Lesson 3: Area. Selected Content Standards. Translating Content Standards into Instruction


 Stephen Hood
 2 years ago
 Views:
Transcription
1 Lesson 3: Area Selected Content Standards Benchmark Assessed: M.3 Estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures, surface area and volume of solids presented in realworld situations) Lesson Focus: This lesson is intended as an introductory lesson to the concept of area. Students should know by the end of this lesson the following information: The conceptual difference between area and perimeter How to use various methods to determine area of plane figures (including using a ruler, grid paper, and calculation) Use of scale in a scale drawing as it applies to area GEE 21 Connection The skills that will be addressed in this lesson include the following: Understand the concept of area Understand what a square unit is and how it is different from a linear measure Find the area of plane figures using grids Calculate the area of plane figures shown in diagrams or described in realworld terms Understand the connection between area of rectangles and triangles Understand numerical relationships among units within each system (customary and metric) Compare approximate relationships between systems in terms of intuitive reference points Translating Content Standards into Instruction A. The first goal of this lesson is to help students to understand what area is and how it is different from perimeter. 1. The first thing to do is to get students to understand what a SURFACE is something that we can cover or paint (such as floors, tabletops, covering of a ball, etc.) 2. We want students to associate the word SURFACE with the word AREA. Explain to students that The amount of surface that an object has is called its AREA. 3. Emphasize the difference between a length (show students a string and explain that length has no width to it it is onedimensional) and an area (show students a rectangular book and explain that the surface has both length and width it is twodimensional). 4. Point out that perimeter (which is a length) and area have two completely different types of units. This will be emphasized throughout the lesson. 20
2 5. Hand out Student Worksheet #1 to students, and ask them which figure they think has the most area associated with it. Show them a sticky tab (this worksheet was designed with the 2 x 3 yellow sticky notes in mind if you can, provide all the students with a set of four each) and ask students to estimate how many of the sticky notes it would take to cover each of the figures on the worksheet. Once students have made their estimates, have students actually use the sticky notes that were provided to cover the figures completely. Students may be surprised to find that all of the figures have the same area. Talk about the results with the students. 6. Have students estimate how many sheets of paper (8 ½ x 11 ) it would take to cover the blackboard in your room. Have each group come to the front of the class and write their estimates on the board. After all groups have made their estimates, talk about the strategies students came up with to get their answers. Model for students using strategies which students recommended to determine how many sheets it would take (Of course, you do not want to cover the entire board we want students to see that if we know how many rows of paper and how many in each row, we could multiply to find the answer). Compare the actual answer with estimates given by the students. B. Have students do Student Worksheet #2 in groups. During this activity, students will make a square foot and a square yard. The teacher should provide students with two large sheets of bulletin board paper in order to do so. After all students have completed the worksheet, go over the results with the class. 1. Stress the fact that area is in square units. Make sure students understand why squares are used rather than circles, etc. 2. Emphasize that we use our standard units of square centimeters, square inches, square feet, square yards, etc. when talking about units for area. Again, stress the difference between area and perimeter. 3. Make sure that students see what a square foot and square yard are and their relationship to one another. Students should see that in every square foot there are 144 square inches. They should see that it takes 9 sq. ft. to make 1 sq. yd. C. In this part of the lesson, lead students into understanding how the area of a rectangle can be found by calculation, that the area of a triangle is ½ the area of the rectangle that it comes from, and that the area of irregular figures can be found by finding the area of the individual rectangular and triangular areas that make it up (all we have to do is add the individual areas to get the total area). 1. Help students understand that unit squares do not have to be drawn on a rectangle to determine the area of the rectangle. To find the area of a rectangle, measure the length (the number of squares that will fit in each row), measure the width (the number of rows), and use this information to determine how many square units it would take to cover the rectangle. Thus, to calculate the area in square centimeters, square inches, or whatever unit is being used, multiply length by width. 2. Help students understand that measuring the length and width of a rectangle, and multiplying the two linear measures results in a new unit, called a square unit. Multiplying centimeters by centimeters results in a new unit called a 21
