UNIT 4: LENGTH, AREA, AND VOLUME WEEK 16: Student Packet
|
|
- Anabel Sherman
- 6 years ago
- Views:
Transcription
1 Name Period Date UNIT 4: LENGTH, AREA, AND VOLUME WEEK 16: Student Packet 16.1 Circles: Area Establish the area formula for a circle. Apply the area formula for a circle to realistic problems. Demonstrate understanding of the area of a circle with symbols, tables, graphs, and words Cylinders: Volume and Surface Area Derive the formulas for surface area and volume of cylinders. Compute the surface area and volume of cylinders Review 1 Review mathematical concepts from the first semester. Demonstrate competency in solving equations (highlighted review) Week 16 SP
2 FOCUS ON VOCABULARY 16 Match the words to the clues and draw a picture next to the word. Words Clues 1. volume a. The total area of the surface of a solid. It is measured in square units. 2. base b. A face of a three-dimensional figure that is perpendicular to its height. 3. radius c. The measure of the interior of a solid, measured in cubic units. 4. surface area d. A solid figure with two circular, congruent bases that are parallel to each other. 5. area of a circle e. A line segment from the center of a circle to any point on the circle. 6. cylinder f. This is the product of pi and the square of the radius. Week 16 SP0
3 16.1 Circle: Area CIRCLE: AREA Ready (Summary) We will use formulas for the area of a rectangle and the circumference of a circle to help us find a formula for the area of a circle. Set (Goals) Establish the area formula for a circle. Apply the area formula for a circle to realistic problems. Demonstrate understanding of the area of a circle with symbols, tables, graphs, and words. Go (Warmup) The diameter of a dinner plate is 12 cm. Find its radius and circumference. Picture: Numbers/Symbols: Words: Week 16 SP1
4 16.1 Circle: Area THE AREA OF A CIRCLE 1. What is the formula for the circumference of a circle in terms of its radius r? 2. Your teacher will give you a piece of paper with a circle on it. Cut out the circle and fold it in half. Fold it in half a second time. Fold it in half a third time. 3. Unfold your circle and cut along the folds to make 8 wedges. (You may want to try more than 8 wedges, like 16, but don t do less.) 4. Arrange the wedges in a row. Alternate the tips up and down to form a shape that resembles a rectangle or parallelogram. Tape, glue stick, or sketch the shape here. Use your knowledge of the area of a rectangle and circumference of a circle to find the area of this shape. (Remember, it began as a circle and is becoming closer to resembling a rectangle. The more wedges you make, the closer it gets to becoming a rectangle.) 5. The width of the rectangle is the of the circle. 6. The length of the rectangle is of the circle. 7. Write an equation for the approximate area of the rectangle. 8. Substitute the expression for the circumference of the circle from #1 above into your formula and simplify. 9. What is the formula for the area of a circle, in terms of the radius? Week 16 SP2
5 16.1 Circle: Area AREA OF A CIRCLE: THE FOURFOLD WAY 1. Symbols: What is a formula for finding the area of a circle? 2. Table: Use the formula to calculate the area of a circle with the given radius. Length of radius (r) (show work) Area of circle (A) 0 1 Area (A) radius (r) 3. Graph: Make a graph that compares area (A) and radius (r). 4. Words: Explain how you would find the area of a circle if you knew the diameter. Week 16 SP3
6 16.1 Circle: Area USE YOUR CIRCLE KNOWLEDGE 2 1. The dish problem: Find the area of a plate whose diameter is 12 inches. Picture: Numbers/Symbols: Words: 2. The water sprinkler problem: A revolving water sprinkler sprays water in a circular fashion to a distance of 20 feet in all directions. What area of grass can it cover? Picture: Numbers/Symbols: Words: Week 16 SP4
7 16.1 Circle: Area USE YOUR CIRCLE KNOWLEDGE 2 (continued) 3. The pizza problem: Pizza House sells 2 different pizza sizes: A 16-inch-diameter pizza and a 12-inch-diameter pizza. How much more pizza do you get by ordering the 16 in. diameter pizza than the smaller one? Picture: Numbers/Symbols: Words: 4. The school track problem: A field at a local school is surrounded by a track. Each straightaway is 425 feet. The distance across the field (top to bottom in the diagram) is 150 feet. Find the area of the field. Picture: Numbers/Symbols: straightaway Words: Week 16 SP5
8 16.2 Cylinders: Volume and Surface Area CYLINDERS: VOLUME AND SURFACE AREA Ready (Summary) We will make sense of the formulas for the surface area and volume of cylinders and apply them to solve problems. Set (Goals) Derive the formulas for surface area and volume of cylinders. Compute the surface area and volume of cylinders. Go (Warmup) 1. The formula for finding the circumference of a circle is: 2. The formula for finding the area of a circle is: A circle has circumference C = inches. 3. Find the radius of the circle. 4. Find the area of the circle. A rectangular prism measures 2 ft. 5 ft. 6 ft. 5. Find the surface area of the prism. 6. Find the volume of the prism. Week 16 SP6
