MA4-12MG : Length, Perimeter and Circumference | Mathematics Stage 4 Year 7

Summary of Sub Strands Duration

S3 Length (Review) S4 Length Sample term3 weeksDetail: 3 weeks, 4 lessons per week (…hours)

Unit overview Outcomes Big Ideas/Guiding Questions

Develop formulae and use to find the perimeter of triangles, rectangles and parallelograms

Investigate circumference and radius of circles

Convert between metric units of length

Mathematics K-10

●MA39MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

●MA41WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols

●MA42WM applies appropriate mathematical techniques to solve problems

●MA412MG calculates the perimeters of plane shapes and the circumferences of circles

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Key Words

Pi (π) is the Greek letter equivalent to 'p' and is the first letter of the Greek word perimetron, meaning 'perimeter'. The symbol for pi was first used to represent the ratio of the circumference to the diameter of a circle in the early eighteenth century.

Some students may find the use of the terms 'length/long', 'breadth/broad', 'width/wide' and 'height/high' difficult. Teachers should model the use of these terms in sentences, both verbally and in written form, when describing diagrams. Students should be encouraged to speak about, listen to, read about and write about the dimensions of given shapes using various combinations of these words, eg 'The length of this rectangle is 7 metres and the width is 4 metres', 'The rectangle is 7 metres long and 4 metres wide'. Students may also benefit from drawing and labelling a shape, given a description of its features in words, eg 'The base of an isosceles triangle is 6 metres long and its perimeter is 20 metres. Draw the triangle and mark on it the lengths of the three sides'.

In Stage 3, students were introduced to the term 'dimensions' to describe the length and width of a rectangle. However, some students may need to be reminded of this.

Key words: (Perimeter)Base, breadth, centimetre, composite shape, height, kilometre, length, measurement, metre, metric system, millimetre, perimetre

Key Words: (Circle)Annulus, annuli, arc, centre, chord, circle, circular, circumference, concentric, diameter, pi, quadrant, radius, radii, sector, major segment, minor segment, semicircle, tangent

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Catholic Perspectives School Free Design

TALK TO MICHAEL FOR WHAT TO PUT HERE

CEO will provide guidance in this area

Example:

The value of sacramentality celebrates the presence of God in every facet of creation.

The Christian message is ultimately one of hope

Mathematics, Reality, and God

Paul A. Schweitzer

DOI:10.1093/acprof:oso/9780199795307.003.0013

Simplicity and symmetry are the heart of beauty in mathematics. Beauty often motivates mathematicians and physicists. Einstein said that his theory of general relativity had to be true because it was so elegant. Archimedes was thrilled with his discovery that the ratio of the volume of a cylinder tightly enclosing the volume of a sphere is 3:2. Mathematics offers beauty without defects. Salvador Dali produced two religious paintings that have important mathematical components. Mathematics have very precise norms for proving theorems, but these generally don’t apply to ordinary life or other academic disciplines. Kurt Gödel brilliantly proved that a mathematical system could be proven either complete or consistent, but not both. This means mathematics is open to the transcendent, as must other disciplines be as well, since they are less precise than mathematics. Every type of rational discourse must be judged according to its own procedures and limitations. By developing n-space, the mind shows it is made in the image of God. It is helpful to compare theology with mathematics. Both subjects always have new problems to solve. It is now

This is a free design area for schools to add local additional areas. This could include:

Context if you prefer the unit overview and context to be separate

School focus for learning – eg blooms taxonomy, solo taxonomy, contemporary learning, habits of mind, BLP (building learning power)

Any specific social and emotional learning which could be embedded into the unit eg enhanced group work

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known that Gödel developed a proof for the existence of God based on the ontological argument.