3 square centimeter. Multiplying inches by inches, we get square inches. Multiplying feet by feet, results in square feet. 3. Present the following problems to students and talk to students about each one. (a) Mrs. Peterson has a rectangular outdoor workshop that is 20 feet wide and 45 feet long. She wants to buy some carpeting to lay across the entire floor of the building. How much carpeting will she need? (b) Mrs. Peterson wants to buy some molding to put all around the edge of the building. How much molding will she need? (c) In teams of two, use your ruler to find the area of your rectangular desk (everyone should use the same size desk). Use inches as your unit of measure. What is the area? (d) Find the area and perimeter of the figure shown. Area = Perimeter= 5 meters 6 meters 2 meters 12 meters 4. Have students work in small groups on Student Worksheet #3, provided for this lesson. After students have finished the worksheet, go over all work and talk about anything which may have given students difficulties. No doubt, there will be some discrepancies in measurement for some of the items remind the students that measurement is not exact. 5. The topic of finding the area of triangles is presented on the worksheet. The teacher may have to get more in depth with the class as to the relationship between the area of a triangle and rectangle. D. Students will use a scale drawing of a basketball court and use the drawing to determine information from it. 1. Have students do the scale drawing activity, Student Worksheet #4, provided with the lesson. 2. Talk to students about finding areas of circles. This information is necessary for them to complete the activity. 3. As an enrichment activity, you may want the students to make measurements of an actual basketball court in the school gym if possible. GEE 21 Connection On the GEE 21 test, students may be required to determine the area of various geometric shapes (including areas of rectangles, triangles, circles, and composite figures). Students may also be required to apply the concept of area in a reallife applications in which the word area may never be asked for directly (such as finding 22
4 the amount of carpeting required for a room, etc.). Converting within units and from system to system may also be tested. Sources of Evidence about Student Learning A. Have students make measurements of rooms or halls around the school in order to calculate the areas. B. Have students do student worksheets in groups provided with the lesson and have students explain their work for the class. GEE 21 Connection See attachment at the end of the Lessons for sample questions related to the GEE 21. Attributes of Student Work at the GotIt level A. When students are making their measurements for the items that are in the room or around the school, make sure that all students are within an acceptable range in their measurements. Any student or group that is outside the acceptable range should be required to remeasure the item to make sure that the error being made is corrected. B. When going over student work on the provided worksheets, allow students to work alone first, then provide time to allow for students to compare their answers in groups. Let the students talk about how they got their answers and if there were any discrepancies between group members, have the members explain what they did to clear up any differences. Make sure that all students are within an acceptable range when writing down a measurement, but all students must understand that measurement is not an exact science. It is an approximation within a certain degree of accuracy, depending on the measurement tool being used. 23
5 Lesson 3: Area Student Worksheet #1 Directions: Use the figures below to do this activity. First, make estimates of how many sticky tabs it would take to cover each figure. After you make your estimates, actually take sticky tabs and try to cover the figure to see how close your estimate is. The sticky tabs cannot overlap. Figure 1: Estimate Actual: Figure 2: Estimate: Actual: Figure 3: Estimate: Actual: 24
6 Lesson 3: Area Student Worksheet #2 1. Which of the figures below would you say has the most area associated with it? Why? 2. If you were trying to cover the floor in the classroom, which figure below do you think it would be easier to use to cover the entire space without any gaps? Explain why? 3. Area is commonly found using square units. Why do you think that is? 4. How many square units,,does it take to cover the entire figure shown? 5. Use the figure below to answer the following questions. (a) What is the area of the figure? (b) What is the perimeter of the figure? (c) What is the length of the figure? width? (d) What multiplication fact does the figure model? x (e) If you multiply the length and width of the figure, what do you notice in connection with the area? 25
