Length, Width, and Depth
|
|
|
- Dennis Phillips
- 5 years ago
- Views:
Transcription
1 Length, Width, and Depth Deepening Understanding of Volume 1 WARM UP Determine the least common multiple of the numbers in each pair. 1., 10. 3, , 1 LEARNING GOALS Determine the volume of right rectangular prisms with fractional edge lengths using unit cubes with unit fractional dimensions. Connect the volume formulas V 5 lwh and V 5 Bh with a unit-cube model of volume for rectangular prisms. Apply the formulas V 5 lwh and V 5 Bh to determine volumes in real-world problems. Fluently add, subtract, and multiply multi-digit decimals using the standard algorithms.. 10, 15 KEY TERMS point line segment polygon geometric solid polyhedron edge vertex right rectangular prism cube pyramid volume You know about three-dimensional figures such as cubes and other rectangular prisms. You also know how to operate with positive rational numbers. How can you use what you know to calculate measurements of any rectangular prism, even one with fractional edge lengths? LESSON 1: Length, Width, and Depth M1-115
2 Getting Started Common Figures Cut out the cards found at the end of the lesson. Sort the figures into two or more groups. Name each category and be prepared to share your reasoning. M1-116 TOPIC 3: Decimals and Volume
3 ACTIVITY 1.1 Name that Figure It is important to speak a common language when studying mathematics. A word you may have used in the past may actually have a more precise definition when dealing with mathematics. For example, the word point has many meanings outside of math. However, the mathematical definition of point is a location in space. A mathematical point has no size or shape, but it is often represented by using a dot and is named by a capital letter. A line segment is a portion of a line that includes two points and all the points between those two points. Knowing these definitions will help you learn the meanings of other geometric words. Poly means many and hedron means. So, a polyhedron is a figure with many s. Recall, a polygon is a closed figure formed by three or more line segments. A geometric solid is a bounded three-dimensional geometric figure. A polyhedron is a three-dimensional solid figure that is made up of polygons. A is one of the polygons that makes up a polyhedron. An edge is the intersection of two s of a three-dimensional figure. The point where multiple edges meet is known as a vertex of a three-dimensional figure. Let s revisit the different figures you sorted. 1. Sort the figures into one of these three categories and explain your reasoning. Polygon Polyhedron Neither LESSON 1: Length, Width, and Depth M1-117
4 Three polyhedra are shown. Figure A Figure B Figure C A unit cube is a cube whose sides are all 1 unit long. Figure A is a right rectangular prism. A right rectangular prism is a polyhedron with three pairs of congruent and parallel rectangular s. Figure B is an example of a cube, which is a special kind of right rectangular prism. A cube is a polyhedron that has congruent squares as s. Figure C is an example of a rectangular pyramid. A pyramid is a polyhedron with one base and the same number of triangular s as there are sides of the base. When you have more than 1 vertex, you say vertices.. Describe the different s of each polyhedron. 3. Study the right rectangular prism. Identify the three pairs of congruent parallel s.. Study the cube. a. Describe the locations of the cube s you can see and the locations of the s you cannot see. b. What do you know about the length, width, and height of the cube? c. Describe how the cube is also an example of a right rectangular prism. M1-118 TOPIC 3: Decimals and Volume
5 5. Compare the numbers of s, edges, and vertices of the cube and the other right rectangular prism. Write what you notice. NOTES 6. Study the rectangular pyramid. How do the s of the rectangular pyramid differ from the s of the rectangular prisms? 7. List examples in the real-world objects that are shaped like right rectangular prisms or pyramids. ACTIVITY 1. Volume of Rectangular Prisms Volume is the amount of space occupied by an object. The volume of an object is measured in cubic units. The volume of a cube is calculated by multiplying the length times the width times the height. Volume of a cube 5 l 3 w 3 h 1. Calculate the volume of each cube with the given side length. a centimeter b centimeters. Suppose a cube has a volume of 7 cubic meters. What are the dimensions of the cube? LESSON 1: Length, Width, and Depth M1-119
6 To determine the volume of a rectangular prism, you can also pack the prism with cubes. You may have done this in elementary school. Consider the rectangular prism shown. What do you notice about the side lengths? Can you determine its volume by packing it with cubes? 3 in. 1 1 in. 1 in. WORKED EXAMPLE To determine the volume of the right rectangular prism with dimensions , you can fill the prism with cubes. However, the unit cubes that you may have used in elementary school will not work here. Instead, smaller unit cubes with fractional side lengths are required. Assign a unit fraction to the dimensions of each cube. Use the least common multiple (LCM) of the fraction denominators to determine the unit fraction. Determine the number of cubes needed to pack the prism in each dimension. LCM(, ) 5 So, each cube will measure 1 in. 3 1 in. 3 1 in. The volume of each unit cube is 1 cubic inches. 6 length width height Determine the number of cubes that make up the right rectangular prism. Multiply the number of cubes by the volume of each cube to determine the volume of the right rectangular prism The volume of the right rectangular prism is 9 cubic inches. 16 M1-10 TOPIC 3: Decimals and Volume