9 16.2 Cylinders: Volume and Surface Area A PAPER CYLINDER Roll a letter-size piece of paper parallel to the 8 1 -inch sides to make a cylinder. Tape 2 the two 8 1 -inch edges together. Imagine your cylinder has two circular bases, or cut 2 out two circular bases and tape them to the top and bottom of the cylinder. 1. Sketch a net of the cylinder and label its dimensions. 2. Sketch the cylinder and label its dimensions. 3. Find the surface area rounded to the nearest hundredth. Formula: SA = Substitute: 4. Find the volume rounded to the nearest hundredth. Formula: V = Substitute: Answer: sq. in. Answer: cu. in. Week 16 SP7
10 16.2 Cylinders: Volume and Surface Area ANOTHER PAPER CYLINDER Roll a letter-size piece of paper parallel to the 11-inch sides to make a cylinder. Tape the two 11-inch edges together. Imagine your cylinder has two circular bases, or cut out two circular bases and attach them to the top and bottom of the cylinder. 1. Sketch a net of the cylinder and label its dimensions. 2. Sketch the cylinder and label its dimensions. 3. Find the surface area rounded to the nearest hundredth. Formula: SA = Substitute: 4. Find the volume rounded to the nearest hundredth. Formula: V = Substitute: Answer: sq. in. Answer: cu. in. Week 16 SP8
11 16.2 Cylinders: Volume and Surface Area CIRCULAR BASES FOR PAPER CYLINDERS Trace two sets of the circles below and cut them out to use as bases for your cylinders. Week 16 SP9
12 16.3 Review 1 SKILL BUILDER 1 Show your work on a separate sheet of paper and choose the best answer. 1. Which properties of arithmetic are illustrated in the equation ( ) + 78 = 15 + (32+78)? A. commutative property of addition B. associative property of addition C. distributive property D. all of the above 2. What does the 8 represent in 45,389,011? E. 8,000 F. 80,000 G. 800,000 H. 10, Which properties of arithmetic are illustrated in the equation = 24 18? A. commutative property of multiplication B. associative property of multiplication C. distributive property D. all of the above 4. Compute E. 205 F. 105 G. 195 H Compute A. 3,408 B. 3,308 C. 852 D (3 5) E. 75 F. 135 G. 3 H What are the prime factors of 24? A B C D Evaluate the expression 3x + 7 for x = 6. E. 25 F. 60 G. 39 H. 24 Week 16 SP10
13 16.3 Review 1 SKILL BUILDER 2A Compute Week 16 SP11
14 16.3 Review 1 SKILL BUILDER 2B Solve = 3( x 2) 11. 2( x 2) = 4x x + 2 = 4(2 + x) 13. Extend the geometric pattern, write a rule and make a graph. A Geometric Pattern Table Step 1 Step 2 Step # (Input) x (Output) y 1 9 Graph Step Step Step 5 x y = 14. Describe the geometric and numerical patterns in words: Week 16 SP12
15 16.3 Review 1 SKILL BUILDER 3A Compute Solve for x. 4. -( x+ 3) = 4x x 4 = = 3( x 4) 7. Complete the table, graph the values, and write an equation for the line. There are 4 quarts in a gallon. gallons (x) x quarts (y) y = Week 16 SP13
16 16.3 Review 1 SKILL BUILDER 3B Show your work on a separate sheet of paper and choose the best answer. 8. What is the value of the expression (13 + 4) (7 2) + (31 17)? A. 45 B. 40 C. 17 D The letters m and n stand for numbers. If m 100 = n 100, which of the following statements is true? E. m = n F. m > n G. m = n H. m > n What number goes in the box to make the number sentence true? (7 3) 5 = 4 A. 5 B. 3 C. 7 D What is the value of y if y 2 = 10? E. 12 F. 10 G. 8 H What value of k makes the equation k 3 = 36 true? A B. 12 C. 33 D Which equation could have been used to create this function table? x y E. y = 2 x F. y = 2x G. y = x 4 H. y = x Which of the following numbers has the greatest value? A. 0.3 B C. -2 D. 4 5 Week 16 SP14
17 16.3 Review 1 TEST PREPARATION 16 Show your work on a separate sheet of paper and choose the best answer. 1. What is the surface area of a cylinder that has a base with a diameter of 18 ft. and a height of 13 ft? A. 234 ft. 2 B ft. 2 C. 1, ft. 2 D. 3, ft The largest possible circle is to be cut from a 10-foot square board. What will be the approximate area, in square feet, of the remaining board (shaded region)? E. 30 F. 50 G. 20 H Solve 5 2x = 7 for x. A. x = 1 B. x = -1 C. x = 6 D. x = Compute E F G. 2 5 H Compute A B C. 6.5 D. 65 Week 16 SP15
18 16.3 Review 1 This page is left intentionally blank for notes. Week 16 SP16
19 16.3 Review 1 KNOWLEDGE CHECK 16 Show your work on a separate sheet of paper and write your answers on this page Circles: Area 1. Find the area of a circular tabletop with a radius of 2.5 feet. 2. Find the area of the circle rounded to the nearest tenth of a square unit. 2.2 mm 16.2 Cylinders: Volume and Surface Area A cylinder has a base with a diameter of 5 ft. and a height of 16 ft. 3. Sketch a net for the cylinder and label the dimensions. 4. Find the surface area of the cylinder. Highlighted Review: Solving Equations Solve for x x = ( x 1) = = 2( x + 6) Week 16 SP17
20 16.3 Review 1 Home-School Connection 16 Here are some questions from this week s lessons to review with your young mathematician. 1. Find the area of the circle rounded to the nearest tenth. 5.4 cm 2. A cylinder has a base with a diameter of 6.2 mm and a height of 4.5 mm. Find its surface area. 3. A cylinder has a base with a radius of 5 mm and a height of 4 mm. Find the volume. Parent (or Guardian) signature Selected California Mathematics Content Standards MG MG Know common estimates of π (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Week 16 SP18
Sample: Do Not Reproduce GEO1 STUDENT PAGES. GEOMETRY AND MEASUREMENT Student Pages for Packet 1: Length and Area.