7 6. Use the grid at the right to draw a figure that has an area of 4 square units with a perimeter of 10 units. 7. Mr. Connor is laying out square tiles on his kitchen floor. So far he has laid out the squares shown. Determine how many squares it would take to cover the entire floor. If it took him 14 minutes to lay the tiles shown here, how long would it take to do the rest of the floor? Explain how you got your answer. 8. Shown below are two squares. Answer the following questions. Square #1 Square #2 (a) Measure the sides of square #1 with a centimeter ruler. What is the length of each side of the square? (b) Measure the sides of square #2 with an inch ruler. What is the length of each side of the square? (c) One of the squares shown is called a square centimeter and one of the square is called a square inch. Which name goes with which square? Explain why you chose your answer. (d) Using the figure shown, determine how many square centimeters it would take to cover the figure. 26
8 (e) Using the figure shown, determine how many square inches it would take to cover the below. (f) Look at the figure shown to the right do you think it would take more square centimeters or square inches to cover it? Explain why. 9. Using large sheets of bulletin board paper that you will get from your teacher, make a square foot and a square yard. Using the models you make, determine the following: (a) How many square feet does it take to make a square yard? (b) How many square inches does it take to make a square foot? (c) How many square inches will it take to cover a square yard? Show how you got your answer to this. 10. Explain in your own words what is different about perimeter and area. 27
9 Lesson 3: Area Student Worksheet #3 1. This is a square centimeter. (a) Use your centimeter ruler to find the length of each side of the square centimeter. What is the length of each side? (b) What is the perimeter of the square centimeter? (c) About how many of these square centimeters would fit inside this rectangle? What is the area in square centimeters of the rectangle? 2. This is a square inch. (a) Using your inch ruler, measure the sides of the square inch. What is the length of each side? (b) What is the perimeter of the square inch? (c) About how many of the square inches would fit inside this rectangle. What is the area of the rectangle? Measure each side of the rectangle to the nearest inch. What is the length of the rectangle? What is the width? If you multiply the length by the width, what do you get? 3. What is the area and perimeter of the rectangle shown below: Area = Perimeter = 6.25 ft ft 28
10 4. Using your ruler, measure the length and width of this rectangle. Use whole centimeters as the unit. Put dots along the length and width to mark each centimeter. Width: cm Length: cm (a) Remember this is what a square centimeter looks like. (b) How many of these square centimeters could be lined up in one row across the bottom of the rectangle? (c) How many rows of square centimeters would fit in the rectangle? (d) How many square centimeters all together will fit inside the rectangle? How did you figure this out? (e) What is the area of the rectangle in square centimeters? (f) Do you have to have all of the squares already drawn on a rectangle to figure out the area? Why or why not? 5. Using what you learned in problem 4, calculate the area of the rectangle here in square centimeters. 29
11 6. Working in teams of two or three, find the following: (a) Find the perimeter of the classroom floor in inches, feet, yards, millimeters, centimeters, and meters. The PERIMETER of the room is: inches or feet or yards millimeters or centimeters or meters (b) Find the area of the classroom floor in square centimeters, square meters, square inches, square feet, and square yards. The AREA of the room is: sq. centimeters or sq. meters sq. in. or sq. ft. or sq. yd. 7. Below is a triangle located inside a rectangle. Using what you have learned about finding areas of rectangles, answer the given questions. (a) If the area of the rectangle is 20 square feet, what would you say the area of the triangle is? Explain how you know. (b) Using your centimeter ruler, calculate the area of the rectangle in square centimeters. What do you think the area of the triangle is? Explain what you would do if you had to find the area of any triangle. 30
12 8. Julie wants to build an exercise pen for her pet rabbit. She has 36 feet of fencing and 4 metal posts to build a rectangular enclosure. She wants to carefully plan her project, measuring in units of whole feet. Find all the possible ways that Julie could build her pen and have a perimeter of 36 feet and whole units for length and width. Fill in the table below and find the area of each case. Length (ft.) Width (ft.) Perimeter (ft.) Area (sq. ft.) (a) What dimensions (length and width) for the pen should Julie build for her rabbit if she wants the largest possible area? (b) What would be a benefit of building the pen in one of the other ways (the pen without the most area)? 9. Carlos bought some land. The scale drawing below shows the layout of his land. What is the total area (approximately) in square feet, for the land that he bought? (Scale: 1 cm = 30 feet) 31
