and collaborative activities in class.

Resources: ICT Lab, Video, Compass point chart, Chart paper to display Ppt: https://prezi.com/3o46jmdxh3aq/application-of-mensuration-in-daily-life/ https://prezi.com/qrxzlfmwdfmx/real-life-applications-of-trigonometry/ Worksheets: 4)-Areas-of-Flags-(4).docx SA---V-of-famous-buildings.docx similar triangles.pdf Recording sheet 1.pdf Activity things per group: 6 drinking straws 1 pair of scissors 1 ruler 2 sticky address labels 2 textbooks per group for the bridge supports 10c coins for weights http://nzmaths.co.nz/resource/introducing-trig Students need to bring their favorites cups or tumblers or cups for Activity based on capacity.

Day1/2 (Days can vary): Exam Paper will be shown and problems will be discussed and next day students will redo the paper and if students will need to revise  any topic it will be done in extra classes . Teaching& Learning Activities:  Day 3-6: Do Now/Activator (25min): “Class brainstorm” to check their basics as mentioned in Prior learning . Mini Lesson /Learner Activity : Start teaching Area and perimeter of two dimensional figures by using the strategy called “Flipped classroom” . This topic is common part of curriculum since 7 th grade and they already have an idea of that . Activity will be followed to jot down their ideas. News Bulletin: Create small groups of four or five students and tell them they have to create a news bulletin about a given subtopic (assigned by teacher) based on Area and Perimeter. Give them around 20 minutes to prepare as on-scene reporters and expert commentators for interviews! They need to cover every important point of the topic which they know . Groups can be given same or different subtopic. Then each group need to present their report.Either way, encourage the ‘audience’ to take notes while watching the each show.  A fact – sheet will be given by teacher for each group to consolidate their learning Activity. Teacher will be observing their presentation as a reporter .Next day some patch work will done by teacher based on their  learning requirement of topic which was not covered in last session and few extended problems will also be considered. A ppt will be shown to make them aware of usage of mensuraton in real life https://prezi.com/3o46jmdxh3aq/application-of-mensuration-in-daily-life/ Learner Activity : Students will solve a sheet 4)-Areas-of-Flags-(4).docx Next day A controlled practice time will be given to the students to work on questions from the text book.. Differentiation: Formula sheet will be provided to support late bloomers. Teacher Role: Observation of individual student involvement in class with a walk around while students are drawing the diagrams. Wrap Up (10 min): To help learners reflect on how their thinking has shifted and changed after class tell them to use phrase and share their thoughts about the topic.  I Used to Think…, Now I Think…  What new questions do u have ? Out of school learning:  Students will create Mind Maps based on Areas and perimeters of 2d shapes .For next class ask them to bring their favourite cups or tumblers or cups with them Day 6-8: Do Now/Activator (10min): Students will bring their mind maps and will explain about it. Reminding students of what they have learnt in previous lesson Start teaching  strategy “Teaching by exploring” Student will bring their tumblers, take them to water tap where they need to fill in water in to tumblers ask them to measure amount of water they are in filling in their cups or tumblers. Connecting that to topic discuss and introduce capacity and volume surface area of different shapes. Mini Lesson (15 min): Further Connecting to their activity discuss about mathematical formulas to work on capacity, volume and Surface Area of given shapes. Formulas will be given with few examples. Learning Activity: Learners will take notes and formulas will be provided. A worksheet will be given where students need to work upon Surface Area and Volume of Famous Buildings SA---V-of-famous-buildings.docx Next day A controlled practice time will be given to the students to work on questions from the text book.  “Thumbs up and down” strategy will be used to assess whether the students understand the question or not. Teacher role :The teacher will supervise the class performance and to facilitate student requirements while solving problems. Differentiation: Teacher will encourage student to participate in class discussions and take rounds around the classroom while students taking notes form board to assist .whoever still don’t understand will be facilitated . Wrap Up (10 min): Headlines: Think of the big ideas and important themes in what you have been learning in this topic . Write headline for the topic that summarizes and captures a key aspect that you feel is significant and important. Out of school learning: Problems will be assigned from book and past papers. Day 9: HW problems will be discussed and solved .Students can make corrections if needed and then students will be asked to leave notebooks in class to get check by teacher and then can collect back from class during study time or at the end of  last period. Do Now/Activator (20min): Connecting to their previous day learning .Teacher will use 4C’s routine which will help them in (Connection making, identifying key concept, raising questions, and considering implication). Connection: What connection do you draw between the topic and your own life and your other learning. Challenge: What ideas or assumption do you want  to challenge or argue with in the content application. Concepts : What Key ideas do you think are important or worth holding on from the topic. Changes : What changes in Attitude ,thinking can be suggested based on topic from you or others? Mini Lesson (10 min ) Recall all the terms and methods for finding Volume and surface area.  Explain some coded problems demonstrating the thought process used in problem solving taking few problems based on Past questions in CIE . Learning Activity (25 min): Students will solve problems form past papers. Stratergy: Peer tutoring Teacher’s Role: Teacher observation glancing at the work done by the students. Wrap Up (5 min): A routine for reflecting on how and why our thinking has changed .Student will share their thoughts about topic using skeleton script:  I Used to Think..., But Now I think... Out of school learning: Few past CIE problems will be given. Day 10-14 : (Trigonometry) Do Now/Activator (10min): HW problems will be discussed and solved and students can make corrections if needed and then students will be asked to leave notebooks in class to get it checked by teacher and then can collect back from class during study time or at the end of  last period . Use the Visible Thinking Compass Points Routine to introduce new topic trigonometry Trigonometry (from Greek trigonon "triangle" + metron "measure"). Ask them ways of measuring sides of a triangle …..To collect their thoughts about the topic provide them a Compass Sheet. Mini Lesson (15 min): After collecting responses share them what is trigonometry and Also share with them how it can help them in real life by taking more examples . Eg Trigonometry is commonly used in finding the