Name Period Date GEOMETRY AND MEASUREMENT Student Pages for Packet 1: GEO1.1 Congruence Plot simple figures on coordinate graphs, and determine their lengths and areas. Make conjectures about perimeters
More informationGeometry Unit 10 Note Sheets Date Name of Lesson. 1.6 Two-Dimensional Figures Areas of Circles and Sectors
Date Name of Lesson 1.6 Two-Dimensional Figures 11.3 Areas of Circles and Sectors Quiz 11.1 Areas of Parallelograms and Triangles 11.2 Areas of Trapezoids, Rhombi and Kites 11.4 Areas of Regular Polygons
More informationSurface Area and Volume
Surface Area and Volume Day 1 - Surface Area of Prisms Surface Area = The total area of the surface of a three-dimensional object (Or think of it as the amount of paper you ll need to wrap the shape.)
More informationAdditional Practice. Name Date Class
Additional Practice Investigation 1 1. The four nets below will fold into rectangular boxes. Net iii folds into an open box. The other nets fold into closed boxes. Answer the following questions for each
More informationSomeone else might choose to describe the closet by determining how many square tiles it would take to cover the floor. 6 ft.
Areas Rectangles One way to describe the size of a room is by naming its dimensions. So a room that measures 12 ft. by 10 ft. could be described by saying its a 12 by 10 foot room. In fact, that is how
More informationChapter 7. Description or Example. Found on Page. Vocabulary Term. Definition. base. center. circumference. chord. complex figure. cone.
C H A P T E R 7 This is an alphabetical list of new vocabulary terms you will learn in Chapter 7. As you complete the study notes for the chapter, you will see Build Your Vocabulary reminders to complete
More informationPage 1 CCM6+7+ UNIT 9 GEOMETRY 2D and 3D. Angle Relationships, Area, and Perimeter/Circumference Surface Area and Volume
Page 1 CCM6+7+ UNIT 9 GEOMETRY 2D and 3D UNIT 9 2015-16 Angle Relationships, Area, and Perimeter/Circumference Surface Area and Volume CCM6+7+ Name: Math Teacher: Projected Test Date: MAIN CONCEPT(S) PAGE(S)
More informationUnit 7: 3D Figures 10.1 & D formulas & Area of Regular Polygon
Unit 7: 3D Figures 10.1 & 10.2 2D formulas & Area of Regular Polygon NAME Name the polygon with the given number of sides: 3-sided: 4-sided: 5-sided: 6-sided: 7-sided: 8-sided: 9-sided: 10-sided: Find
More informationMODULE 18 VOLUME FORMULAS
MODULE 18 VOLUME FORMULAS Objectives Use formulas routinely for finding the perimeter and area of basic prisms, pyramids, cylinders, cones, and spheres. Vocabulary: Volume, right vs oblique Assignments:
More informationFebruary 07, Dimensional Geometry Notebook.notebook. Glossary & Standards. Prisms and Cylinders. Return to Table of Contents
Prisms and Cylinders Glossary & Standards Return to Table of Contents 1 Polyhedrons 3-Dimensional Solids A 3-D figure whose faces are all polygons Sort the figures into the appropriate side. 2. Sides are
More informationPage 1 CCM6+7+ UNIT 9 GEOMETRY 2D and 3D 2D & 3D GEOMETRY PERIMETER/CIRCUMFERENCE & AREA SURFACE AREA & VOLUME
Page 1 CCM6+7+ UNIT 9 GEOMETRY 2D and 3D UNIT 9 2016-17 2D & 3D GEOMETRY PERIMETER/CIRCUMFERENCE & AREA SURFACE AREA & VOLUME CCM6+7+ Name: Math Teacher: Projected Test Date: MAIN CONCEPT(S) PAGE(S) Vocabulary
More informationG-GMD.1- I can explain the formulas for volume of a cylinder, pyramid, and cone by using dissection, Cavalieri s, informal limit argument.