13 Lesson 3: Area Student Worksheet #4 Directions: Below is a scale drawing of a basketball court. Use the scale drawing to answer the given questions. Jump Area Free Throw Lane ft 19 ft 6 ft radius Circular Outer Jump Area 2 ft inner radius The Arc What is the total area of the basketball court? 2. What is the area of the free throw lane? 3. What is the area of the Jump Area? 4. What is the area of the Circular Outer Jump Area? 5. What is the area of The Arc? 6. What is the perimeter of the basketball court? 7. How many times would you have to run around the basketball court if you wanted to run a mile? Show or explain how you got your answer. 32
14 Lesson 3 Area Answer Sheet Student Worksheet #1 *The answers here depend on the size of the sticky tabs used. Use answers based upon their own particular classes. However, it should be noted that all of the figures have the EXACT SAME AREA. Student Worksheet #2 1. The rectangle has the most area associated with it (it has the most surface). 2. It would be easier to cover the floor with the squares because there would be no empty spaces in the flooring. 3. Area is found in square units because other units would leave spaces, and would not entirely cover the object square units 5. (a) 24 square units (b) 20 units (c) l = 6 units, w = 4 units (or vice versa) (d) 4 x 6 or 6 x 4 (d) You get the area of the figure 6. Answers may vary. 7. It would take him 80 squares to cover the entire floor; every 14 minutes he can lay 26 tiles. In another 14 minutes he would lay an additional 26 tiles (52 so far). In another 14 minutes he would lay an additional 26 tiles (78 so far) So he would need to lay another two tiles at that point (each tile takes about thirty seconds to lay so this is an additional minute of time). Altogether, it would take an about an additional 29 minutes, for a total time to lay the floor of about 43 minutes. (This is of course one way of doing this problem through proportional reasoning). 8. (a) 1 cm (b) 1 inch (c) Square # 1 is the square centimeter; Square #2 is square the square inch (d) 8 square centimeters (e) 4 square inches (f) It would take more square centimeters to cover it because they are smaller than the square inches. 9. All of these answers should be found by actually making the square foot and square yard. DO NOT just show students the answers on a chart. (a) 9 square feet = 1 square yard (b) 144 square inches = 1 square foot (c) 9x144 sq in = 1296 square inches 10. Perimeter is a linear measurement (1 dimension) and is the total distance around a figure. Area is a measure of the amount of surface an object has. Its units are totally different than that of perimeter called square units (2 dimensions). 33
15 Lesson 3: Area Answer Sheet Student Worksheet #3 1. (a) 1 cm (b) 4 cm (c) Since it would take 18 square centimeters to fit inside the figure, this is also the area associated with the figure. 2. (a) 1 in (b) 4 in (c) 9 sq in; 9 sq in; length = 3 in, width = 3 in; 9 sq in 3. Area is about 147 sq ft; Perimeter = 59.5 ft 4. length = 8 cm; width = 6 cm (b) 8 (c) 6 (d) 48 square centimeters (e) 48 sq cm (f) You do not have to have all of the squares drawn because you can just measure each side of the rectangle and multiply the two numbers to find the area sq cm 6. Answers will vary from class to class. 7. (a) The area of the triangle is ½ the area of the rectangle, so area of triangle is 10 square feet. (b) The area of the rectangle is 15 sq cm, so the area of the triangle is ½ this amount, or 7.5 sq cm 8. Length (ft) Width (ft) Perimeter (ft) Area (sq ft) 1 ft 17 ft 36 ft 17 sq ft 2 ft 16 ft 36 ft 32 sq ft 3 ft 15 ft 36 ft 45 sq ft 4 ft 14 ft 36 ft 56 sq ft 5 ft 13 ft 36 ft 65 sq ft 6 ft 12 ft 36 ft 72 sq ft 7 ft 11 f. 36 ft 77 sq ft 8 ft 10 ft 36 ft 80 sq ft 9 ft 9 ft 36 ft 81 sq ft 10 ft 8 ft 36 ft 80 sq ft Starts to repeat (a) The dimensions which result in the largest possible area are 9ft by 9 ft. (b) Maybe you wanted a longer pen for the rabbit to be able to run a longer distance without having to turn around, or maybe the space which the yard has won t permit the length or width associated with one of the other measures. 8. The approximate area is 28,800 sq ft. Student Worksheet # sq ft sq ft 3. About 12 sq ft 4. About 96 sq ft 5. About 54 sq ft ft is about 18 times around the gym floor to make a mile (It s actually a little more than that.) 34
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
More informationArea and Perimeter Teaching Suggestions:
Area and Perimeter Teaching Suggestions: Use math definition posters to discuss: dimension, twodimensional shapes, length, width, perimeter and area. Brainstorm examples of each, and develop vocabulary
More informationGrade 4 Mathematics Measurement: Lesson 2
Grade 4 Mathematics Measurement: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside
More informationPerimeter, 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
More informationLesson 4: Surface Area
Lesson 4: Surface Area Selected Content Standards Benchmark Assessed M.3 Estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures,
More informationNumber Models for Area
Number Models for Area Objectives To guide children as they develop the concept of area by measuring with identical squares; and to demonstrate how to calculate the area of rectangles using number models.