7 3. Interpret the worked example. a. How was the number of cubes needed to pack the prism in each dimension determined? NOTES b. Instead of cubes with a width of 1 inch, suppose you used cubes each with a width of 1 8 inch. How does this change the volume of the rectangular prism?. Use the method from the worked example to determine the volume of each rectangular prism. a. b. 1 3 in. by 1 3 in. by 1 in. 1 in. 3 in. 3 8 in. LESSON 1: Length, Width, and Depth M1-11
8 ACTIVITY 1.3 Volume Formulas You have calculated the volume of a rectangular prism using the formula V 5 lwh, where V is the volume, l is the length, w is the width, and h is the height. You also know that the area of a rectangle can be calculated using the formula A 5 l? w. Consider the two formulas: V 5 l? w? h A 5 l? w If B is used to represent the area of the base of a rectangular prism, then you can rewrite the formula for area: B 5 l? w. Now consider the two formulas: You can use the formula V 5 Bh to calculate the volume of any prism. However, the formula for calculating the value of B will change depending on the shape of the base. V 5 l? w? h B 5 l? w Using both of these formulas, you can rewrite the formula for the volume of a rectangular prism as V 5 B? h, where V represents the volume, B represents the area of the base, and h represents the height. In order to calculate the volume of various geometric solids you will need to perform multiplication. In this activity, you will calculate the volume of rectangular prisms with decimal side lengths. Consider the right rectangular prism shown. It is good practice to estimate before you actually calculate. If you have an estimate, you can use it to decide whether your answer is correct m 3.6 m 7.3 m M1-1 TOPIC 3: Decimals and Volume
9 To calculate the volume of the prism, first calculate the area of the base, B, by multiplying 3.6 meters by 7.3 meters. Kenny said, I use estimation to help place the decimal point correctly in the product. WORKED EXAMPLE The area of the base is 3.6 meters meters. He estimates his two numbers. 3.6 is close to is close to Multiply decimals as you would with whole numbers. Then place the decimal point in the product. So he knows his product is close to 10, but larger since he rounded down. Next, he calculates the product of Kenny knows the product will be close to but greater than 10, so he must place the decimal point after the 8. The area of the base of the rectangular prism is 38.7 square meters. 1. Calculate the volume of the right rectangular prism. LESSON 1: Length, Width, and Depth M1-13
10 . Each number sentence represents the base, B, times height, h, of different rectangular prisms. Complete each number sentence by inserting a decimal point to show the correct volume. a sq. ft ft 5 88 cu. ft b. 7.9 sq. cm cm 5 7 cu. cm c. 0.9 sq. m 3.9 m cu. m 3. Casey thought that using a pattern would help her understand how to calculate the product in a decimal multiplication problem. a. Complete the table. Problem Product Problem Product Problem Product b. Describe any patterns that you notice. M1-1 TOPIC 3: Decimals and Volume
11 . A rectangular prism with B 5 6 square centimeters and h 5 31 centimeters has a volume of 806 cubic centimeters. Use this information to determine the volume of the other rectangular prisms. a..6 sq. cm 3 31 cm b..6 sq. cm cm c. 0.6 sq. cm cm d..6 sq. cm cm e. 0.6 sq. cm 3 31 cm f..6 sq. cm cm g sq. cm cm h. 0.6 sq. cm cm 5. Look at the patterns in Question. a. How can some of the rectangular prisms have the same volume? b. How can you tell without multiplying which rectangular prisms will have the same volume? LESSON 1: Length, Width, and Depth M1-15
12 NOTES TALK the TALK Fractionally Full 1. Determine the volume of a right rectangular prism with dimensions 1 1 feet 3 1 foot 3 1 foot using the unit fraction method you learned in this lesson.. Haley makes earrings and packages them into cube boxes that measure 1 6 -foot wide. How many 1 6 -foot cubic boxes can she fit into a shipping box that is feet by 1 3 foot by 1 3 foot? 3. The school athletic director has a storage closet that is 1 feet long, 3 feet deep, and 6 feet tall. a. She wants to put carpet in the closet. How much carpeting will she need? b. The athletic director wants to store cube boxes that are 1 foot wide. How many boxes will the storage closet hold?. Estimate the volume of each right rectangular prism. Then calculate its volume. a. 0.1 ft 1.9 ft 1.1 ft b..5 ft. ft 9.3 ft M1-16 TOPIC 3: Decimals and Volume
13 Figure 1 Figure Figure 3 Figure Figure 5 Figure 6 Figure 7 Figure 8 LESSON 1: Length, Width, and Depth M1-17
14