Keywords:   beauty, golden,mean, Einstein, Dali, Gödel, completeness, consistency, theology, ontological argument

Below Connected Website

http://www.csodbb.catholic.edu.au/about/news/pdfs/numeracy%20statement%202010.pdf

Numeracy and the Catholic World View

Numeracy operates within a variety of social contexts. From a Catholic perspective, numeracy must be imbued with a vision of the innate dignity of all students, as created in the image and likeness of a loving, generous and creating God. Teachers in Catholic schools have an obligation to not only teach their students the skills and knowledge to be numerate, but to teach from a Catholic perspective. Teachers are called to challenge their students to use the skills and knowledge they have acquired to bring about social change in the world.

Below is from St Josephs Narrabeen

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Below is from Mount St Patrick College, Murwillumbah

PRIMARY AIM

The primary aim of the Department, as a whole, is to inculcate the skills, knowledge and attitudes as outlined in the syllabuses with a Catholic Perspective.

GENERAL AIMS

• To provide a structured and caring environment for the learning of Mathematics.

• To develop the significance and relevance of Mathematics in everyday life.

• To attempt to equip all student with the Mathematical skills and knowledge which will help them to cope with everyday life.

• To make Mathematics meaningful and relevant to students.

• To make Mathematics interesting and enjoyable.

• To teach students to think clearly and logically.

• To teach students good study habits.

• To bring student to the realisation that they are not just learning Mathematics to pass examinations.

• To develop staff professionally.

• To foster the language of Mathematics as a form of communication.

• To provide a sense of justice and equity in Mathematics regardless of racial origin or religion and to avoid stereotyping of roles for each sex.

THE NATURE OF MATHEMATICS LEARNING

Mathematics is learnt by individual students at different rates.

It must be remembered that:-

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• students learn best when motivated

• students learn Mathematics through interacting and reflecting.

• students learn Mathematics through investigating.

• students learn Mathematics through language.

• students learn Mathematics as individuals in the context of cultural, intellectual, physical and social growth.

CATHOLIC PERSPECTIVE

'We are committed to the development of Catholic schools which demonstrate a special concern for, and understanding of, the uniqueness of each person.'

Tick Points History

CATHOLIC (GOSPEL) VALUES:

    GV1    Celebration

  GV2    Common Good

GV3    Community

GV4    Compassion

    GV5    Cultural Critique

    GV6    Faith

    GV7    Hope

GV8    Human Rights

    GV9    Joy

GV10   Justice

    GV11  Peace

    GV12  Reconciliation

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    GV13  Sacredness of  Life

GV14   Stewardship of  Creation

    GV15  Service

GV16  Wisdom

Tick Points Science

Catholic Perspective Keywords1. Awe and Wonder2. Celebration3. Common Good4. Charity5. Commitment to community6. Community Conservation7. Compassion8. Courage9. Cultural Critique10. Dignity of each human person11. Endurance / perseverance12. Faith13. Family14. Forgiveness15. Global Solidarity and the Earth Community16. Hope17. Hospitality18. Human Rights Justice19. Joy20. Justice21. Love22. Multicultural Understanding23. Peace24. Reconciliation

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25. Reverence26. Sacredness of Life27. Service28. Sense of wonder29. Servant leadership30. Stewardship of Creation31. Structural Change32. Self Respect (Self Esteem)33. Truth

Assessment Overview

Generally, teachers should design specific assessment tasks that can be drawn from a variety of the following sources of information and assessment strategies:• student responses to questions, including open ended questions,

• student explanation and demonstration to others,

• questions posed by students,

• samples of student work,

• student produced overviews or summaries of topics,

• investigations or projects,

• students oral and written report

• practical tasks and assignments,

• short quizzes

• pen and paper tests, including multiple choice, short answer questions and questions requiring longer responses, including interdependent questions ( where one answer depends on the answer obtained in the preceding part)

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• open book tests

• comprehension and interpretation exercise

• student produced worked samples,

• teacher/student discussion or interviews

• observation of students during learning activities including the student’s correct use of terminology

• observation of a student participating in a group activity

References can be made to the relevant end of chapter review or screening tests found in textbooks or other resource areas

Content Teaching, learning and assessment Resources

Mathematics K-10Stage 4 - LengthStudents:

Find perimeters of parallelograms, trapeziums, rhombuses and kites (ACMMG196)