More informationWHAT IS AREA? CFE 3319V
WHAT IS AREA? CFE 3319V OPEN CAPTIONED ALLIED VIDEO CORPORATION 1992 Grade Levels: 59 17 minutes DESCRIPTION What is area? Lesson One defines and clarifies what area means and also teaches the concept
More informationLesson 4: Surface Area
Lesson 4: Surface Area Selected Content Standards Benchmarks Addressed: M1M Applying the concepts of length, area, surface area, volume, capacity, weight, mass, money, time, temperature, and rate to
More informationArea LongTerm Memory Review Review 1
Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter
More information4. Molly walked all the way around the edge of her yard. The distance she walked is the yard's
Name: Date: 1. Derrius has 24 feet of fencing to use for a rectangular dog pen. Which dimensions would give him the most room (area) for his dog? A. 1 foot by 11 feet B. 3 feet by 9 feet C. 4 feet by 8
More informationAssessment Management
Areas of Rectangles Objective To reinforce students understanding of area concepts and units of area. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family
More informationLESSON 10 GEOMETRY I: PERIMETER & AREA
LESSON 10 GEOMETRY I: PERIMETER & AREA INTRODUCTION Geometry is the study of shapes and space. In this lesson, we will focus on shapes and measures of onedimension and twodimensions. In the next lesson,
More informationGrade 5 supplement. Set D1 Measurement: Area & Perimeter. Includes. Skills & Concepts
Grade 5 supplement Set D1 Measurement: Area & Perimeter Includes Activity 1: Measuring Area D1.1 Activity 2: Measuring Perimeter D1.5 Activity 3: The Ladybugs Garden D1.9 Activity 4: Hexarights D1.15 Independent
More informationFree PreAlgebra Lesson 3 page 1. Example: Find the perimeter of each figure. Assume measurements are in centimeters.
Free PreAlgebra Lesson 3 page 1 Lesson 3 Perimeter and Area Enclose a flat space; say with a fence or wall. The length of the fence (how far you walk around the edge) is the perimeter, and the measure
More informationRectangle Square Triangle
HFCC Math Lab Beginning Algebra  15 PERIMETER WORD PROBLEMS The perimeter of a plane geometric figure is the sum of the lengths of its sides. In this handout, we will deal with perimeter problems involving
More informationSolving 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
More informationPerimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Teacher Materials
Lesson 1 Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Teacher Materials Perimeter: The Line Club T1: Before class: Copy one set of student pages for each student in the
More informationBuilding Perimeter. Measurement and Data. Objective. Common Core State Standards Talk About It. Solve It. More Ideas. Formative Assessment
7 Building Perimeter Objective Having a student measure the perimeter of a shape is the first step in understanding the concept of perimeter. The next step is requiring students to apply their knowledge
More informationPerimeter. 14ft. 5ft. 11ft.
Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine
More informationCustomary Units of Length
Customary Units of Length R 91 Customary Units of Length 12 inches (in.) 1 foot (ft) 36 in. 3 ft 1 yard (yd) 5,280 ft 1,760 yd 1 mile (mi) How to change between one customary unit of length and another:
More informationMeasure the side of the figure to the nearest centimeter. Then find the perimeter. 1.
Measure the side of the figure to the nearest centimeter. Then find the perimeter. 1. a. 3 cm b. 6 cm c. 8 cm d. 9 cm 2. a. 4 cm b. 6 cm c. 8 cm d. 10 cm Powered by Cognero Page 1 Find the perimeter of
More informationFormulas 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
More information3 rd Grade Mathematics
3 rd Grade Mathematics Unit #3 : Relating Area to Multiplication and Division Pacing: 29 Days Unit Overview In this unit, students extend their understanding of multiplication and division (Unit 2) by
More informationMeasurement: Converting Distances
Measurement: Converting Distances Measuring Distances Measuring distances is done by measuring length. You may use a different system to measure length differently than other places in the world. This
More informationLesson 1: Linear Measurement
Lesson 1: Linear Selected Content Standards Benchmarks Addressed: M1M Applying the concepts of length, area, surface area, volume, capacity, weight, mass, money, time, temperature, and rate to realworld
More informationDemystifying Surface Area and Volume Teachers Edition
Demystifying Surface and Volume Teachers Edition These constructions and worksheets can be done in pairs, small groups or individually. Also, may use as guided notes and done together with teacher. CYLINDER
More information93. Area of Irregular Figures Going Deeper EXPLORE. Essential question: How do you find the area of composite figures? Area of a Composite Figure
Name Class Date 93 1 Area of Irregular Figures Going Deeper Essential question: How do you find the area of composite figures? CC.7.G.6 EXPLORE Area of a Composite Figure video tutor Aaron was plotting
More informationArea and Perimeter. Name: Class: Date: Short Answer
Name: Class: Date: ID: A Area and Perimeter Short Answer 1. The squares on this grid are 1 centimeter long and 1 centimeter wide. Outline two different figures with an area of 12 square centimeters and
More informationPerimeter, 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
More informationMATH 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
More informationChapter 4: The Concept of Area
Chapter 4: The Concept of Area Defining Area The area of a shape or object can be defined in everyday words as the amount of stuff needed to cover the shape. Common uses of the concept of area are finding
More informationMeasure Up. Label each ruler with the correct measurements. The rulers are in inches.