15 Assignment Write Suppose a rectangular prism has fractional edge lengths. Describe how you can determine the dimensions of cubes that will fill the rectangular prism completely with no overlaps or gaps. Remember The volume of a rectangular prism is a product of its length, width, and height: V 5 l? w? h. Practice 1. Consider the right rectangular prism shown cm 8.5 cm.5 cm a. List the numbers of s, edges, and vertices of the rectangular prism. b. Estimate the volume of the rectangular prism. c. Calculate the volume of the rectangular prism.. Calculate the volume of the rectangular prism with each set of given dimensions. a. 7 in. 3 in. 3 in. b. 5. cm 3 5. cm 3 1 cm c cm cm cm d..5 m 3 9 m m e.. ft ft 3 15 ft Stretch Calculate the volume for the triangular prism. 6 cm 5. cm 10 cm LESSON 1: Length, Width, and Depth M1-19
16 Review 1. Elena wants to put together some of her favorite songs on her computer. She wants to store 60 minutes worth of music. Elena wonders how many songs she will be able to include. She looks online and finds a source that says the average song length is 3 1 minutes. If this is true, about how many songs will Elena be able to store? Show your work.. Ling is a camp counselor at a local summer camp. She is in charge of the weekly craft activity for 0 campers. Ling plans to make fabric-covered frames that each require 1 yard of fabric. When Ling sets up 6 for her craft activity, she measures the four separate fabric remnants her director gave her. The table shows how much of each fabric she has. How many campers can use plaid fabric? Show your work. Fabric Amount (yards) Plaid 11 1 Tie-dyed Striped 9 Polka-dotted Represent each product using an area model. Then calculate the product. a b Determine the GCF of each set of numbers. a. 7 and 30 b. 30 and 5 5. Determine the LCM of each set of numbers. a. 10 and 1 b. 8 and 9 M1-130 TOPIC 3: Decimals and Volume
Volume 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
3.1 Deepening Understandings of Volume Parts 1_2.notebook. September 05, 2018 M Jun 27 10:28 AM
M1 115 Jun 27 10:28 AM 1 Learning Targets Jun 20 10:53 AM 2 9/4 /18 # Glue pages 1 & 2 into notebook M1: 3.1 Deepening Understanding of Volume Essential Question: How can you use what you know to calculate
Polygons. 5 sides 5 angles. pentagon. no no R89. Name
Lesson 11.1 Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number of angles
Math 6: Geometry 3-Dimensional Figures
Math 6: Geometry 3-Dimensional Figures Three-Dimensional Figures A solid is a three-dimensional figure that occupies a part of space. The polygons that form the sides of a solid are called a faces. Where
Polygons. 5 sides 5 angles. pentagon. Name
Lesson 11.1 Reteach Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number
GEOMETRY. slide #3. 6th Grade Math Unit 7. 6th Grade Unit 7: GEOMETRY. Name: Table of Contents. Area of Rectangles
Name: 6th Grade Math Unit 7 GEOMETRY 2012 10 17 www.njctl.org 1 Table of Contents Area of Rectangles Area of Parallelograms Area of Triangles Area of Trapezoids Mixed Review Area of Irregular Figures Area
Practice 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
The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net.
The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net. A net is the pattern made when the surface of a solid
CC Investigation 4: Measurement
CC Investigation : Measurement A net is a two-dimensional model that can be folded into a threedimensional figure. Prisms are three-dimensional figures that have two congruent and parallel faces that are
Volume 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
11.4 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
Unit 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
Lesson 9. Three-Dimensional Geometry
Lesson 9 Three-Dimensional Geometry 1 Planes A plane is a flat surface (think tabletop) that extends forever in all directions. It is a two-dimensional figure. Three non-collinear points determine a plane.
About Finish Line Mathematics 5
Table of COntents About Finish Line Mathematics 5 Unit 1: Big Ideas from Grade 4 7 Lesson 1 4.NBT.5, 6 Multiplying and Dividing Whole Numbers [connects to 5.NBT.5, 6] 8 Lesson 2 4.NF.6, 7 Understanding
Lesson 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
Section 9.4. Volume and Surface Area. Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 9.4 Volume and Surface Area What You Will Learn Volume Surface Area 9.4-2 Volume Volume is the measure of the capacity of a three-dimensional figure. It is the amount of material you can put inside
The Grade 5 Common Core State Standards for Measurement and Data specify that students should
Measurement and Data Students have learned that measurement is the process of comparing a quantity to a standard unit. In fifth grade, students convert units within a given measurement system and use these
Grade 6 Mathematics Item Specifications Florida Standards Assessments
Content Standard MAFS.6.G Geometry MAFS.6.G.1 Solve real-world and mathematical problems involving area, surface area, and volume. Assessment Limits Calculator s Context A shape is shown. MAFS.6.G.1.1
Unit 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
Geometry Solids Identify Three-Dimensional Figures Notes
26 Geometry Solids Identify Three-Dimensional Figures Notes A three dimensional figure has THREE dimensions length, width, and height (or depth). Intersecting planes can form three dimensional figures
Problem Solving Find Unknown Lengths OBJECTIVE Solve problems using the strategy guess, check, and revise. Read the Problem.