■ find the perimeters of a range of plane shapes, including parallelograms, trapeziums, rhombuses, kites and simple composite figures

● compare perimeters of rectangles with the same area (Problem Solving)

■ solve problems involving the perimeters of plane shapes, eg find the dimensions of a rectangle, given its perimeter and the length of one side

■ Consider the degree of accuracy needed when making measurements in practical situations

■ Conversion of length “units” review■ Choose appropriate units of measurement based on the

required degree of accuracy Measurement activity involving body parts is fun?--> good discussion on accuracy

■ Make reasonable estimates for length and area and check by measuring

■ Select and use appropriate devices to measure lengths and distances

■ Discuss why measurements are never exact■ Apply measurement skills to everyday situations

eg determining the area of the basketball court Use the terms Key Words appropriately

■ Extend mathematical tasks by asking questions eg ‘If I change the dimensions of a rectangle but keep the perimeter the same, will the area change?’

Perimeter Formulashttp://www.math.com/tables/geometry/perimeter.htm

Interactive Perimetershttp://www.shodor.org/interactivate/lessons/Perimeter/

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■ Interpret measurements on simple plans■ Investigate the areas of rectangles that have the same

perimeter

■ Given three objects, measure and record their lengths (in table form) in millimetre, centimetres, metres and kilometres.

■ Working in pairs:tell me everything that you know about perimeter

■ Open ended questions can be used to find out what students know and can do from earlier stages.

■ Card Matching Activity

■ Match a diagram with a statement of the area, perimeter and its solution.

Discussion Questions:■ The larger the perimeter, the larger the area. Always,

sometimes or never true?

■ Sketch as many rectangles as you can whose area is equal to 24 centimetres squared.

■ Sketch as many rectangles as you can that have a perimeter of 36 cm.

■ Explain the relationship between the

perimeter and(ii) area of a rectangle whose side lengths have been doubled. Can you sketch a triangle that shows the same relationship?

■ In pairs, measure the height of each other, in cm. Then convert the results to mm, m and km

■ Classify and name 2D shape

■ Students are given a sheet of 2D shapes to classify, name and measure the length of each side to determine the perimeter

Great Intro to Perimeterhttp://www.mathgoodies.com/lessons/vol1/perimeter.html

Really Good Description for Perimeterhttp://mscraftynyla.blogspot.com.au/2012/10/the-many-ways-of-defining-term-perimeter.html

Visual Interactivehttp://www.shodor.org/interactivate/activities/PerimeterExplorer/Really good HOW to Lesson for Perimeter Explorerhttp://www.shodor.org/interactivate/lessons/PerimeterElem/

Using a Spreadsheet to find Perimeter and Area Comparisons

http://www2.ups.edu/community/tofu/lev2/mathconcepts/geometry/areaper.htm

Teach 21 Practical Based Learninghttp://wvde.state.wv.us/teach21/

Illuminations Lessons

http://illuminations.nctm.org/Lessons.aspx

Measurement Resources

http://www.teachervision.fen.com/measurement/teacher-resources/34507.html

Hot Chalk Lesson Plans

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■ Investigate the perimeter in relation to area(eg. How many different shapes can be made with the perimeter of 20cm?)

■ What changes with perimeter results

■ Find the perimeter of composite shapes with missing side values

■ (eg. L-shapes and C-shapes)Finding perimeter of shapes with measurements given in different units

Adjustment

Review common quadrilaterals (eg identify names matching diagram)Use only same units for dimensions on each diagram

Find perimeters that are rectangles

Keep values as integers

http://lessonplanspage.com/math/seventh-grade/

Investigate the concept of irrational numbers, including (ACMNA186)

■ demonstrate by practical means that the ratio of the circumference to the diameter of a circle is constant, eg measure and compare the diameters and circumferences of various cylinders or use dynamic geometry software to measure circumferences and diameters

■ define the number as the ratio of the circumference to the diameter of any circle

● compare the various approximations for used throughout

■ Irrational concepts ~ should have an understanding of square root 2 from Pythagoras

■ Find out all that you can about the history of pi.