height of towers and mountains. It is used in oceanography in calculating the height of tides in oceans. Future Learning: Future learning will be discussed using  https://prezi.com/qrxzlfmwdfmx/real-life-applications-of-trigonometry/  http://nzmaths.co.nz/resource/introducing-trig It would be also useful and interesting for the students to look at the historical background of trigonometry . and few videos will be shown to bring in interest in the topic. Learner Activity :Students will share their responses and ideas . Wrap up: Student will share their thoughts about topic using skeleton script:  I Used to Think..., But Now I think... Day 11-14: (Trigonometry) Do now: Initially to begin with topic ,let the students explore and share the importance of triangles and how scale drawings can be used to solve problems and their limitations. Mini Lesson : After a discussion about the limitations of scale drawings, help students to develop the concepts of trigonometry through practical measuring tasks. Eight sets of similar triangles with eight different angles are prepared. Sets of these triangles are issued to each group, and the students measure the lengths of each side and calculate the ratios. The students have an opportunity to check the reasonableness of their answers by discovering that the ratios appear to be the same for the same angle and any apparent errors can be discussed. At this stage, class results are graphed and the students discover that there appears to be a pattern occurring which again gives them an opportunity to discuss any apparent errors. The ratios are now given a name – sine cosine and tangent – and the students are shown that by using trigonometry, heights and distances can be found more accurately than by scale drawings. Learner Activity: Students will Measure the lengths of the sides of sets of similar right angled triangles and find the ratio of sides Students will investigate the relationship between these ratios and the angle size. Students can use calculators or tables to find the sine, cosine and tangent of angles .similar triangles.pdf Recording sheet 1.pdf Next day Practical measuring task will be taken which will allow students for improved understanding of the concepts and how they apply to real life situations. Required Resource Materials:  resources for bridge building activity, drinking straws, sticky labels measuring equipment, protractors, rulers, large measuring tapes copies of recording sheet 1 sets of similar triangles Activity:  Getting started Bridge building activity Each group has: 6 drinking straws 1 pair of scissors 1 ruler 2 sticky address labels 2 textbooks per group for the bridge supports 10c coins for weights The students should be asked to think of bridges in the district and what they have in common. The text books should be placed so that the distance between them is further than the length of one straw. The books represent the banks of a river infested with crocodiles. The group has to build a bridge to cross the river that will carry people from one side to the other using the straws and the sticky labels. At the end of the time – probably 30 minutes – a piece of paper should be placed on the bridge, and it should be tested for strength using coins The first lesson is for the students to discover that probably the best bridge that they can build using the equipment provided will involve triangles in some way Students need to investigate the use of right angled triangles as a mathematical model by looking at structures and buildings in the school environment, and in other examples such as: tents rotating clothes line pile of sand ice-cream cone ladder against a wall a pyramid  Demonstrate them how can we use trigonometry in finding missing sides of a triangle using SOH CAH TOA pyramids. Using SOH CAH TOA few examples will be given on board. Differentiation: Giving late bloomers the hints for the questions which was asked. Learning Activity (25 min): 1.      The students will take notes while discussion. 2.      Problem solving next day. Formative Assessment through student and teacher interaction while discussion. Wrap Up (10 min):. Headlines: Think of the big ideas and important themes in what you have been learning in this topic . Write headline for the topic that summarizes and captures a key aspect that you feel is significant and important Out of school learning: Few book problems will be assigned based on SOH  CAH TOA  Day 15: HW problems will be discussed and solved and students can make corrections if needed and then students will be asked to leave notebooks in class to get it checked by teacher and then can collect back from class during study time or at the end of  last period . Do Now/Activator (10min): Ask them few questions based on missing side of a triangle using SOH CAH TOA. Mini Lesson: Demonstrate the use of sine and Cosine rule by showing a ppt. taking various examples. Problem sheet will be given based on Law of sine and cosine. Differentiation:  print outs will be given While solving problem Teacher support or peer support.  Learning Activity (25 min): Learners will be answering questions from Ppt. Learners will take notes of important terms and examples. Learners will work on some assigned mixed problems based on knowledge and application. Teacher Role: To make every student involve in discussing ppt. questions. The teacher will facilitate students concerns while solving problems. Verbal feedback will be given during seat work. Out of school learning: Past paper problems will be given. Day 16: HW problems will be discussed and solved and students can make corrections if needed and then students will be asked to leave notebooks in class to get it checked by teacher and then can collect back from class during study time or at the end of  last period . Mini Lesson (15 min): Connect Reminding students of what they have learnt in previous lesson connecting to this lesson by using strategy “Teaching by asking”. The students will be asked question based on trigonometry and Mensuration. Extend Students will be taught and demonstrated how to do extended  problems based on CIE requirements, using their knowledge discussed  in the first part through solved examples and discussions .Then The class will be assigned   number of  problems  mainly  related to application skills to practice.   Challenge (Learning  Activity ) 1.       The students will be given complex structured problems from the past question papers to simplify using the skills and formulas. 2.      Discuss few problems based on Past questions in CIE based on percentiles.  “Thumbs up and down” strategy will be used to assess whether the students understand the question or not. Wrap Up (10 min): ):. Headlines: Think of the big ideas and important themes in what you have been learning in this topic . Write headline for the topic that summarizes and captures a key aspect that you feel is significant and important Out of school learning: Students will be given some problems based on Trigonometry. Day 17:  1 hr Class test will be taken (As there is no Monthly test  for January so I will be taking their Class test to check their understanding). Day 18 :Class test problems will be discussed