G.MG.2 I can use the concept of density in the process of modeling a situation. 1. Each side of a cube measures 3.9 centimeters. Its mass is 95.8 grams. Find the density of the cube. Round to the nearest
More informationVolume of Cylinders. Volume of Cones. Example Find the volume of the cylinder. Round to the nearest tenth.
Volume of Cylinders As with prisms, the area of the base of a cylinder tells the number of cubic units in one layer. The height tells how many layers there are in the cylinder. The volume V of a cylinder
More informationLesson 1 - Area Review Shape Words Formula
Lesson 1 - Area Review Shape Words Formula Rectangle The area A of a rectangle is the product of the length and the width w. A = w Parallelogram The area A of a parallelogram is the product of any base
More informationReteaching. Solids. These three-dimensional figures are space figures, or solids. A cylinder has two congruent circular bases.
9- Solids These three-dimensional figures are space figures, or solids A B C D cylinder cone prism pyramid A cylinder has two congruent circular bases AB is a radius A cone has one circular base CD is
More informationGeometry 10 and 11 Notes
Geometry 10 and 11 Notes Area and Volume Name Per Date 10.1 Area is the amount of space inside of a two dimensional object. When working with irregular shapes, we can find its area by breaking it up into
More information3 Dimensional Solids. Table of Contents. 3 Dimensional Solids Nets Volume Prisms and Cylinders Pyramids, Cones & Spheres
Table of Contents 3 Dimensional Solids Nets Volume Prisms and Cylinders Pyramids, Cones & Spheres Surface Area Prisms Pyramids Cylinders Spheres More Practice/ Review 3 Dimensional Solids Polyhedron A
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 informationPre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume
Pre-Algebra Notes Unit 0: Geometric Figures & Their Properties; Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (4.6) The student will validate conclusions about geometric figures and
More information5th Grade Mathematics Essential Standards
Standard 1 Number Sense (10-20% of ISTEP/Acuity) Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions, and percents. They understand the
More informationLesson 14.1 Skills Practice
Lesson 14.1 Skills Practice Name Date Cut, Fold, and Voila! Nets Vocabulary Define each term in your own words. 1. geometric solids 2. net 3. prototype 4. edge 5. face 6. vertex Problem Set Sketch and
More informationPre-Algebra, Unit 10: Measurement, Area, and Volume Notes
Pre-Algebra, Unit 0: Measurement, Area, and Volume Notes Triangles, Quadrilaterals, and Polygons Objective: (4.6) The student will classify polygons. Take this opportunity to review vocabulary and previous
More information7 th Grade CCGPS Math LFS Unit 5: Geometry
7 th Grade CCGPS Math LFS Unit 5: Geometry Standards: Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them. MCC7.G.2 (DOK2) Draw (freehand, with ruler
More informationDRAFT CHAPTER. Surface Area GET READY. xxx. Math Link. 5.1 Warm Up xxx. 5.1 Views of Three-Dimensional Objects xxx. 5.
CHAPTER 5 Surface Area GET READY Math Link xxx xxx 5.1 Warm Up xxx 5.1 Views of Three-Dimensional Objects xxx 5.2 Warm Up xxx 5.2 Nets of Three-Dimensional Objects xxx 5.3 Warm Up xxx 5.3 Surface Area
More information11.4 Volume of Prisms and Cylinders
11.4 Volume of Prisms and Cylinders Learning Objectives Find the volume of a prism. Find the volume of a cylinder. Review Queue 1. Define volume in your own words. 2. What is the surface area of a cube
More informationKansas City Area Teachers of Mathematics 2018 KCATM Math Competition
Kansas City Area Teachers of Mathematics 2018 KCATM Math Competition GEOMETRY AND MEASUREMENT TEST GRADE 6 #51-90 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes
More informationTo find the surface area of a pyramid and a cone
11-3 Surface Areas of Pyramids and Cones Common Core State Standards G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects. MP 1, MP 3, MP 4, MP 6, MP 7 Objective To find
More information12 m. 30 m. The Volume of a sphere is 36 cubic units. Find the length of the radius.
