# EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 2. Chapter 5. Working with shape and space

Save this PDF as:

Size: px
Start display at page:

Download "EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 2. Chapter 5. Working with shape and space"

## Transcription

1 EDEXCEL FUNCTIONAL SKILLS PILOT Maths Level 2 Chapter 5 Working with shape and space SECTION H 1 Perimeter 75 2 Area 77 3 Volume D Representations of 3-D Objects 81 5 Remember what you have learned 82 Pearson Education 2008 Functional Maths Level 2 Chapter 5 Draft for Pilot

2 EDEXCEL FUNCTIONAL SKILLS PILOT Maths Level 2 Su Nicholson Draft for pilot centres Chapter 1: Working with Whole Numbers Chapter 2: Working with Fractions, Decimals & Percentages Chapter 3: Working with Ratio, Proportion, Formulae and Equations Chapter 4: Working with Measures Chapter 5: Working with Shape & Space Chapter 6: Working with Handling Data Chapter 7: Working with Probability Chapter 8: Test preparation & progress track How to use the Functional mathematics materials The skills pages enable learners to develop the skills that are outlined in the QCA Functional Skills Standards for mathematics. Within each section, the units provide both a summary of key learning points in the Learn the skill text, and the opportunity for learners to develop skills using the Try the skill activities. The Remember what you have learned units at the end of each section enable learners to consolidate their grasp of the skills covered within the section. All Functional Skills standards are covered in a clear and direct way using engaging accompanying texts, while at the same time familiarising learners with the kinds of approaches and questions that reflect the Edexcel Functional Skills SAMs (see edexcel.org.uk/fs/ under assessment ). The Teacher s Notes suggest one-to-one, small-group and whole-group activities to facilitate learning of the skills, with the aim of engaging all the learners in the learning process through discussion and social interaction. Common misconceptions for each unit are addressed, with suggestions for how these can be overcome. One important aspect of Functional mathematics teaching is to ensure that learners develop the necessary process skills of representing, analysing and interpreting. At Level 2, learners should select the methods and procedures and adopt an organised approach to the task. The teacher may provide guidance, but learners should make their own decisions about finding the solutions to the task. The inclusion of Apply the skills in the Teacher s Notes for each section, aims to provide real-life scenarios to encourage application of the skills that have been practised. To make the most of them, talk through how the tasks require the use of the skills developed within the section. The tasks can be undertaken as small-group activities so that the findings from each group can be compared and discussed in a whole-group activity. The scenarios can be extended and developed according to the abilities and needs of the learners. As part of the discussion, learners should identify other real-life situations where the skills may be useful. Published by Pearson Education, Edinburgh Gate, Harlow CM20 2JE Pearson Education 2008 This material may be used only within the Edexcel pilot centre that has retrieved it. It may be desk printed and/or photocopied for use by learners within that institution. All rights are otherwise reserved and no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanic, photocopying, recording or otherwise without either the prior written permission of the Publishers or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6 10 Kirby Street, London EC1N 8TS. First published Typeset by Oxford Designers & Illustrators, Oxford Draft for Pilot Functional Maths Level 2 Chapter 5 Pearson Education 2008

3 Working with shape and space 5 H Working with perimeter, area, volume and nets You should already know how to: work out the perimeters of simple shapes work out the areas of rectangles work out volumes of simple solids, such as cuboids solve problems, using the mathematical properties of regular 2-D shapes draw 2-D shapes in different orientations tesselate 2-D shapes. By the end of this section you will know how to: find perimeters and areas of regular shapes find areas of composite shapes find volumes of regular shapes solve problems in three dimensions use 2-D representations of 3-D objects. 1 Perimeter Learn the skill The perimeter of a shape is the total length of its boundary. For a rectangle, the perimeter, P, is given by the formula: P = 2(l + w) where l is the length and w is the width. The perimeter of a circle is called its circumference. The circumference, C, of a circle can be written in two ways: C = πd where d = diameter C = 2πr where r = radius Tip π is a special number, equal to the ratio of the circumference of a circle to its diameter. π is an irrational number, which means it cannot be written as a fraction. π is approximately equal to The π key on your calculator gives π to more places of decimals Pearson Education 2008 Functional Maths Level 2 Chapter 5 page 75 Draft for Pilot