Curriculum (Based on Cambridge) E4.1 Use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units. E4.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these. E4.3 Carry out calculations involving the circumference and area of a circle. Solve problems involving the arc length and sector area as fractions of the circumference and area of a circle. E4.4 Carry out calculations involving the volume of a cuboid, prism and cylinder and the surface area of a cuboid and a cylinder. E6.1 Interpret and use three-figure bearings. Measured clockwise from the North i.e. 000°–360° E6.2 Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right-angled triangle. Solve trigonometrical problems in two dimensions involving angles of elevation and depression. Extend sine and cosine values to angles between 90° and 180°. E6.3 Solve problems using the sine and cosine Learning Objectives: In Mensuration Students will learn about 2D and 3D figures.  In trigonometry students will learn how to Find the sine, cosine, and tangent of angles of right triangles, given the measures of at least two sides.

Assessment: Formative Assessment: Bridge Building Activity Summative Assessment: Class test

Learning Outcomes: By the end of this unit, students will Upon completion of this lesson, students will: have been introduced to the notion of surface area and volume. have learned the terminology used with surface area and volume. have experimented with the surface area and volume of different prisms. Identify the hypotenuse, adjacent side, and opposite side of an acute angle in a right triangle. Determine the six trigonometric ratios for a given angle in a right triangle. Recognize the reciprocal relationship between sine/cosecant, cosine/secant, and tangent/cotangent. Use a calculator to find the value of the six trigonometric functions for any acute angle. Reading-students will learn close reading of the text of given problem-comprehend what is read and then Carry out a transformation from the words of the problem to the selection of an appropriate mathematical strategy. Writing –Students will learn how to Encode the answer in an acceptable written form. Listening and Speaking- Students will be able to interpret and communicate formulas based on Mensuration and Trigonometry.

Unit Planners Mathematics

Unit Planner

Teacher Name: Gauri Pathak                             Grade & Section:11 C              Subject: Mathematics

Unit Name: Statistics(Representation of Data (S1) ,Measures of Location (S1),Permutation and combination)

Duration  for completion of Unit: 20 days

About the Unit:  In this unit students will cover topics based on statistics which comes under AS Level Mathematics S1 exam which includes (Representation of Data (S1) ,Measures of Location (S1) Measure of spread(S1) Probability). In Representation of Data. Students will learn difference between qualitative and quantitative data and will learn how to display numerical data using diagrams.  In Measures of Location students will learn three different measure of locating mean ,mode, median. In Probability student will understand about calculating probability using different ways.

