Teacher NameGauri Pathak Grade & Section:10 C Subject: Mathematics
Unit Name: (Mesuration ,Trigonometry)
Duration and Dates for completion of Unit: 6 January to 9th February
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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.
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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 .
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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.
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Future Learning:
Future learning will be discussed before starting a topic
For Mensuartion ppt will be shown
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
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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.
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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.
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Resources:
ICT Lab, Video, Compass point chart, Chart paper to display
Worksheets: 4)-Areas-of-Flags-(4).docx
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
Students need to bring their favorites cups or tumblers or cups for Activity based on capacity.
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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
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
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 .
Future Learning:
Future learning will be discussed using
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
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
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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.
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Assessment:
Formative Assessment: Bridge Building Activity
Summative Assessment: Class test
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Learning Outcomes:
By the end of this unit, students will Upon completion of this lesson, students will:
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.
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