■ PI Day 21st March (Google Pi) world pi day is 14/3

■ Investigate Eratosthenes and his work on the circumference of the earth. Write a brief report of your findings or design a poster to display your findings. (Applying Strategies, Reflecting, Communicating)

■ Use mental strategies to estimate the circumference of circles, using an approximate value of eg 3

■ Find the perimeter of quadrants and semi-circles■ Find radii of circles given their circumference■ Solve problems involving , giving an exact answer in

http://mathvids.com/lesson/mathhelp/45-fun-with-piA video discussing pi. This video talks about what pi is, how to calculate pi, where pi is found, and fun facts / activities with pi.

This is great for a person who wants to learn more about pi, especially on or around Pi Day. Ideas are presented clearly and thoroughly with a brief introduction to several aspects of pi. The resources also do a great job providing more information on pi.

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the ages and investigate the concept of irrational numbers (Communicating)

● recognise that the symbol is used to represent a constant numerical value (Communicating)

terms of and an approximate answer using , 3.14 or a calculator’s approximation for

■ Compare the perimeter of a regular hexagon inscribed in a circle with the circle’s circumference to demonstrate that > 3

AdjustmentVisual practical activities

Physically create the parts of the circle as groups outside

(eg. As a group form the circumference, form a human tangent on the drawn circle, chord, secant, etc)

All these books are from the website given ~http://www.livingmath.net/Reviews/ReviewsChildrensMathLit/Senefer/tabid/1076/language/en-US/Default.aspxSong about Perimeter and Circles

http://songsforteaching.com/math/geometry/measuringcircles.htm

Additional Resources:

Slides from the video - SmartBoard slides in PDF format from the pi lesson.

Teach Pi Website - A website dedicated pi and

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pi day resources. It includes a list of the longest pi chains ever created.

Joy of Pi Website - This website has many resources, pi facts, and pi links, including information about The Joy of Pi book.

Exploratorium - History of pi, discovering pi, and many other resources dedicated to learning about pi.

Pi Resources - A bunch of links about pi!

Expansions of pi - Several expansion formulas for pi

Definition of Pi - A definition of what pi is and some information about pi.

Pi Facts - A list of 50 interesting facts about pi -- quite an impressive collection.

Pi Infographic - A banner graphic with some fun facts about pi and its history. A great resource for teachers!

Investigate the relationship between features of circles, such as the circumference, radius and diameter; use formulas to solve problems involving circumference (ACMMG197)

■ identify and name parts of a circle and related lines, including arc, tangent, chord, sector and segment

■ develop and use the formulas to find the circumferences of circles in terms of the diameter d or radius r:

■ Write down everything that you know about circles and their perimeter and area.

■ Example:(eg. Tom rides a bike with a wheel radius of 26 cm. His brother Jack has a smaller bike with a wheel radius of 20 cm. The boys ride from Bulli to North Wollongong, a distance of 15 km. Whose bike will make the most revolutions and by how many? (Applying Strategies, Reflecting))

■ Examine the relationship between circumference and diameter, radius by using tape or string to measure around some common objects (CD’s, cans, plates). Write a sentence summarizing your findings. (Reflecting,

http://www.thirteen.org/edonline/lessons/pi/index.htmlStudents learn the mathematical value of pi through the process of measuring circumference. Students conduct hands-on calculations for cylindrical objects, demonstrate the properties of a circle, and discover for themselves how pi works.

Game for Parts of the Circle

http://www.learnalberta.ca/content/mec/html/index.html

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● use mental strategies to estimate the circumferences of circles, using an approximate value of such as 3 (Problem Solving)

● find the diameter and/or radius of a circle, given its circumference (Problem Solving)

■ find the perimeters of quadrants and semicircles

■ find the perimeters of simple composite figures consisting of two shapes, including quadrants and semicircles

■ find arc lengths and the perimeters of sectors

Communicating)■ Use grid paper to estimate the area of some circles

(Applying Strategies)■ Investigate practical applications such as the appropriate

sprinkler for a particular area. Write a brief report on your findings and discuss this in light of current water restrictions. (Applying Strategies, Reflecting, Communicating)

■ Investigate the relationship between right-angled triangles and semi-circles drawn on their sides.