Where the Unit fits in: This unit will help students to Develop their mathematical skills in learning Statistics  in a way which encourages confidence in solving CIE problems. It will help  to acquire  a range of Statistical  skills , particularly those which will enable them to use in applications of statistics  in the context of everyday situations and of other subjects they may be studying .It will also help to acquire the mathematical background necessary for further study in this or related subjects. It Covers ~30 % of total S1 exam paper. It aims to teach students the basics of statistics , so that when you move onto the later units (Statistics) you will have a basic understanding.

Prior Learning: It is helpful if the students have the knowledge of Statistics Basics before .So one class will be taken as to revise Statistical Fundamentals and discussing future learning  .

Future Learning: One class will be taken to make them understand how they can use Statistics in real life . Students can use their knowledge and understanding to understand  Mean •          It helps teachers to see the average marks of the students. •          It is used in factories, for the authorities to recognize whether the benefits of the workers is continued or not. •          It is also used to contrast the salaries of the workers. •          To calculate the average speed of anything. •          It is also used by the government to find the income or expenses of any person. •          Using this the family could balance their expenses with their average income. Applications of Mode •          Mode contains the highest frequency in any data. Its applications areas follows:- •          It is used to influx of the public transport. •          The no. of games succeeded by any team of players. •          The frequency of the need of infants. •           Used to find the number of the mode is also seen in calculation of the wages, in the patients going to the hospitals, the mode of travel etc

Expectations: At the end of this unit:(Based on CIE Requirements) Most students will be able to comprehend translations of common realistic contexts into mathematics; use the results of calculations to make predictions, or comment on the context; and, where appropriate, read critically and comprehend longer mathematical arguments or examples of applications; .Students will be able to use use mathematical models and analyze change in both real and abstract contexts. AO2 construct rigorous mathematical arguments and proofs through use of precise statements, logical deduction and inference and by the manipulation of mathematical expressions, including the construction of extended arguments for handling substantial problems presented in unstructured form; AO3 recall, select and use their knowledge of standard mathematical models to represent situations in the real world; recognise and understand given representations involving standard models; present and interpret results from such models in terms of the original situation, including discussion of the assumptions made and refinement of such models; Some students will not have made so much progress will be able to recall, select and use their knowledge of statistical facts, concepts and techniques in a variety of contexts; Some students will progress further will be able to derive understanding of the connections between different elements of the subject. They will be able to integrate and   draw together of knowledge, understanding and skills learned in the unit in different parts of the A level course through using and applying methods developed at earlier stages of study in solving problems. Based on Unit : Develop their statistical knowledge and skills Develop an understanding of statistical principles Analyse problems logically Develop the ability to select an appropriate measures of location to use in a given situation.

Language for Learning: Through the activities in this unit students will be able to understand, use and spell correctly academic/ new vocabulary words: Student Personalized dictionary: Guide them to make a  Personalized dictionary where everytime they learn a new vocabulary work in any exercise or unit they can keep a record in a diary or at the end of notebook. Reading-students will learn close reading of the text-comprehend what is read and then Carry out a transformation from the words of the problem to the selection of an appropriate mathematical strategy. Writing –Students will learn how to  Encode the answer in an acceptable written form. Listening and Speaking- students will learn to prepare for and participate effectively in a range of conversations and collaborative activities in class.

Resources: (Materials both print and electronic that we draw upon for our instruction) Resources include collected past year problems based on this unit. Post its ,Marker, ICT Lab,If possible Field trip to collect data,SUBWAY Worksheet ,Rubrics.