4 Example 1: A circular pond, 3.6 metres in diameter, has a fence around it, at a constant distance of 0.6 metres from the edge. Find the length of the fence. You first need to find the radius of the outer circle which is dotted in the diagram. The diameter of the pond is 3.6 metres, so the radius is metres = 1.8 metres. This means the radius of the outer circle is = 2.4 m. Circumference = 2πr, so the length of the fence is 2 x π x 2.4. Using the π key on your calculator gives metres. Your answer can only be as accurate as the information you are given. As the lengths are given to 0.1 m, the length of the fence should be given as 15.1 metres. Answer: 15.1 metres Try the skill 1. A cake shop sells birthday cakes that are 20 cm in diameter. What is the shortest length of ribbon that would fit round the outside of the cake? 2. The plan shows the dimensions of an L-shaped sitting room. The house owner wants to buy skirting board to go around the edge of the room, leaving gaps at the doors. What is the shortest length of skirting board he can buy? 3. A semicircular window has a diameter of 1.6 m. The window frame is made of plastic strips along the outside edge. What is the total length of the plastic strip around the window frame? 4. A lawn has the shape of a rectangle with one semicircular end. There is concrete edging around the outside of the lawn. What is the length of the concrete edging? Draft for Pilot Functional Maths Level 2 Chapter 5 page 76 Pearson Education 2008

5 2 Area Working with shape and space 5 Learn the skill The area of a shape is a measure of the amount of space it covers. For a circle the area, A, is given by the formula: A = πr 2, where r is the radius. Tip Metric units of area are mm 2, cm 2, m 2 and km 2. Example 1: The diameter of a dart board is 45 centimetres. What is the area of the dart board? The radius of the dart board is 45 2 = 22.5 cm. Area = πr 2 = π x = cm 2 Answer 1590 m 2 Remember Follow the BIDMAS rule and work out r 2 first. r 2 means r r. You work out the area of a composite shape by splitting it into simple shapes. Example 2: This kitchen floor is to be covered in cushioned vinyl. What area of cushioned vinyl is needed? Split the L-shaped room into two rectangles A and B. Area of A Area of B = = 2.5 (7 4.5) = 22.5 m 2 = = 6.25 m 2 Total area = = m 2 Answer: m 2 Example 3: The diagram shows the plan of a patio. The patio is to be paved with square paving slabs with sides of 0.5 metres. How many paving slabs will it take? Work out how many paving slabs would be needed for the full rectangle and then take away the number that would be needed in the cut-out piece. The slabs are 0.5 m long, so two are needed for every metre. For the 10 m width, 20 slabs are needed. For the 6 m length, 12 slabs are needed. Number of slabs for the whole rectangle = = 240. The cut-out piece is 2 m by 2 m. This would take 4 4 = 16 slabs. The total is = 224 paving slabs. Answer: 224 Pearson Education 2008 Functional Maths Level 2 Chapter 5 page 77 Draft for Pilot

6 You sometimes need to find the area of a triangle. The area of a triangle = 1 2 base perpendicular height base 6 cm 5 cm perpendicular height Tip The area of this triangle is 6 5 = 15 cm2 1 2 Try the skill 1. The diagram shows a work surface in a kitchen. a What is the area of the work surface? b The worktop is to be covered with square tiles, each measuring 4 cm by 4 cm. How many tiles are needed to cover the worktop? 2. In the 2006 World Cup, circles of cloth were used to cover the centre circle at the start of each match. The radius of a centre circle is 9.15 m and 12 football pitches were used. Estimate the total area of cloth used. 3. The diagram shows a wall of a room, 4 m wide and 2.5 m high, which is to be painted. The door is 0.9 m wide and 2 m high. What area of wall needs to be painted? 2.5m 4m 4m 2m 4. A sheet of card is 20 centimetres by 30 centimetres. What is the maximum number of circular name badges, of diameter 60 millimetres, that can be cut from this piece of card? 4.5m 0.9m Not drawn to scale 5. The diagram shows the floor plan of an office. What is the area of the floor? 50m 40m Tip Split into a rectangle and a triangle. 40m Not drawn to scale 55m Draft for Pilot Functional Maths Level 2 Chapter 5 page 78 Pearson Education 2008