NAME DATE PER. REVIEW #18: SPHERES, COMPOSITE FIGURES, & CHANGING DIMENSIONS PART 1: SURFACE AREA & VOLUME OF SPHERES Find the measure(s) indicated. Answers to even numbered problems should be rounded
More informationPark Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):
Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Solid (Volume and Surface Area) 3. Number Theory:
More informationPark Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):
Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Solid (Volume and Surface Area) 3. Number Theory:
More informationFair Game Review. Chapter 15. Name Date. Find the area of the figure ft
Name Date Chapter 15 Fair Game Review Find the area of the figure. 1. 3 m 3 m 2. 5 m 7 m 14 m 9 m 3 m 3. 4 in. 1 in. 4. 12 in. 5 in. 9 in. 12 in. 7 in. 12 in. 5. 6. 5 ft 3 ft 15 ft 1 ft 4 in. 10 in. 8
More informationChapter 10 BUILD YOUR VOCABULARY
C H A P T E R 10 BUILD YOUR VOCABULARY This is an alphabetical list of new vocabulary terms you will learn in Chapter 10. As you complete the study notes for the chapter, you will see Build Your Vocabulary
More informationCHAPTER 12. Extending Surface Area and Volume
CHAPTER 12 Extending Surface Area and Volume 0 Learning Targets Students will be able to draw isometric views of three-dimensional figures. Students will be able to investigate cross-sections of three-dimensional
More informationTEST REVIEW: UNIT 8 Surface Area 2018
Class: Date: TEST REVIEW: UNIT 8 Surface Area 2018 Find the area. The figure is not drawn to scale. 1. 5. Find the area. All lengths are in centimeters. Round answer to the nearest tenth. 2. 6. A can of
More informationLesson 10T ~ Three-Dimensional Figures
Lesson 10T ~ Three-Dimensional Figures Name Period Date Use the table of names at the right to name each solid. 1. 2. Names of Solids 3. 4. 4 cm 4 cm Cone Cylinder Hexagonal prism Pentagonal pyramid Rectangular
More information3. Draw the orthographic projection (front, right, and top) for the following solid. Also, state how many cubic units the volume is.
PAP Geometry Unit 7 Review Name: Leave your answers as exact answers unless otherwise specified. 1. Describe the cross sections made by the intersection of the plane and the solids. Determine if the shape
More informationAreas of Rectangles and Parallelograms
CONDENSED LESSON 8.1 Areas of Rectangles and Parallelograms In this lesson, you Review the formula for the area of a rectangle Use the area formula for rectangles to find areas of other shapes Discover
More informationMeasurement and Geometry: Area and Volume of Geometric Figures and Objects *
OpenStax-CNX module: m35023 1 Measurement and Geometry: and Volume of Geometric Figures and Objects * Wade Ellis Denny Burzynski This work is produced by OpenStax-CNX and licensed under the Creative Commons
More informationACCELERATED MATHEMATICS CHAPTER 11 DIMENSIONAL GEOMETRY TOPICS COVERED:
ACCELERATED MATHEMATICS CHAPTER DIMENSIONAL GEOMETRY TOPICS COVERED: Naming 3D shapes Nets Volume of Prisms Volume of Pyramids Surface Area of Prisms Surface Area of Pyramids Surface Area using Nets Accelerated
More informationKansas City Area Teachers of Mathematics 2013 KCATM Math Competition
Kansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY AND MEASUREMENT TEST GRADE 6 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may
More information2. a. approximately cm 3 or 9p cm b. 20 layers c. approximately cm 3 or 180p cm Answers will vary.
Answers Investigation ACE Assignment Choices Problem. Core Other Connections Problem. Core,, Other Applications 7, ; Connections 7 0; unassigned choices from previous problems Problem. Core 7 Other Connections,
More informationBUILD YOUR VOCABULARY
C H A P T E R 12 BUILD YOUR VOCABULARY This is an alphabetical list of new vocabulary terms you will learn in Chapter 12. As you complete the study notes for the chapter, you will see Build Your Vocabulary
More informationTest Chapter 11. Matching
Test Chapter 11 Matching Match each vocabulary term with its definition. a. cube b. cylinder c. cone d. sphere e. prism f. pyramid g. hemisphere 1. a polyhedron formed by a polygonal base and triangular
More information4. Describe the correlation shown by the scatter plot. 8. Find the distance between the lines with the equations and.
Integrated Math III Summer Review Packet DUE THE FIRST DAY OF SCHOOL The problems in this packet are designed to help you review topics from previous mathematics courses that are essential to your success
More information9.1. Perimeter & Circumference. For this Challenge Activity, you will need to see your teacher. Measurement & Geometry
Perimeter & Circumference 9.1 Find the perimeter of each polygon. Find the perimeter of each rectangle. Find the circumference of each circle to the nearest tenth. Use 3.14 or 22 7 for. 7. 8. 9. Use 22
More information422 UNIT 12 SOLID FIGURES. The volume of an engine s cylinders affects its power.