Teaching& Learning Activities:  Day 2: Do Now/Activator (15min): Start teaching by using the strategy called “Class Brainstorm” in which the students will be asked to give as many ideas as possible about the term “Data”.Show them a chart which display Which will make them understand vocabulary related to Data Collection. . Mini Lesson (15 min):Then the students will be explained terminology related to representation of data and how to draw stem and leaf diagram for combining the raw data with the help of examples. Differentiation: Class is  divided into groups such that each group has a leader who explains the stem and leaf diagram to his peers (peer explanation).  Learning Activity (25 min): The students will draw stem and leaf diagram related to the problems on page no. 8 of book “Statistics I” by Steve Dobbs and Jane Miller . Teacher Role: Observation of individual student involvement in class with a walk around while students are drawing the diagrams. Wrap Up (10 min): Have students draw a mind map of  the steps they learned for stem leaf diagram. Out of school learning:  Students will complete their Mind Maps given based on  stem and leaf and will also solve problems given from book. Day 3: Do Now/Activator (10min): HW Problems will be discussed .Students will bring their mind maps and will explain about it. Mini Lesson (15 min): Reminding students of what they have learnt in previous lesson connecting to this lesson by using strategy “Teaching by asking”. The students will be asked some of the questions related to histograms and cumulative graphs. Differentiation: Teacher help will be given by a short description of the topics to late bloomers. Learning Activity: Collect and visualize data as Histograms: ·         Have students collect data that can be continuous such as height. Record their height in inches on a White Board. ·         Draw and label an X- and Y-axis on the board with categories of classification that are as wide as a White Board.  ·         Ask your students to place their Post-it Note in the correct category, stacking them as they go. ·         Immediately everyone will see the shape of the histogram. ·         Sample: ·         Learners will make a histogram and cumulative frequency graphs for a given data. 1.      Then Students will solve problems based on CIE past papers. 2.      “Thumbs up and down” strategy will be used to assess whether the students understand the question or not Wrap Up (10 min): Give each pair of students a picture of a stop light. In the green box, they write something they already knew about today’s topic. In yellow, they write something they learned today and in red, they write something they didn’t understand about what was discussed and discuss what was not understood. Out of school learning: Students generate word problems: Have students create word problems based on histogram. Through the construction of a problem the students learn what to look for when solving word problems they are assigned.  Students will solve CIE problems based on topic . Day 4: Do Now/Activator (10min): Discuss about problems which were given as homework and if any queries will be rectified in the beginning of the class. Mini Lesson (15 min ) Recall all the terms and methods for Representation of data . Using explicit explanations of the steps of problem solving through teacher demonstrating the thought process used in problem solving taking few problems based on Past questions in CIE . Learning Activity (25 min): The students will solve questions 2,4 (pg16) & questions 2,4 (pg 18) of book “Statistics I” by Steve Dobbs and Jane Miller Stratergy:Reciprocal peer tutoring (RPT) to improve math achievement: having students pair, choose a team goal to work toward, tutor each other on math problems, and then individually work a sheet of drill problems.  Students get points for correct problems and work toward a goal. Teacher’s Role: Teacher observation glancing at the work done by the students. Wrap Up (10 min): Key Ideas :Students list the key ideas from the lesson  and ways to solve it. Out of school learning: Students will create  Graphing Anchor Chart  as a Group . Sample: Day 5: Do Now/Activator (10min): Collect their charts and display and ask them to explain about it. Two Minute Talks To activate prior knowledge and focus ,student learning on the topic  will be addressed. Students will share with a partner by brainstorming everything they already know (prior knowledge) about the  topic.  In doing so, they are establishing a foundation of knowledge in preparation for learning new information about the topic. Mini Lesson (15 min): Introduce the three different measures of location (mean, median and mode) taking few examples on board. Discuss few problems based on Past questions in CIE . Differentiation: Giving late bloomers the formula required- mean, median or mode. Learning Activity (25 min): 1.      A discussion on each  “Measures of location” and relating them to a given situation will follow, with each student sharing an example of each method. 2.      The students will take notes while discussion. Formative Assessment through student and teacher interaction while discussion. Wrap Up (10 min): Have students line up at the door at the end of the period and as they leave they must share an idea or concept they learned. Each student must give a different answer. Out of school learning: Students will create A Web based  Project of their own choice based on Application of (Mean ,Mode ,Median) in real life. Before selecting a project they are suggested to do research on Application of Mean Mode Median in real life. 3 days will be given to complete the project (Permission will be taken form Ritu  to use Computer Lab or students can work on their Laptops by taking permission ).They can go to nurse or Account office after school (After taking permission) to work on project depending on their choice on  project . Example : They can search on work on How mean median mode is used in Medical Fields. They can search on work on How mean median mode is used in Economics. They can look for how mean median mode can be  used in Miri Piri Academy or any Institute ……….etc. (can ask for help if required) I want them to come up with idea how can they  use Mean ,Median ,Mode  which ever field they select .It will suggested them  to come up with real data collection  . Using any one application they create a ppt ,chart ,excel sheet or anything they find suitable(they will work in groups assigned by teacher) Day 6: Do Now/Activator (10min): “Quick write” Tell students to write whatever comes to mind about the previous  topic, without regard to written conventions—a brainstorming on paper for a limited amount of time.  Mini Lesson (15 min): ·         Teacher will be Connecting the three different measures of location (mean, median and mode) through a quick class quiz. ·         Then some examples based on median will be solved on the board. ·         Discuss few problems based on Past questions in CIE . Differentiation: Giving the formula of median as required according to the odd or even frequency. Learning Activity (25 min): The students will take notes of the examples and then solve questions of pg. no. 26 Wrap Up (10 min): Exit Ticket : Write formula for median on exit cards Out of school learning: :Students will continue working on their project . Day 7: Do Now/Activator (10min): Post “An Average Rhyme” on the door  before they enter class just to create interest  In the topic.  