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|MA5.1 – 8MG Area and Surface Area | Mathematics Stage 5.1 Year 9 2014 |
|Summary of Sub Strands |Duration: 5 weeks |
|S4 Length (Pythagoras’ theorem) |Start Date: |
|S4 Area (area formulas) |Completion Date |
| |Teacher and Class: |
|Unit overview |Outcomes |Big Ideas/Guiding Questions |
|In this unit, students will calculate the area |MA5.1-1WM uses appropriate terminology, diagrams | |
|of composite shapes (including an annulus) and |and symbols in mathematical contexts | |
|the surface area of right prisms, cylinders. |MA5.1-2WM selects and uses appropriate strategies | |
|They will solve problems related to these |to solve problems | |
|concepts using a variety of real life |MA5.1-8MG calculates the areas of composite shapes, | |
|applications. |and the surface areas of rectangular and triangular | |
| |prisms | |
| | |Key Words |
| | |Area, composite shapes, triangles, quadrilaterals, quadrants, semicircles, sectors, symmetry, |
| | |annulus, surface area, right prism, rectangular prism, triangular prism, net, Pythagoras’ theorem, |
| | |surface area, cylinder, composite solid |
|Catholic Perspectives |School Free Design |
|MacKillop College Bathurst is a Catholic faith community, dedicated to the education of young women. |This is a free design area for schools to add local additional areas. This could include: |
|The Mathematics teachers undertake to uphold the ethos and teachings of the Catholic church and to |Context if you prefer the unit overview and context to be separate |
|support the liturgical life of the College. They promote in the classroom a sense of compassion, |School focus for learning – eg blooms taxonomy, solo taxonomy, contemporary learning, habits of |
|respect between students and staff and a positive and supportive learning environment. |mind, BLP (building learning power) |
|Numeracy operates within a variety of social contexts. From a Catholic perspective, numeracy must be |Any specific social and emotional learning which could be embedded into the unit eg enhanced group |
|infused with a vision of the innate dignity of all students, as created in the image and likeness of a|work |
|loving, generous and creating God. Teachers of Mathematics 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. | |
|Assessment Overview |
|Pretest on Stage 4 ‘Angles and Two-dimensional Shapes’ and ‘Area of Plane Shapes’. |
|Undertake an investigation such as ‘Work out the surface area of a cylinder which will hold three tennis balls in a row’. |
|Ask questions such as ‘Do solids with the same surface area have the same volume or capacity? |
|Estimate the relative area of each of the states from a map of Australia |
|Answer questions like the following: (a) do rectangles with the same perimeter have the same area? (b) do parallelograms with the same perimeter have the same area? |
|Reg |Content |Teaching, learning and assessment |Resources |
| |At the end of this unit the student should be able to: |Review the area of plane shapes using an activity such as a matching exercise (match the shape with the| |
| |Calculate the areas of composite shapes (ACMMG216) |area formula), worksheet, smartboard activity or a pretest. | |
| |calculate the areas of composite figures by dissection into |Students calculate the area of a simple shape in their environment, for example, the classroom or a |Measuring tapes, rulers, trundle wheels |
| |triangles, special quadrilaterals, quadrants, semicircles and |sports field. | |
| |sectors |Then introduce the concept of composite shapes. Students brainstorm a method to calculate the area of | |
| |identify different possible dissections for a given composite |the shape and then carry it out using a range of measuring instruments. | |
| |figure and select an appropriate dissection to facilitate |At this point, discuss the different ways in which the one shape could be dissected. Use an example in | |
| |calculation of the area (Problem Solving) [pic] |their environment. | |
| | |Adjustment | |
| | |Shapes can increase in complexity as students become more confident. |Composite shape templates |
| | |Provide students with a range of composite shapes to explore. They can cut the composite shapes into | |
| | |the component shapes and calculate the area. |(utube – Area of a Composite Figure) |
| | |For example, the shape below can be divided into two semicircles and a square as shown by the dotted | |
| | |line. Its area can then be found using the formulas for a circle and a square. | |
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| | |Include composite shapes such as the one below which require a subtraction method. | |
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| |solve a variety of practical problems involving the areas of | | |
| |quadrilaterals and composite shapes | | |
| | |Practical problems could include the following: | |
| | |‘Fence It’ – imagine you had 40 one metre sections of fencing. What is the largest rectangular area of | |
| | |land you could fence off? | (‘Fence it’). |
| | |The local swimming pool (or school pool if possible) needs to be cleaned. Using measuring instruments, | (problems |
| | |calculate the area of wall that needs to be kept clean. |related to area, perimeter, surface area |
| | |Calculate the cost of laying turf on the school grounds. |and volume). |
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| |apply properties of geometrical shapes to assist in finding |Students should have already discussed the derivation of the formula for area of triangle in Stage 4. | |