7 3 Volume Working with shape and space 5 Learn the skill The volume of a 3-D shape is a measure of the amount of space it occupies. The volume of a cuboid is l w h where l = length, w = width and h = height. The volume, V, of a cylinder is: V = πr 2 h where r is the base radius and h is the height. Remember Metric units of volume are mm 3, cm 3, m 3 and km 3. Remember πr 2 h means π r 2 h Follow the BIDMAS rule and work out r 2 first. Example 1: A can of cola has a diameter of 6 cm and a height of 12 cm. What is the volume of the can? The diameter is 6 cm so the radius is 3 cm. Volume = πr 2 h = π = 329 cm 3 Answer: 324 cm 3 Remember 1 litre = cm 3 = ml This means the can will hold 324 ml of liquid. You may need to solve problems in three dimensions. Example 2: A tin of shoe polish is 8 cm in diameter and 2 cm high. The shoe polish must be stored in an upright position. How many tins of shoe polish will fit into a carton that is 40 cm long by 32 cm wide by 10 cm high? The base of the carton is 40 cm by 32 cm. The tins are 8 cm wide. This means that 40 8 = 5 tins will fit along one edge and = 4 tins will fit along the other edge So a total of 5 4 = 20 tins will fit on the bottom of the carton. The carton is 10 cm high, which means 10 2 = 5 tins will fit, one on top of another. The total number of tins in the carton is 20 5 = 100. Answer: 100 Test tip A sketch diagram can help you understand the question: Tip A plan is a view from above. A view from the front is called a front elevation. Pearson Education 2008 Functional Maths Level 2 Chapter 5 page 79 Draft for Pilot

8 Try the skill 1. A cube has sides of length 8 cm. What is the volume of the cube? 2. What is the volume of the recycling box shown in the diagram? 3. A waste bin is in the shape of a cylinder. The diameter of the base is 20 cm and the height is 25 cm. What is the volume of the waste bin? 4. A polytunnel for growing plants has a semi-circular opening. The diameter of the opening is 14 feet and the length is 10 feet. The air inside the polytunnel needs to be heated to grow the plants. What is the volume of air inside the polytunnel in cubic feet? 5. A crate is 24 cm by 18 cm by 15 cm. It is to be packed with boxes that are 8 cm by 6 cm by 5 cm. What is the largest number of boxes that can fit in the crate? 6. A firm makes circular drink mats, of radius 4.5 cm, that are 3 mm thick. They want to produce a rectangular box to hold a pile of 12 mats. What are the minimum dimensions of the box? Draft for Pilot Functional Maths Level 2 Chapter 5 page 80 Pearson Education 2008

9 Learn the skill Three dimensional shapes have edges, vertices, (corners) and faces. You should familiarize yourself with the following 3-D shapes and the number of faces, edges and vertices. Working with shape and space D representations of 3-D objects cube cuboid cylinder 3-D shape Number of faces Number of edges Number of vertices square-based pyramid triangular prism A shape which can be folded up to form a 3-D shape is called a net. The following are examples of nets for common 3-D shapes. Try the skill 1. Draw a net for a cylinder. 2. Draw a net for a triangular based pyramid. a how many faces, edges and vertices does a triangular based pyramid have? 3. Draw a net for a cube with sides of length 4 centimetres. a what is the total area of your net? b what is the total length of the edges of the cube? 4. Complete the following table: 3-D shape Shape of faces cube cuboid cylinder square based pyramid triangular prism Pearson Education 2008 Functional Maths Level 2 Chapter 5 page 81 Draft for Pilot

10 5 Remember what you have learned Learn the skill The of a shape is the total length of its boundary. The perimeter of a circle is called its. The of a shape is the amount of space it covers. The of a 3-D shape is the amount of space it occupies. You should know these formulae: of a = πd or 2πr of a = length width Use the skill of a = 1 2 base perpendicular height of a = πr 2 of a = length width height of a = πr 2 h 1. The diagram shows the floor plan of an office. What is the area of the floor? A 16.5 m 2 B 20 m 2 C 20.5 m 2 D 22 m 2 2. The diagram shows a running track made up of a rectangle with two semicircular ends. What is the total length around the outside edge of the running track? A B C D 294 m 326 m 389 m 577 m 3. What is the total area of the running track? A 6000 m 2 B 6296 m 2 C 8827 m 2 D m 2 Draft for Pilot Functional Maths Level 2 Chapter 5 page 82 Pearson Education 2008