Entrance Ticket : Students will be  asked questions based on Mean ,Mode which will help to  bring background knowledge to the forefront, make connections with the previous day’s lesson Mini Lesson (15 min): 1.      Relation between the median and mode will be explained. 2.      Formulas will be given . 3.      Discuss few problems based on Past questions in CIE . Learning Activity (25 min): Students will take notes Everyone will be given some different problems to solve . Students  will work at different levels individually in one classroom.  CIE past papers problems will be given after deconstructing. Peer assessment followed by the teacher assessment. Wrap Up (10 min):Students will discuss their answers and problem they faced while solving problems.Students will leave giving a verbal answer about  what they learnt today. Out of school learning:Students will continue working on their project. . Day 8: Do Now/Activator (30 min): Assigned project will be collected and dicussed.  Mini Lesson (10 min): Recall all the measures of location by comparing and contrasting the three measures of location for ungrouped data. A model will be given which has the comparison of  mean , median and mode and then students are asked to solve the miscellaneous question which is based on all three measures of location. Differentiation:The learners will be explained by breaking the miscellaneous question into parts using strategy “CUBES” . Learning Activity (10 min): The students will learn the comparison of three measures of location and solve question no. 2 of pg.no. 36.Discuss few problems based on Past questions in CIE based on stratergy Signal cards : Students use a card to indicate their level of understanding of a concept. Cards may be labeled as follows: Yes/ No Wrap Up (10 min): At the end of the lesson, students should write  What’s  still confusing me …..Ask students to provide a brief, written identification of what topics they consider to be confusing and not fully understood. Out of school learning: Day8: Expert to Expert:Students will be given some problems where Students will  work collaborative to teach each other keywords and decoded terms and formulas determined by the teachers.  Day 9: Do Now/Activator (10min): Work on their doubts .Their collaborative work will be discussed and then Use a brief video clip(on Laptop) on a pertinent topic Range and quartile  to activate student interest in the focus of an upcoming lesson. Mini Lesson (15 min): Introducing the different measures of spread (range and quartiles) and sharing examples with the students to find the interquartile range from the given quartiles. the diagrams Learner Activity(25 min): The students will be divided into groups such that each group has a leader who explains the range and interquartile range to his peers (peer explanation) . The students will take notes of the examples and then solve q.no.6,7 (pg.48) Teacher’s role: Observation of individual student involvement in class with a walk around while students are drawing Wrap Up (10 min): Discuss the key points of the topic. Out of school learning: : They will solve 3 Past paper problems will be given after helping them in Deconstructing. Day 10: Do Now/Activator (10min): Address their queries  in their homework Mini Lesson (15 min): 1.      Reminding students of what they have learnt in previous lesson connecting to this lesson by using strategy “Teaching by asking”. The students will be asked the steps of finding the inter quartile range. 2.      Box and Whisker plot will be explained to the students. 3.      Discuss few problems based on Past questions in CIE based on Box and Whisker plot. Learning Activity (25 min ) : The students will understand the Box and Whisker plot by taking notes  and then solve q.no.10 (pg.49) “Thumbs up and down” strategy will be used to assess whether the students understand the question or not. Wrap Up (10 min): Give each pair of students an index card. Ask them to write out everything they can remember about the day’s content they like . Out of school learning: Students will be given some problems based on Box and Whisker plot. Day 11: Do Now/Activator (10min): Discuss about problems which were given as homework and if any queries, will be rectified in the beginning of the class. Plus/Minus/Intriguing :The teacher should write prompts, controversial statements, etc. (related to the focus of the upcoming lesson) ahead of time to which students will be asked to respond.  Have them identify the statements they agree with (+), the statements they disagree with or question (-), and the statements they find intriguing (I). Mini Lesson (15 min): Review of previous day’s work by asking students the comparison of histograms and box and whisker plots and is followed by the discussion. Differentiation: Teacher help will be given by a short description of the topics. Learning Activity (25 min). The students will give reasons whether box and whisker plots or histograms are better for comparing two distributions. Students will solve Problems 2problems from past papers. Formative assessment based on the discussion. Wrap Up (10 min):Verbal Exit Ticket based on their learning Experience in class for that day . Out of school learning: Read for the next  topic “Variance and Standard Deviation”. Day 12: Do Now/Activator (10min): Give students the key word which will be addressed in the lesson. Ask them to write a detail or descriptor with which they are already familiar that starts with each of the key word. Mini Lesson (15 min): Connecting to previous day’s homework  Examples of finding Standard deviation will be given. Giving them the formula required- standard deviation. Learning Activity (25 min): ·         The students will take notes of the examples and then solve q.no.1-3 (pg.53) ·         Peer assessment Wrap Up (10 min):Taken as learning Activity. Out of school learning: Book Miscellaneous Questions will be given After deconstructing by themselves. Day 13: Do Now/Activator (10min): Discuss about problems which were given as homework and if any queries will be rectified in the beginning of the class. Explain a Procedure :Ask students to Explain how to Derive standard deviation in data giving an example based on previous day work. Mini Lesson (15 min): Demonstrating the way to calculate the variance from a frequency table and sharing two different formulas . Formative Assessment: Marking students’ work Learning Activity (25 min): .The students will apply the given formulas to do Q.no. 1,3,5,7,8 (pg.57) Rubrics will be given with  Problem solving instruction: explicit instruction in the steps to solving a mathematical problem including understanding the question, identifying relevant and irrelevant information, choosing a plan to solve the problem, solving it, and checking answers. Wrap Up (10 min): Problems approaches will be discussed based on rubrics. Out of school learning: Summary of what are the steps to solve various ways  of variance in given data and problems 1CIE problem to solve after decoding in class. Day 14: Do Now/Activator (10min): Collect summary Discuss about problems which were given as homework and if any queries will be rectified in the beginning of the class.  