Student Activity 1 Name Measure Up Label each ruler with the correct measurements. The rulers are in inches. Use a ruler and draw a line that is: 4. 3 1/4 inches 5. 2 1/8 inches Be Precise Student Materials
More informationGeorgia Department of Education Common Core Georgia Performance Standards Framework Fourth Grade Mathematics Unit
Fourth Grade Mathematics Unit Constructing Task: Area and Perimeter Adapted from Fixed Perimeters and Fixed Areas in Teaching StudentCentered MATHEMATICS Grades 35 by John Van de Walle and LouAnn Lovin.
More information910. NCSC Sample Instructional Unit. Investigating Measurement in the Real World. Mathematics: Measurement
Mathematics: Measurement NCSC Sample Instructional Unit 910 Investigating Measurement in the Real World The contents of this product were developed under a grant from the Department of Education (PR/Award
More informationUnit 5 Geometry. Using imperial, metric and conversions when necessary. Maximum area for a given perimeter
Unit 5 Geometry BIG PICTURE MAP 4C Foundations for College Mathematics Students will: Understand the relationships between imperial and metric units Consolidate understanding of perimeter, area, surface
More informationKeyTrain Level 5. For. Level 5. Published by SAI Interactive, Inc., 340 Frazier Avenue, Chattanooga, TN
Introduction For Level 5 Published by SAI Interactive, Inc., 340 Frazier Avenue, Chattanooga, TN 37405. Copyright 2000 by SAI Interactive, Inc. KeyTrain is a registered trademark of SAI Interactive, Inc.
More informationMATH 110 Landscape Horticulture Worksheet #4
MATH 110 Landscape Horticulture Worksheet #4 Ratios The math name for a fraction is ratio. It is just a comparison of one quantity with another quantity that is similar. As a Landscape Horticulturist,
More informationMATH STUDENT BOOK. 7th Grade Unit 9
MATH STUDENT BOOK 7th Grade Unit 9 Unit 9 Measurement and Area Math 709 Measurement and Area Introduction 3 1. Perimeter 5 Perimeter 5 Circumference 11 Composite Figures 16 Self Test 1: Perimeter 24 2.
More informationKeyTrain Competencies Level 6
KeyTrain Competencies Level 6 Reduce Fractions 20 5 = 4 24 2 = 12 2 = 6 2 = 3 25 5 = 5 40 2 = 20 2 = 10 2 = 5 OR 24 4 = 6 2 = 3 40 4 = 10 2 = 5 To reduce fractions, you must divide the top number of the
More informationSigns, Signs, Every Place There Are Signs! Area of Regular Polygons p. 171 Boundary Lines Area of Parallelograms and Triangles p.
C H A P T E R Perimeter and Area Regatta is another word for boat race. In sailing regattas, sailboats compete on courses defined by marks or buoys. These courses often start and end at the same mark,
More informationMetric Units of Length
7.2 Metric Units of Length 7.2 OBJECTIVES. Know the meaning of metric prefixes 2. Estimate metric units of length 3. Convert metric units of length NOTE Even in the United States, the metric system is
More informationGrade 11 Essential Mathematics Unit 6: Measurement and Geometry
Grade 11 Essential Mathematics Unit 6: INTRODUCTION When people first began to take measurements, they would use parts of the hands and arms. For example, a digit was the width of a thumb. This kind of
More informationStudent Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)
Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.