UNIT 12 Solid Figures The volume of an engine s cylinders affects its power. 422 UNIT 12 SOLID FIGURES Gas-powered engines are driven by little explosions that move pistons up and down in cylinders. When
More informationL22 Measurement in Three Dimensions. 22a Three Dimensions Warmup
22a Three Dimensions Warmup Let s take a look at two-dimensional and three-dimensional objects below. A vertex (plural: vertices) (#VOC) in a 2 or 3-dimensional object is a point where two or more straight
More informationEMERGENCY SHELTER DESIGN STEM LEARNING AT ITS BEST
KSB * 1 ( * KNOWLEDGE AND SKILL BUILDER) Geometric shapes student Name: Period: school: date: Hofstra University Center for Technological Literacy Simulations and Modeling for Technology Education This
More informationAnswer Key: Three-Dimensional Cross Sections
Geometry A Unit Answer Key: Three-Dimensional Cross Sections Name Date Objectives In this lesson, you will: visualize three-dimensional objects from different perspectives be able to create a projection
More informationHS Pre-Algebra Notes Unit 10: Measurement, Area, and Volume
HS Pre-Algebra Notes Unit 0: Measurement, Area, and Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (5.6) The student will classify polygons. (5.5) The student will validate conclusions
More informationTeacher Page. 1. Find the surface area of the prism. a. 315 in 2 b. 630 in 2 c. 450 in 2 d. 820 in 2
Teacher Page Geometry / Day #12 Surface Area 45 Minutes 9-12.G.1.3 Draw three-dimensional objects and calculate the surface areas and volumes of these figures (e.g. prisms, cylinders, pyramids, cones,
More informationVolume and Surface Area Unit 28 Remember Volume of a solid figure is calculated in cubic units and measures three dimensions.
Volume and Surface Area Unit 28 Remember Volume of a solid figure is calculated in cubic units and measures three dimensions. Surface Area is calculated in square units and measures two dimensions. Prisms
More information17.2 Surface Area of Prisms
h a b c h a b c Locker LESSON 17. Surface Area of Prisms and Cylinders Texas Math Standards The student is expected to: G.11.C Apply the formulas for the total and lateral surface area of three-dimensional
More informationA plane that is to the base of the figure will create a cross section that is the same shape as the base.
Objective: 9.1 3 Notes: Surface Area of Solids Name Cross Sections: A cuts through a solid figure to create a cross section. Depending on the way in which the plane cuts through the figure will determine
More informationCHAPTER 12. Extending Surface Area and Volume
CHAPTER 12 Extending Surface Area and Volume 0 1 Learning Targets Students will be able to draw isometric views of three-dimensional figures. Students will be able to investigate cross-sections of three-dimensional
More informationUnit 5. Area & Volume. Area Composite Area Surface Area Volume. Math 6 Unit 5 Calendar 1/14 1/15 1/16 1/17 1/18. Name: Math Teacher:
Math 6 Unit 5 Calendar 1/14 1/15 1/16 1/17 1/18 Name: Unit 5 Area & Volume Area Composite Area Surface Area Volume Review Or Computer Lab Unit 5 Test Or Computer Lab Unit 5 Test Or Computer Lab Unit 5
More informationKansas City Area Teachers of Mathematics 2010 KCATM Math Competition
Kansas ity rea Teachers of Mathematics 2010 KTM Math ompetition GEOMETRY N MESUREMENT TEST GRE 5 INSTRUTIONS o not open this booklet until instructed to do so. Time limit: 15 minutes You may use calculators
More informationMathematics Background
Measurement All measurements are approximations. In their work in this Unit, students explore ways to find measures for two and three dimensional figures. Even using exact formulas depends on how students
More information6. If QRSTU is a regular pentagon, what is the measure of T? 1. If STUV is a parallelogram, what are the coordinates of point U?
1. If UV is a parallelogram, what are the coordinates of point U?. If RU is a regular pentagon, what is the measure of? (0, y) U(?,?) (, 0) V( + z, 0) 7. hree siblings are to share an inheritance of $1,0
More informationHouston County School System Mathematics
Student Name: Teacher Name: Grade: 6th Unit #: 5 Unit Title: Area and Volume Approximate Start Date of Unit: Approximate End Date (and Test Date) of Unit: The following Statements and examples show the
More informationName: Target 12.2: Find and apply surface of Spheres and Composites 12.2a: Surface Area of Spheres 12.2b: Surface Area of Composites Solids
Unit 12: Surface Area and Volume of Solids Target 12.0: Euler s Formula and Introduction to Solids Target 12.1: Find and apply surface area of solids 12.1a: Surface Area of Prisms and Cylinders 12.1b:
More informationVocabulary. Term Page Definition Clarifying Example. cone. cube. cylinder. edge of a threedimensional. figure. face of a polyhedron.