Pose a question based on their previous knowledge that What might be the definition of probability? Mini Lesson (15 min): Introducing the concept of probability by explaining the related terminology (assigning probability, probabilities of events and the addition law for mutually exclusive events). Sharing some of the examples of all the above mentioned concepts Discuss few problems based past CIE papers. Learning Activity (25 min): The students will take notes of the examples and then solve q.no.1-5 (pg.71) Carousel Brainstorming: On chart paper around the room (or on paper that is passed around groups), ask small groups of students (3-4) to respond to a question or statement based on few real life examples  posed at the top of the paper.  Wrap Up (10 min): Discuss answers of assigned problems and how they have approaches to particular way of solving it. Out of school learning: : Students will be assigned Past papers problems based on Probablility. Day 15: Do Now/Activator (10min): Discuss about problems which were given as homework and if any queries will be rectified in the beginning of the class. Pose a question or specific aspect of focus for the upcoming topic which is Conditional probability.  Ask students to “quick write” (write whatever comes to mind about the topic, without regard to written conventions—a brainstorming on paper) for a limited amount of time.  Begin with short time periods of 1-2 minutes, because students must write the entire time. Students will be explained how to interpret something Mini Lesson: Describing the students the laws about the conditional probability and independent events(using Tree Diagrams ). The problems will be explained after discussing it. “Thumbs up and down” strategy will be used to assess whether the students understand the question or not. Learning Activity (25 min): The students will take notes of the examples and then solve q.no.1,2,3 (pg.79) Wrap Up (10 min): Key Ideas Students list the key ideas from the lesson and why they were important. Out of school learning: Problems will be given from text book based on taught topic. Day 16: Do Now/Activator (10min): Discuss about problems which were given as homework and  queries will be rectified in the beginning of the class. Ask to create questions based on yesterday’s learning. In response to a prompt or question, direct students to “turn and talk” to a shoulder partner Mini Lesson (15 min): Recall all the laws of conditional probability and independent events. The students will be asked questions related to previous day’s description. Discuss few problems based on Past questions in CIE.. Learning Activity (25 min): ·         The students will raise their hands if they know the answer and give answer . ·         The answers given by one student will be discussed among the other students and after discussion will solve q.no.4-6 and 8-13 (pg.79). ·         Marking students’ work. ·         The problems will be explained by teacher after demystifying it. Wrap Up (10 min): Sticky Notes Give students sticky notes and a question or topic to which they should respond.  Have them post their notes on the board, door, wall, or a chart (that can have divisions.).  Students will return to those responses at the end of the lesson to confirm or revise their thinking. Out of school learning: :CIE problems will be Given with a rubric based on their knowledge . Day 17: Do Now/Activator (10min): Discuss about problems which were given as homework and if any queries will be rectified in the beginning of the class. Word Splash Students are given a “splash” of the key words from the unit.  They should write a few meaningful sentences to capture  (relying on their background knowledge) using these words. Mini Lesson (15 min): Introduction to the “Permutations and combinations” by using Teaching by asking. The students will be asked about the ‘Factorial’ and how to calculate it .Then the teacher will relate the factorial with permutations taking examples of everyday life when the objects are distinct and describing the formula of permutation.  Also explaining the permutation when the objects are not distinct. Learning Activity (25 min): The students will answer the questions the teacher ask and learn about the permutations (application of factorials) and then take notes. Students will be given some problems based on Past CIE after deconstructing. Wrap Up (10 min): Exit Slip :Students will write main idea of concept they have Out of school learning: CIE past papers problems will be Given after Deconstructing few questions  in class only with rubric (Assignment Attached) . Day 18: Do Now/Activator (10min): Discuss about problems which were given as homework and if any queries will be rectified in the beginning of the class. . Mini Lesson (15 min): Connection to previous day’s work. The questions given in previous day’s homework will be discussed. The teacher will continue by explaining the combinations through various examples. Analyzing a Real World Problem through Permutations/Combinations:                               Many restaurants out there are doing math and showing it off? I want  my students to do the math and analyze the validity of these advertisements. Divide number of students in group :1 group will work on Wendy burger   Wendy burger  "We figured out that there are 256 ways to personalize a Wendy's hamburger. Luckily someone was paying attention in math class." Is it really so???? This is an old package which displays ways to personalize a Wendy's hamburger. Discuss  the number of toppings available at Wendy's (9 total) and then decide to use combinations to figure out the number of arrangements possible since order does not matter.and then check if its really true ???? Other group will work on Sonic   Sonic claims that they have over 398,929 drink combinations available on their menu. They have 8 base drinks and 16 add-ins.students can work on permutations and combinations and checkfor their validity. Use website     http://portlandsonic.com/twc/   Learning Activity (25 min): The students will be Sharing thoughts and  take notes. Wrap Up (10 min): Exit Slip :Students will write main idea of concept they have learnt. Out of school learning: A project  will be Assigned  on Friday(Integrated Learning ):  - Analyzing a Real World Problem through Permutations/Combinations                           As a group students will go to subway or check it out on internet  and find out how many ways they can personalize their SUB Bread using  permuation and combination they can make out to customize their SUB Bread.They can create their own posters  for  which shows how many ways they can personalize their sub in a creative way. A worksheet will also  be given to collect their results. . . Day 19/20: Do Now/Activator (10min): Discusss about their assigned project . Mini Lesson (15 min): Reminding students of what they have learnt in previous lesson connecting to this lesson by using strategy “Teaching by asking”. Examples related to applications of permutation and combination will be discussed . Review of the whole topic  through a class discussion and problems done so far for the mock test  next day. Learning Activity (25 min ) : The students will answer the question and solve problem 1-4 (pg.96) “Thumbs up and down” strategy will be used to assess whether the students understand the question or not. Wrap Up (10 min): Give each pair of students an index card. Ask them to write out everything they can remember about the day’s content like Out of school learning: Students needs to revise complete chapter. Day 21: Do Now/Activator (10min): Address their queries  about the topic Mini Lesson (15 min): Mock Test based on Past CIE paper problems. Wrap Up (10 min):Discuss their problems and their queries while taking Assessment Out of school learning: Home Assignment will be given.