■ Practical activity of all different cylindrical shapes. With soft tape measure circumference and diameter of each. Record results into a table. Final column C divide D. What happens??

AdjustmentReview and practise finding the radius and diameter of a variety of circles

Identify and use GIVEN formula to solve for solution

Basketball Circumference Game http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw41551

Circumference of a Circle Description

http://www.mathgoodies.com/lessons/vol2/circumference.html

Online Calculator for Circumference

http://math.about.com/library/blcirclecalculator.htm

Circle Parts Description

http://math.about.com/library/blcircle.htm

Finding Circumference given Radius

http://lessonplanspage.com/mathfindcircumferencegivenradius67-htm/

Solve a variety of practical problems involving circles and parts of circles, giving an exact answer in terms of and an approximate answer using a calculator's approximation for

Writing Activities to Show Reflection WM

■ Write down everything that you know about circles and their perimeter and area.

■ Tom rides a bike with a wheel radius of 26 cm. His brother Jack has a smaller bike with a wheel radius of 20 cm. The boys ride from Bulli to North Wollongong, a distance of 15

One way that is very practical is the idea of putting an underground watering system into a yard around a house and other objects that need to be dodged to not get wet. This is really great for area with part sizes. The students have to consider the saturation factors of the grass too.

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km. Whose bike will make the most revolutions and by how many? (Applying Strategies, Reflecting)

■ You are to build a stained glass window of concentric circles. The inner circle has a radius of 20 cm and the outer circle has a radius of 40 cm. The inner circle is to be divided into 8 equal sections. If each section is to be outlined in wire

■ how much wire will be needed to construct the window?

■ how much glass is needed?

■ Investigate the area and perimeter of the inner circle in one-day cricket (Mathscape 8 page 392-393) and draw a diagram of your findings. (Applying Strategies, Communicating)

This can be compared to the goat attached to the rope problems.

http://brainmass.com/math/geometry/5120

http://www.purplemath.com/modules/perimetr5.htm

http://www.smart-kit.com/s3260/the-involuting-goat/

http://www.mymathforum.com/viewtopic.php?f=8&t=4115

Registration Evaluation

Class: __________________________ Teachers evaluate the extent to which the planning of the unit has remained focused on the syllabus

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Start Date: _______________________

Finish Date: ______________________

Teacher’s Signature: _______________________

outcomes. After the unit has been implemented, there should be opportunity for both teachers and students to reflect on and evaluate the degree to which students have progressed as a result of their experiences, and what should be done next to assist them in their learning.

Evaluation reflects:

The effectiveness of the program in meeting the diverse needs of students and identifies curriculum adjustmentsLevel to which syllabus outcomes have been demonstrated by studentsThe effectiveness of pedagogical practices employedSuggested program adjustmentsElements of the school’s Contemporary Learning Framework

Sample questions

Highlight the response that best describes your view to the following statements and provide comments in the spaces provided.

1. The set text/s (if relevant) were suitable for the student needs and interests:

STRONGLY AGREE AGREE UNSURE STRONGLY DISAGREE

2. There were sufficient and suitable resources to teach the unit:

STRONGLY AGREE AGREE UNSURE STRONGLY DISAGREE

3. There was sufficient time to teach the set content:

STRONGLY AGREE AGREE UNSURE STRONGLY DISAGREE

4. Assess the degree to which syllabus outcomes have been demonstrated by students in this unit:

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5. Evaluate the degree to which the diverse needs of learners have been addressed in this unit:

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6. Comment on the effectiveness of pedagogical practices employed in this unit:

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7. Assessment was meaningful and appropriate to reflect student learning and achievement:

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8. Suggested program adjustments / other comments:

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