More informationIntegrated 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
More informationDiscovering Math: Measurement Teacher s Guide
Teacher s Guide Grade Level: 3 5 Curriculum Focus: Mathematics Lesson Duration: 3 4 class periods Program Description Discovering Math: Measurement From miles per gallon and metric conversion to circumference
More informationLinear, Square and Cubic Units Grade Five
Ohio Standards Connection Measurement Benchmark F Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed. Indicator 4 Demonstrate
More informationCircumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite
More informationGrade 3 Measurement and Data 3.MD.5 & 6
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 3 Measurement and Data 3.MD.5 & 6 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES THE NEWARK PUBLIC SCHOOLS Office of Mathematics MATHTASKS Measurement
More informationGrade 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
More informationBasic Garden Math. This document is organized into the following sections:
Basic Garden Math Gardening is an activity which occasionally requires the use of math, such as when you are computing how much fertilizer to use or how much compost to buy. Luckily, the math involved
More informationArea, Perimeter, Surface Area and Change Overview
Area, Perimeter, Surface Area and Change Overview Enduring Understanding: (5)ME01: Demonstrate understanding of the concept of area (5)ME02: Demonstrate understanding of the differences between length
More informationImperial Length Measurements
Unit I Measuring Length 1 Section 2.1 Imperial Length Measurements Goals Reading Fractions Reading Halves on a Measuring Tape Reading Quarters on a Measuring Tape Reading Eights on a Measuring Tape Reading
More informationArea 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
More informationLesson 19: Computing Actual Areas from a Scale Drawing
Student Outcomes Students identify the scale factor. Given a scale drawing, students compute the area in the actual picture. Classwork Examples 1 (1 minutes): Exploring Area Relationships In this series
More informationAssessment Management
Area Objectives To provide experiences with the concept of area, distinguishing between area and perimeter, and finding areas of rectangular figures by partitioning and counting squares. www.everydaymathonline.com
More information3.2 Converting Measurements
1 3.2 Converting Measurements We need to be able to convert metric measurements to larger or smaller metric measurements. In addition, since we live close to the United States we need to know how to convert
More informationName: Class: Date: Geometry Chapter 3 Review
Name: Class: Date: ID: A Geometry Chapter 3 Review. 1. The area of a rectangular field is 6800 square meters. If the width of the field is 80 meters, what is the perimeter of the field? Draw a diagram
More informationArea and Circumference
4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert
More informationExample 1 Find an unknown measure given the area.
Name Find Unknown Measures Essential Question How can you find an unknown measure of a rectangle given its area or perimeter Lesson 13.4 Measurement and Data 4.MD.A.3 MATHEMATICAL PRACTICES MP2, MP4, MP7
More informationPART 3 MODULE 8 PROBLEMS INVOLVING AREA
PART 3 MODULE 8 PROBLEMS INVOLVING AREA We will be examining a variety of realworld problems that can be solved by referring to familiar facts from elementary geometry. These problems will usually require
More informationGeometry Chapter 12. Volume. Surface Area. Similar shapes ratio area & volume
Geometry Chapter 12 Volume Surface Area Similar shapes ratio area & volume Date Due Section Topics Assignment Written Exercises 12.1 Prisms Altitude Lateral Faces/Edges Right vs. Oblique Cylinders 12.3
More informationName: Date: Geometry Solid Geometry. Name: Teacher: Pd:
Name: Date: Geometry 20122013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 17 HW: Pgs: 810 DAY 2: SWBAT: Calculate the Volume of
More informationCalculating 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
More informationShow 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
More informationChapter 1 Measurement
Chapter 1 Measurement Math 1201 1 Chapter 1 Measurement Sections 1.11.3: Goals: Converting between imperial units by unit analysis Converting between SI units Converting between SI and imperial units
More information.001.01.1 1 10 100 1000. milli centi deci deci hecto kilo. Explain that the same procedure is used for all metric units (meters, grams, and liters).
Week & ay Week 15 ay 1 oncept/skill ompare metric measurements. Standard 7 MG: 1.1ompare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles
More information2. Length, Area, and Volume
Name Date Class TEACHING RESOURCES BASIC SKILLS 2. In 1960, the scientific community decided to adopt a common system of measurement so communication among scientists would be easier. The system they agreed
More informationGeometry 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
More informationUnit 6 Measurement and Data: Area and Volume
Unit 6 Measurement and Data: Area and Volume Introduction In this unit, students will learn about area and volume. As they find the areas of rectangles and shapes made from rectangles, students will need
More informationCARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM
GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write
More informationVolume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.
Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts
More informationSection 7.2 Area. The Area of Rectangles and Triangles
Section 7. Area The Area of Rectangles and Triangles We encounter two dimensional objects all the time. We see objects that take on the shapes similar to squares, rectangle, trapezoids, triangles, and
More informationVolume of Spheres. A geometric plane passing through the center of a sphere divides it into. into the Northern Hemisphere and the Southern Hemisphere.