Curriculum S1 1.  Representation of data: ·         select a suitable way of presenting raw statistical data, and discuss ·         advantages and/or disadvantages that particular representations may have ·          understand and use different measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation), e.g. in comparing and contrasting sets of data ·         use a cumulative frequency graph to estimate the median value, the quartiles and the interquartile range of a set of data ·         understand and use different measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation), e.g. in comparing and contrasting sets of data ·         use a cumulative frequency graph to estimate the median value, the quartiles and the interquartile range of a set of data 2. Permutations and combinations ·         understand the terms permutation and combination, and solve simple problems involving selections ·         solve problems about arrangements of objects in a line, including those involving: ·          repetition (e.g. the number of ways of arranging the letters of the word ‘NEEDLESS’) ·          restriction (e.g. the number of ways several people can stand in a line if 2 particular people must — or must not — stand next to each other). 3. Probability ·          evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g. for the total score when two fair dice are thrown), or by calculation using permutations or combinations ·         use addition and multiplication of probabilities, as appropriate, in simple cases Learning Objectives: (Based on Cambridge) Students • understand relevant mathematical concepts, terminology and notation of Statisitcs  ; • recognise the appropriate mathematical procedure for a given situation; • apply combinations of mathematical skills and techniques in solving problems;

Assessment: Formative Assessment: KWL Formative Assessment :Explaining the Procedure (Learner Activity) Formative Assessment: Problem solving using Rubric Summative Assessment: Monthly test ·

Learning Outcomes: By the end of this unit, students will be able to attain a  deeper understanding of mathematical principles based on Statistics; can analyze problems logically, recognizing when and how a situation may be represented statistically. Develop the ability to select an appropriate  measures of location to use in a given situation. Reading-students will learn close reading of the text of given problem-comprehend what is read and then Carry out a transformation from the words of the problem to the selection of an appropriate mathematical strategy. Writing –Students will learn how to Encode the answer in an acceptable written form. Students will be able to label  Statistical graphs with appropriate units and scaling . Listening and Speaking- Students will be able to communicate to others the results of statistical studies.

  

1.                       How many different ways do you think there are to personalize a Sub ?

2.                    List out Different toppings and sauces  to put on sub at SUBWAY??

3.                  TO calculate ,we will use permutation or combination .which one shoud we use ?why?

4.                  What is formula for combination?

5.                   What is formula for permutation?

6.                   Calculate the number of ways to make a sub based on topping that you come up with?