11 Working with shape and space 5 4. A cylindrical water butt has a diameter of 50 cm and is 80 cm high. What is the maximum amount of water it can hold? A B C D 15.7 litres 62.8 litres 157 litres 628 litres Remember 1 litre = 1000 cm 3 5. The diagram shows the dimensions of the baskets inside a freezer. 16cm 45cm 48cm Not drawn to scale 48cm 54cm The baskets are packed with blocks of ice-cream, in packets with dimensions as shown in the diagram. 7cm 12cm 12cm Not drawn to scale 18cm What is the maximum number of ice-cream blocks that can fit into the basket? 6. Plastic ice cube trays make ice cubes that measure 2 cm by 2 cm by 2 cm. How many ice cubes can be made from 5 litres of water? A 7 B 12 C 14 D 24 A 625 B 833 C 834 D 1250 Pearson Education 2008 Functional Maths Level 2 Chapter 5 page 83 Draft for Pilot

### EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES. Maths Level 2. Chapter 5. Shape and space

Shape and space 5 EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES Maths Level 2 Chapter 5 Shape and space SECTION H 1 Perimeter 2 Area 3 Volume 4 2-D Representations of 3-D Objects 5 Remember what you

### EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 1. Chapter 5. Working with shape and space

EDEXCEL FUNCTIONAL SKILLS PILOT Maths Level 1 Chapter 5 Working with shape and space SECTION H 1 Calculating perimeter 86 2 Calculating area 87 3 Calculating volume 89 4 Angles 91 5 Line symmetry 92 6

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS A solid is a three-dimensional (3D) object, that is, it has length, width and height. One of these dimensions is sometimes called thickness or depth.

### Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 2. SURFACE AREAS OF SOLIDS If you need to know more about plane shapes, areas, perimeters, solids or volumes of solids, please refer to CONNECT: Areas, Perimeters 1. AREAS

### EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES. Maths Level 2. Chapter 2. Working with fractions, decimals and percentages

EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES Maths Level 2 Chapter 2 Working with fractions, decimals and percentages SECTION B Types of fraction 5 2 Using a calculator for fractions 7 Fractions of

### GCSE Revision Notes Mathematics. Volume and Cylinders

GCSE Revision Notes Mathematics Volume and Cylinders irevise.com 2014. All revision notes have been produced by mockness ltd for irevise.com. Email: info@irevise.com Copyrighted material. All rights reserved;

### Fundamentals of Geometry

10A Page 1 10 A Fundamentals of Geometry 1. The perimeter of an object in a plane is the length of its boundary. A circle s perimeter is called its circumference. 2. The area of an object is the amount

### Module: Mathematical Reasoning

Module: Mathematical Reasoning Lesson Title: Using Nets for Finding Surface Area Objectives and Standards Students will: Draw and construct nets for 3-D objects. Determine the surface area of rectangular

### GCSE Exam Questions on Volume Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice.

Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice. Cylindrical glasses of height 10 cm and radius 3 cm are to be filled from the carton. How

### LESSON SUMMARY. Measuring Shapes

LESSON SUMMARY CXC CSEC MATHEMATICS UNIT SIX: Measurement Lesson 11 Measuring Shapes Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1 (Some helpful exercises and page numbers are given

### VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

### Unit 1 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Unit 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Convert 8 yd. to inches. a. 24 in. b. 288 in. c. 44 in. d. 96 in. 2. Convert 114 in. to yards,

### Draft copy. Circles, cylinders and prisms. Circles

12 Circles, cylinders and prisms You are familiar with formulae for area and volume of some plane shapes and solids. In this chapter you will build on what you learnt in Mathematics for Common Entrance

### Maximum and minimum problems. Information sheet. Think about

Maximum and minimum problems This activity is about using graphs to solve some maximum and minimum problems which occur in industry and in working life. The graphs can be drawn using a graphic calculator

### SOLID SHAPES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier

Mathematics Revision Guides Solid Shapes Page 1 of 19 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier SOLID SHAPES Version: 2.1 Date: 10-11-2015 Mathematics Revision Guides Solid

### By the end of this set of exercises, you should be able to:

BASIC GEOMETRIC PROPERTIES By the end of this set of exercises, you should be able to: find the area of a simple composite shape find the volume of a cube or a cuboid find the area and circumference of

### Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object.

Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object. Surface area is the sum of areas of all the faces or sides of a three-dimensional

### CONNECT: Areas, Perimeters

CONNECT: Areas, Perimeters 1. AREAS OF PLANE SHAPES A plane figure or shape is a two-dimensional, flat shape. Here are 3 plane shapes: All of them have two dimensions that we usually call length and width

### AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional)

AREA AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) Area is always measured in units 2 The most basic questions that you will see will involve calculating the area of a square

### Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

### The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- Area = 1 2 D x d CIRCLE.

Revision - Areas Chapter 8 Volumes The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- SQUARE RECTANGE RHOMBUS KITE B dd d D D Area = 2 Area = x B

### 9 Area, Perimeter and Volume

9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right

### Geometry Notes VOLUME AND SURFACE AREA

Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate

### 1 cm 3. 1 cm. 1 cubic centimetre. height or Volume = area of cross-section length length

Volume Many things are made in the shape of a cuboid, such as drink cartons and cereal boxes. This activity is about finding the volumes of cuboids. Information sheet The volume of an object is the amount

### Area of Parallelograms (pages 546 549)

A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

### Exercise 11.1. Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

11 MENSURATION Exercise 11.1 Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area? (a) Side = 60 m (Given) Perimeter of

### Pizza! Pizza! Assessment

Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the

### Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

### Yimin Math Centre. Year 6 Problem Solving Part 2. 2.1 Measurements... 1. 2.2 Practical Exam Questions... 8. 2.3 Quiz... 10. Page: 10 11 12 Total

Year 6 Problem Solving Part 2 Student Name: Grade: Date: Score: Table of Contents 2 Problem Solving Part 2 1 2.1 Measurements....................................... 1 2.2 Practical Exam Questions.................................

### Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

### Grade 7/8 Math Circles Winter D Geometry

1 University of Waterloo Faculty of Mathematics Grade 7/8 Math Circles Winter 2013 3D Geometry Introductory Problem Mary s mom bought a box of 60 cookies for Mary to bring to school. Mary decides to bring

### CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change

### In Problems #1 - #4, find the surface area and volume of each prism.

Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

### CHAPTER 27 AREAS OF COMMON SHAPES

EXERCISE 113 Page 65 CHAPTER 7 AREAS OF COMMON SHAPES 1. Find the angles p and q in the diagram below: p = 180 75 = 105 (interior opposite angles of a parallelogram are equal) q = 180 105 0 = 35. Find

### VOLUME AND SURFACE AREAS OF SOLIDS

VOLUME AND SURFACE AREAS OF SOLIDS Q.1. Find the total surface area and volume of a rectangular solid (cuboid) measuring 1 m by 50 cm by 0.5 m. 50 1 Ans. Length of cuboid l = 1 m, Breadth of cuboid, b

### 16 Circles and Cylinders

16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two

### Perimeter, Area, and Volume

Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the

### Perimeter, Area, and Volume

Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all

### Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

### 5. Surface Area Practice Chapter Test

ID: A Date: / / Name: Block ID: 5. Surface Area Practice Chapter Test Multiple Choice Identify the choice that best completes the statement or answers the question. Choose the best answer. 1. Which combination

### b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit

Area is the number of square units that make up the inside of the shape of 1 of any unit is a square with a side length Jan 29-7:58 AM b = base h = height Jan 29-8:31 AM 1 Example 6 in Jan 29-8:33 AM A

### Measuring Prisms and Cylinders. Suggested Time: 5 Weeks

Measuring Prisms and Cylinders Suggested Time: 5 Weeks Unit Overview Focus and Context In this unit, students will use two-dimensional nets to create threedimensional solids. They will begin to calculate

### SURFACE AREA AND VOLUME

SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has

### Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number

### Formulas for Area Area of Trapezoid

Area of Triangle Formulas for Area Area of Trapezoid Area of Parallelograms Use the formula sheet and what you know about area to solve the following problems. Find the area. 5 feet 6 feet 4 feet 8.5 feet

### Lesson 22. Circumference and Area of a Circle. Circumference. Chapter 2: Perimeter, Area & Volume. Radius and Diameter. Name of Lecturer: Mr. J.