CHAPTER 10 Vocabulary The table contains important vocabulary terms from Chapter 10. As you work through the chapter, fill in the page number, definition, and a clarifying example. cone Term Page Definition
More informationMath Mealy Mountain Collegiate. Sample Midterm Exam. Name:
Math 2202 Mealy Mountain Collegiate Sample Midterm Exam Name: Formulas Square Rectangle A = s 2 A = l x w P 2l 2 w Triangle C 2 r A b h 2 Circle A r 2 C d or Cube Rectangle Prism SA = 6s 2 SA =2(l x w)+2(lxh)+2(wxh)
More informationCircular Reasoning. Solving Area and Circumference. Problems. WARM UP Determine the area of each circle. Use 3.14 for π.
Circular Reasoning Solving Area and Circumference 3 Problems WARM UP Determine the area of each circle. Use 3.14 for π. 1. 4 in. 2. 3.8 cm LEARNING GOALS Use the area and circumference formulas for a circle
More informationA. 180 B. 108 C. 360 D. 540
Part I - Multiple Choice - Circle your answer: REVIEW FOR FINAL EXAM - GEOMETRY 2 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C.
More informationA C E. Applications. Applications Connections Extensions
A C E Applications Connections Extensions Applications 1. Suppose that the polygons below were drawn on centimeter grid paper. How many 1-centimeter cubes (some cut in pieces) would it take to cover each
More informationArea rectangles & parallelograms
Area rectangles & parallelograms Rectangles One way to describe the size of a room is by naming its dimensions. So a room that measures 12 ft. by 10 ft. could be described by saying its a 12 by 10 foot
More informationG r a d e 1 0 I n t r o d u c t i o n t o A p p l i e d a n d P r e - C a l c u l u s M a t h e m a t i c s ( 2 0 S )
G r a d e 0 I n t r o d u c t i o n t o A p p l i e d a n d P r e - C a l c u l u s M a t h e m a t i c s ( 0 S ) Midterm Practice Exam Answer Key G r a d e 0 I n t r o d u c t i o n t o A p p l i e d
More informationPark Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):
Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Solid (Volume and Surface Area) 3. Number Theory:
More informationVolume of Rectangular Prisms and Pyramids. Use the formula. Substitute for l and w. Use the formula. Substitute for B and h.
? LESSON 10.1 ESSENTIAL QUESTION Volume of Rectangular Prisms and Pyramids How do you find the volume of a rectangular prism and a rectangular pyramid? Finding the Volume of a Rectangular Prism Remember
More informationNumber/Computation. addend Any number being added. digit Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
14 Number/Computation addend Any number being added algorithm A step-by-step method for computing array A picture that shows a number of items arranged in rows and columns to form a rectangle associative
More informationFree Response. Test A. 1. What is the estimated area of the figure?
Test A 1. What is the estimated area of the 6. An 8.5 in. by 11 in. sheet of paper is enlarged to make a poster by doubling its length and width. What is the new perimeter? 7. How does the area of a square
More informationStudents construct nets of three dimensional objects using the measurements of a solid s edges.
Student Outcomes Students construct nets of three dimensional objects using the measurements of a solid s edges. Lesson Notes In the previous lesson, a cereal box was cut down to one of its nets. On the
More informationEngage NY Lesson 15: Representing Three-Dimensional Figures Using Nets
Name: Surface Area & Volume Packet Engage NY Lesson 15: Representing Three-Dimensional Figures Using Nets Classwork Cereal Box Similarities: Cereal Box Differences: Exercise 1 1. Some of the drawings below
More informationThe Geometry of Solids
CONDENSED LESSON 10.1 The Geometry of Solids In this lesson you will Learn about polyhedrons, including prisms and pyramids Learn about solids with curved surfaces, including cylinders, cones, and spheres
More information6 th Grade Math Cylinder Task. c) Draw a net (pattern) for the manufacturer to use to make the can.
6 th Grade Math a) Explain what is meant by surface area. What steps would you take to find the surface area of a cylinder? b) One of the major expenses in manufacturing a can is the amount of metal that
More informationGeometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.
Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know
More informationVolume of Prisms and Cylinders
Name Date Teacher Practice A Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth of a unit. Prism: V = Bh. Cylinder: V = π 2 r h. Use 3.14 for π. 1. 2. 3. 4. 5. 6. 7. 8.
More informationName Date Class. 1. What is the volume of a cube whose side length measures 21 cm? Show your thinking.
Name Date Class 1. What is the volume of a cube whose side length measures 21 cm? Show your thinking. 2. The volume of a cube is 13,824 mm 3. What is the side length of the cube? Show your thinking. 3.
More informationMeasurement and Geometry
Name Date Class Review for Mastery: Converting Customary Units You can use the table below to convert customary units. Length 1 foot = 1 inches 1 yard = 36 inches 1 yard = 3 feet 1 mile = 5,80 feet 1 mile
More informationMeasurement 1 PYTHAGOREAN THEOREM. The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of
Measurement 1 PYTHAGOREAN THEOREM Remember the Pythagorean Theorem: The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two sides.