Page 1 of 7 9.6 Surface Area and Volume of Spheres Goal Find surface areas and volumes of spheres. Key Words sphere hemisphere A globe is an example of a sphere. A sphere is the set of all points in space
More informationArea 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
More informationMathematics as Reasoning Students will use reasoning skills to determine the best method for maximizing area.
Title: A Pen for Penny Brief Overview: This unit is a reinforcement of the concepts of area and perimeter of rectangles. Methods for maximizing area while perimeter remains the same are also included.
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More informationMD526 Stacking Blocks Pages 115 116
MD526 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.
More informationRelationships Between Quantities
Relationships Between Quantities MODULE 1? ESSENTIAL QUESTION How do you calculate when the numbers are measurements? CALIFORNIA COMMON CORE LESSON 1.1 Precision and Significant Digits N.Q.3 LESSON 1.2
More informationGrade 3. Measurement and Data 3.MD.7.ad 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 3 Measurement and Data 3.MD.7.ad 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES THE NEWARK PUBLIC SCHOOLS Office of Mathematics MATH TASKS Measurement
More informationLesson 2: Pythagorean Theorem
Lesson 2: Pythagorean Theorem Selected Content Standards Benchmarks Addressed: G5M Making and testing conjectures about geometric shapes and their properties G7M Demonstrating the connection of geometry
More informationVolume 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
More informationApplications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
More informationPerfume 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 costefficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters
More informationArea and Perimeter: The Mysterious Connection TEACHER EDITION
Area and Perimeter: The Mysterious Connection TEACHER EDITION (TC0) In these problems you will be working on understanding the relationship between area and perimeter. Pay special attention to any patterns
More information4 th Grade ISTEP+ Toolkit
4 th Grade Mathematics Instructional Week 26 Apply Area and Perimeter Formulas for Rectangles to Solve RealWorld Problems Paced Standards: 4.M.4: Apply the area and perimeter formulas for rectangles to
More informationWrite each measurement in millimeters (mm). Round the measurement to the nearest centimeter (cm).
51 Write each measurement in millimeters (mm). Round the measurement to the nearest centimeter (cm). 1 2 3 4 5 6 7 8 mm 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 cm 26 27 28 29 30 31
More informationLESSON PLAN #1. Name: Kevin Laley Date: March 1, NYS Mathematics, Science, and Technology Learning Standards Addressed
LESSON PLAN #1 Name: Kevin Laley Date: March 1, 2005 Today s Lesson: Circumference Exploration Unit Topic: Applying Fractions Course: Math 7 NYS Mathematics, Science, and Technology Learning Standards
More informationVolume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.
Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
More information17.1 INVESTIGATE. Model Perimeter. Are You Ready? Lesson Opener Making Connections. Resources. Texas Essential Knowledge and Skills.
. INVESTIGATE? Essential Question How can you find perimeter? How can you find perimeter? Lesson Opener Making Connections Invite students to tell you what they know about the distance around objects.
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
5 th GRADE Archdiocese of Washington Catholic Schools Standard 1  Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,
More informationBuilding Physical Intuition Measurement 1
II6 Name: Building Physical Intuition Measurement 1 Groups: form groups of three Equipment: each group should have a onemeterstick, a twometerstick, and a tape measure Lengths Objectives: Estimates
More informationArea and Circumference of Circles
Teacher Created Materials 21208 Focused Mathematics Student Guided Practice Book of Circles Learning Objectives Geometry Know the formulas for the area and circumference of a circle and use them to solve
More informationME311 Measuring Perimeter
ME311 Measuring Perimeter Goals: Students will estimate and measure perimeters using nonstandard units. Prior Knowledge Required: What measurement means Practice and comfort with other forms of linear
More informationAREA 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
More informationLesson 21. Circles. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Circles Objectives Understand the concepts of radius and diameter Determine the circumference of a circle, given the diameter or radius Determine
More informationGeometry 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
More informationMetric Measurement Mania!
Metric Measurement Mania! Be sure your students skills measure up with this monstrously fun measurement activity! Purpose: To estimate and measure metric units of length Students will do the following:
More informationPerimeter, Circumference, and Area
9 Perimeter, Circumference, and Area 9. Plan What You ll Learn To find perimeters of rectangles and squares, and circumferences of circles To find areas of rectangles, squares, and circles... And Why
More informationPizza! 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
More information