Lesson 22 Chapter 2: Perimeter, Area & Volume Circumference and Area of a Circle Circumference The distance around the edge of a circle (or any curvy shape). It is a kind of perimeter. Radius and Diameter

### DIFFERENTIATION OPTIMIZATION PROBLEMS

DIFFERENTIATION OPTIMIZATION PROBLEMS Question 1 (***) 4cm 64cm figure 1 figure An open bo is to be made out of a rectangular piece of card measuring 64 cm by 4 cm. Figure 1 shows how a square of side

### GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book

GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18

### The teacher gives the student a ruler, shows her the shape below and asks the student to calculate the shape s area.

Complex area Georgia is able to calculate the area of a complex shape by mentally separating the shape into familiar shapes. She is able to use her knowledge of the formula for the area of a rectangle

### 12-2 Surface Areas of Prisms and Cylinders. 1. Find the lateral area of the prism. SOLUTION: ANSWER: in 2

1. Find the lateral area of the prism. 3. The base of the prism is a right triangle with the legs 8 ft and 6 ft long. Use the Pythagorean Theorem to find the length of the hypotenuse of the base. 112.5

### Finding Volume of Rectangular Prisms

MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of three-dimensional composite shapes.

### B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3

45 Volume Surface area measures the area of the two-dimensional boundary of a threedimensional figure; it is the area of the outside surface of a solid. Volume, on the other hand, is a measure of the space

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

### Wednesday 15 January 2014 Morning Time: 2 hours

Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Wednesday 15 January 2014 Morning Time: 2 hours Candidate Number

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

### AREA AND PERIMETER OF COMPLEX PLANE FIGURES

AREA AND PERIMETER OF OMPLEX PLANE FIGURES AREA AND PERIMETER OF POLYGONAL FIGURES DISSETION PRINIPLE: Every polygon can be dissected (or broken up) into triangles (or rectangles), which have no interior

### CALCULATING PERIMETER. WHAT IS PERIMETER? Perimeter is the total length or distance around a figure.

CALCULATING PERIMETER WHAT IS PERIMETER? Perimeter is the total length or distance around a figure. HOW DO WE CALCULATE PERIMETER? The formula one can use to calculate perimeter depends on the type of

### The Area is the width times the height: Area = w h

Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what

### Calculating Area, Perimeter and Volume

Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly

### EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 1. Chapter 3. Working with ratio, proportion and formulae

EDEXCEL FUNCTIONL SKILLS PILOT Maths Level 1 Chapter 3 Working with ratio, proportion and formulae SECTION E 1 Understanding ratios 55 2 Using ratios to find quantities 57 3 Direct proportion 58 4 Using

### PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY

PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY The Student Handout is page 11. Give this page to students as a separate sheet. Area of Circles and Squares Circumference and Perimeters Volume of Cylinders

### Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in

Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in

### Assessing pupils progress in mathematics at Key Stage 3. Year 9 assessment package Shape, space and measures Teacher pack

Assessing pupils progress in mathematics at Key Stage 3 Year 9 assessment package Shape, space and measures Teacher pack Year 9 Shape task: Wrap around and Prismatic Levels ( 3/ )4/5/6 Note that for classes

### Solids. Objective A: Volume of a Solids

Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular

### Tallahassee Community College PERIMETER

Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides

### Surface Area Quick Review: CH 5

I hope you had an exceptional Christmas Break.. Now it's time to learn some more math!! :) Surface Area Quick Review: CH 5 Find the surface area of each of these shapes: 8 cm 12 cm 4cm 11 cm 7 cm Find

### Q1. Here is a flag. Calculate the area of the shaded cross. Q2. The diagram shows a right-angled triangle inside a circle.

Q1. Here is a flag. Calculate the area of the shaded cross. 2 marks Q2. The diagram shows a right-angled triangle inside a circle. The circle has a radius of 5 centimetres. Calculate the area of the triangle.

### Solving Geometric Applications

1.8 Solving Geometric Applications 1.8 OBJECTIVES 1. Find a perimeter 2. Solve applications that involve perimeter 3. Find the area of a rectangular figure 4. Apply area formulas 5. Apply volume formulas

### What You ll Learn. Why It s Important

These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why

### Finding Areas of Shapes

Baking Math Learning Centre Finding Areas of Shapes Bakers often need to know the area of a shape in order to plan their work. A few formulas are required to find area. First, some vocabulary: Diameter

### Revision Notes Adult Numeracy Level 2

Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands

### Week #15 - Word Problems & Differential Equations Section 8.1

Week #15 - Word Problems & Differential Equations Section 8.1 From Calculus, Single Variable by Hughes-Hallett, Gleason, McCallum et. al. Copyright 25 by John Wiley & Sons, Inc. This material is used by