More informationName Period Date. UNIT 3: EXPRESSIONS AND EQUATIONS WEEK 12: Student Packet
Name Period Date UNIT : EXPRESSIONS AND EQUATIONS WEEK 2: Student Packet 2. Inputs and Outputs Use tables, graphs, equations, and words to solve problems. Informally introduce the slope-intercept form
More information2D Geometry Part 2: Area
Slide 1 / 81 Slide 2 / 81 2D Geometry Part 2: Area Rectangles Parallelograms Triangles Trapezoids Circles Mixed Review Irregular Shapes Shaded Regions Click on a topic to go to that section Slide 3 / 81
More information, 6.7,, Order the numbers from least to greatest. 1. 1, 0, 2, 5, 4. Simplify the expression. 10.
Getting Ready for Pre-Algebra or Algebra Summer Math Practice The following are practice questions to evaluate the students understanding of concepts and skills taught in seventh grade as a readiness for
More informationPractice A Introduction to Three-Dimensional Figures
Name Date Class Identify the base of each prism or pyramid. Then choose the name of the prism or pyramid from the box. rectangular prism square pyramid triangular prism pentagonal prism square prism triangular
More informationMy Notes CONNECT TO SCIENCE. Horticulture is the science and art of growing fruit, flowers, ornamental plants, and vegetables.
SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/ Retell, Use Manipulatives, Activating Prior Knowledge, Self/ Peer Revision The Horticulture Club has been given some land to build a greenhouse. The
More informationName: Period: 2018 Geometry Spring Final Exam Review
2018 Geometry Spring Final Exam Review 1. Find the number of lunch combinations that can be created if you order a soup, sandwich, drink and dessert. There are 4 soup choices, 5 sandwich choices, 3 drink
More informationUnit 3 Part 2. HONORS Geometry Final Exam Review 2 nd Semester. 2. Solve for x. A) B)
HONORS Geometry Final Exam Review 2 nd Semester Name: Unit 3 Part 2 1. 2. Solve for x. ) ) x 14 8 9 x 50 3. 12 ft ladder is leaning against a house. The bottom of the ladder is 7 ft from the base of the
More information2D Geometry Part 2: Area
Slide 1 / 81 2D Geometry Part 2: Area Table of Contents Slide 2 / 81 Rectangles Parallelograms Triangles Trapezoids Circles Mixed Review Irregular Shapes Shaded Regions Click on a topic to go to that section
More information10-3 Composite Figures
10-3 Composite Figures Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the area of each figure. 1. a rectangle in which b = 14 cm and h = 5 cm A = 70 cm 2 2. a triangle in which b = 6 in.
More informationGeometry. Week 32: April 13-17, 2015
G.13 Geometry Week 32: April 13-17, 2015 The student will use formulas for surface area and volume of threedimensional objects to solve real-world problems. G.14 The student will use similar geometric
More informationVocabulary. Triangular pyramid Square pyramid Oblique square pyramid Pentagonal pyramid Hexagonal Pyramid
CP1 Math 2 Unit 8: S.A., Volume, Trigonometry: Day 7 Name Surface Area Objectives: Define important vocabulary for 3-dimensional figures Find the surface area for various prisms Generalize a formula for
More informationSection 4.1 Investigating Circles
Section 4.1 Investigating Circles A circle is formed when all the points in a plane that are the same distance away from a center point. The distance from the center of the circle to any point on the edge
More informationMD5-26 Stacking Blocks Pages
MD5-26 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 informationUnit 1, Lesson 1: Tiling the Plane
Unit 1, Lesson 1: Tiling the Plane Let s look at tiling patterns and think about area. 1.1: Which One Doesn t Belong: Tilings Which pattern doesn t belong? 1 1.2: More Red, Green, or Blue? m.openup.org//6-1-1-2
More informationMeasurement and Geometry
8A A Family Letter: Area Dear Family, The student will learn how to convert between units within the customary and metric measuring systems. The table below shows the conversions for the customary system.
More informationReal-World Problems: Surface Area and Volume. Solve word problems about the volume of rectangular prisms.
12.4 Real-World Problems: Surface Area and Volume Lesson Objective Solve problems involving surface area and volume of prisms. Learn Solve word problems about the volume of rectangular prisms. A rectangular
More informationUnit 4 End-of-Unit Assessment Study Guide
Circles Unit 4 End-of-Unit Assessment Study Guide Definitions Radius (r) = distance from the center of a circle to the circle s edge Diameter (d) = distance across a circle, from edge to edge, through
More informationUnit Lesson Plan: Measuring Length and Area: Area of shapes
Unit Lesson Plan: Measuring Length and Area: Area of shapes Day 1: Area of Square, Rectangles, and Parallelograms Day 2: Area of Triangles Trapezoids, Rhombuses, and Kites Day 3: Quiz over Area of those
More informationA triangle that has three acute angles Example:
1. acute angle : An angle that measures less than a right angle (90 ). 2. acute triangle : A triangle that has three acute angles 3. angle : A figure formed by two rays that meet at a common endpoint 4.
More information