| |areas, eg symmetry (Problem Solving, Reasoning) [pic] |Briefly discuss and demonstrate with examples. | |
| | |For example, look at the triangle below which has been formed by cutting a rectangle in half. | |
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| | |Students can see that the area of a triangle is equal to half the area of a rectangle of the same base | |
| | |length and height. | |
| | |Trapeziums can be broken into a rectangle and two triangles (equal triangles in the case of an | |
| | |isosceles trapezium below). | |
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| | |Rhombuses and kites can be split into two identical triangles. | |
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| | |Adjustment | |
| | |Some students could carry out a practical investigation. For example, they could investigate car | |
| | |parking spaces. | |
| | |Car parking bays are based on either rectangles or parallelograms as shown: | |
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| | |Students could investigate: | |
| | |What dimensions of each shape would be needed to provide a suitable size for parking a car. (Remember | |
| | |to allow for clearance between adjacent cars). | |
| | |Which arrangement uses the greatest area. | |
| | |What are the advantages and disadvantages of each arrangement. | |
| | |Students could visit carparks to make measurements and to consider other constraints eg. Number of | |
| | |entrances, turning circles of vehicles, etc. | |
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| | |Allow students to discover a method for calculating the area of an annulus independently, ie.by | |
| | |subtracting the area of the smaller circle from the larger circle. | |
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| |calculate the area of an annulus (Problem Solving) |Adjustment | |
| | |The formula for the area of an annulus could be introduced to the more capable students. | |
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| | |Students could investigate the torus (plural: tori) which is a three dimensional representation of a | |
| | |revolving circle, for example, a doughnut. | |
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| | |Check that students can define what a prism is. Describe and/or show how slices can be cut from a prism| |
| | |so that each one has the same size and shape. The cross-sections formed by slicing the prism are | |
| | |congruent. | |
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| |Solve problems involving the surface areas of right prisms | | |
| |(ACMMG218) |Students could be given nets of rectangular prisms and triangular prisms. They could name them and then|Practical Surface Area: Design a Toblerone |
| |identify the edge lengths and the areas making up the ‘surface|draw the solid that it represents. |Box |
| |area’ of rectangular and triangular prisms [pic] [pic] |Students could then measure the necessary edges and calculate the surface area. |
| |visualise and name a right prism, given its net [pic] [pic] |The solid could then be constructed and compared with the student’s diagram. |sign.pdf |
| |recognise whether a diagram represents a net of a right prism |Students bring in a variety of solids from their home environment eg. Food packaging | |
| |(Reasoning) [pic] | | |
| |visualise and sketch the nets of right prisms [pic] |Adjustment | |
| |find the surface areas of rectangular and triangular prisms, |Some students can explore the surface area of more complicated solids. For example, a tissue box with | |
| |given their net |an ellipse opening removed on the top. Students could research the area formula for an ellipse to use. | |
| |calculate the surface areas of rectangular and triangular |Assessment | |
| |prisms |Explore the relationship between surface area and volume. Areas of investigation could include fat | |
| | |content of French fries, the function of the alveoli in the lungs and sizes of organisms. | |
| | |Investigate the surface area of the human body. Is there a formula to estimate this? | |
| | |Check that students can use Pythagoras’ theorem to find the hypotenuse and a short side in right-angled| |
| | |triangles. This was introduced in Stage 4. Then apply to problems related to triangular prisms. | |
| | |Give students a variety of problems to solve, ensuring that they choose one that is based on a | |
| | |rectangular prism and one that is about a triangular prism. Suggestions include the following: | |
| | |Investigate the cost of packaging foods. What shapes are more economical? | |
| | |What area of canvas is needed to make a tent? Students could construct the tent. | |
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| | | |Body surface area calculator |
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| |apply Pythagoras' theorem to assist with finding the surface | | |
| |areas of triangular prisms (Problem Solving) | | |
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| |solve a variety of practical problems involving the surface | | |
| |areas of rectangular and triangular prisms | | |
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| | | |Surface area and chocolate (includes |
| | | |activities about packaging chocolate). |
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| | | |-and-chocolate |
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