### I Perimeter, Area, Learning Goals 304

U N I T Perimeter, Area, Greeting cards come in a variety of shapes and sizes. You can buy a greeting card for just about any occasion! Learning Goals measure and calculate perimeter estimate, measure,

### Dŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet

Dŵr y Felin Comprehensive School Perimeter, Area and Volume Methodology Booklet Perimeter, Area & Volume Perimeters, Area & Volume are key concepts within the Shape & Space aspect of Mathematics. Pupils

### Surface Area of Prisms

Surface Area of Prisms Find the Surface Area for each prism. Show all of your work. Surface Area: The sum of the areas of all the surface (faces) if the threedimensional figure. Rectangular Prism: A prism

### Let s find the volume of this cone. Again we can leave our answer in terms of pi or use 3.14 to approximate the answer.

8.5 Volume of Rounded Objects A basic definition of volume is how much space an object takes up. Since this is a three-dimensional measurement, the unit is usually cubed. For example, we might talk about

### ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates

### Math 2201 Chapter 8 Review

Olga Math 2201 Chapter 8 Review Multiple Choice 1. A 2 L carton of milk costs \$3.26. What is the unit rate? a. \$0.83/500 ml b. \$3.27/2 L c. \$0.61/L d. \$1.63/L 2.. drove 346 km and used up 28.7 L of gas.

### Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.

Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism

### Area, Perimeter, Volume and Pythagorean Theorem Assessment

Area, Perimeter, Volume and Pythagorean Theorem Assessment Name: 1. Find the perimeter of a right triangle with legs measuring 10 inches and 24 inches a. 34 inches b. 60 inches c. 120 inches d. 240 inches

### Surface Areas of Prisms and Cylinders

12.2 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G.10.B G.11.C Surface Areas of Prisms and Cylinders Essential Question How can you find te surface area of a prism or a cylinder? Recall tat te surface area of

### Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional

### Build your skills: Perimeter and area Part 1. Working out the perimeter and area of different shapes

Working out the perimeter and area of different shapes This task has two parts. Part 1 In this part, you can brush up your skills and find out about perimeter and area. Part 2 In the second part, you can

### EDEXCEL FUNCTIONAL SKILLS PILOT

EDEXCEL FUNCTIONAL SKILLS PILOT Maths Level 2 Chapter 4 Working with measures SECTION G 1 Time 62 2 Temperature 64 3 Length 65 4 Weight 66 5 Capacity 67 6 Conversion between metric units 68 7 Conversion

### Right Prisms Let s find the surface area of the right prism given in Figure 44.1. Figure 44.1

44 Surface Area The surface area of a space figure is the total area of all the faces of the figure. In this section, we discuss the surface areas of some of the space figures introduced in Section 41.

### Volume of Pyramids and Cones

Volume of Pyramids and Cones Objective To provide experiences with investigating the relationships between the volumes of geometric solids. www.everydaymathonline.com epresentations etoolkit Algorithms

### MATH STUDENT BOOK. 6th Grade Unit 8

MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF

### The GED math test gives you a page of math formulas that

Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

### Surface Area. Explore Symmetry and Surface Area. measure 1 cm by 4 cm by 2 cm. Six boxes are wrapped and shipped together.

1.3 Surface Area Focus on After this lesson, you will be able to determine the area of overlap in composite 3-D objects find the surface area for composite 3-D objects solve problems involving surface

### EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 2. Chapter 3. Working with ratio, proportion, formulae and equations

EDEXCEL FUNCTIONL SKILLS PILOT Maths Level 2 Chapter 3 Working with ratio, proportion, formulae and equations SECTION E 1 Writing a ratio 45 2 Scaling quantities up or down 47 3 Calculations with ratio

### Mensuration. The shapes covered are 2-dimensional square circle sector 3-dimensional cube cylinder sphere

Mensuration This a mixed selection of worksheets on a standard mathematical topic. A glance at each will be sufficient to determine its purpose and usefulness in any given situation. These notes are intended

### 1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?

Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is

### Basic Math for the Small Public Water Systems Operator

Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the

### Calculating the Surface Area of a Cylinder

Calculating the Measurement Calculating The Surface Area of a Cylinder PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping

### 2nd Semester Geometry Final Exam Review

Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular

### SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid

Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.

### Activity Set 4. Trainer Guide

Geometry and Measurement of Solid Figures Activity Set 4 Trainer Guide Mid_SGe_04_TG Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF SOLID FIGURES