LESSON 72 Problem Solving Find Unknown Lengths OBJECTIVE Solve problems using the strategy guess, check, and revise. CC.5.NF.5b Zach built a rectangular deck in his backyard. The area of the deck is 00
NAME DATE PERIOD. If the fish tank shown is 80% filled with water, how much water is in the tank? 6.G.2, MP 1
Lesson 1 Multi-Step Example Multi-Step Problem Solving If the fish tank shown is 80% filled with water, how much water is in the tank? 6.G.2, MP 1 A 5,772 cubic inches B 4,617.6 cubic inches C 1,154.4
Volume and Surface Area of Rectangular Prisms All Boxed Up
Volume and Surface Area of Rectangular Prisms SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge, Use Manipulatives, Visualization, Group Presentation, Think/Pair/Share The shape in Figure is a
A 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
Section 9.4. Volume and Surface Area. Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 9.4 Volume and Surface Area INB Table of Contents Date Topic Page # February 6, 2013 Area and Perimeter Table 36 February 6, 2013 Section 9.3 Notes 37 February 11, 2013 Volume and Surface Area
Dividend in the House
Dividend in the House Dividing with Volume and Surface Area 4 WARM UP Estimate each quotient. 1. 268 5 2. 1181 23 LEARNING GOALS Fluently divide multi-digit whole numbers and decimals using long division.
MATH-8 Review Volume of 3D shapes 2018 N Exam not valid for Paper Pencil Test Sessions
MATH-8 Review Volume of 3D shapes 2018 N Exam not valid for Paper Pencil Test Sessions [Exam ID:2YBSPT 1 What is the volume of a cube with a length of 8 inches? A 96 in 3 B 256 in 3 C 512 in 3 D 384 in
SAMPLE TASKS. Concepts Embedded Skills Vocabulary. unit cube. unit cube volume side lengths
Common Core Learning Standards Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.3a. A cube with side length 1 unit, called a unit cube, is
Engage 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
9.2. Formulas for Volume. Are You Ready? Lesson Opener Making Connections. Resources. Essential Question. Texas Essential Knowledge and Skills
9.2 Formulas for Volume? Essential Question How can you use formulas to find the volume of rectangular prisms? How can you use formulas to find the volume of rectangular prisms? Lesson Opener Making Connections
February 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
CCM6+ Unit 12 Surface Area and Volume page 1 CCM6+ UNIT 12 Surface Area and Volume Name Teacher Kim Li
CCM6+ Unit 12 Surface Area and Volume page 1 CCM6+ UNIT 12 Surface Area and Volume Name Teacher Kim Li MAIN CONCEPTS Page(s) Unit 12 Vocabulary 2 3D Figures 3-8 Volume of Prisms 9-19 Surface Area 20-26
Standard 1 Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals.
Stretch Standard 1 Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals. Objective 1: Represent whole numbers and decimals from
Notes: Geometry (6.G.1 4)
Perimeter Add up all the sides (P =s + s + s...) Square A = side 2 A = S 2 Perimeter The distance around a polygon. Rectangle w s L A = Length x Width A = lw Parallelogram A = Base x Height A = h h Triangle
CCBC Math 081 Geometry Section 2.2
2.2 Geometry Geometry is the study of shapes and their mathematical properties. In this section, we will learn to calculate the perimeter, area, and volume of a few basic geometric shapes. Perimeter We
Volume 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.
Someone 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
Chapter 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
Lesson 23: Surface Area
Lesson 23 Lesson 23: Classwork Opening Exercise Calculate the surface area of the square pyramid. Example 1 a. Calculate the surface area of the rectangular prism. Lesson 23: S.142 Lesson 23 b. Imagine
c. If each square foot of sod costs 65 cents, how much will she have to pay to cover her yard?
Name Date 1. Use your ruler to draw a rectangle that measures 4 1 by 2 3 inches, and find its area. 2 4 2. Heather has a rectangular yard. She measures it and finds out it is 24 1 feet long by 12 4 feet
Surface Area and Volume of Solids
Surface Area and Volume of Solids? MODULE 5 LESSON 5. ESSENTIAL QUESTION Nets and Surface Area How can a model help you to solve surface area and volume problems? 6.G. LESSON 5. Volume of Rectangular Prisms
10.1 Prisms and Pyramids
AreasandVolumesofprismsandpyramids20052006.nb 0. Prisms and Pyramids We have already learned to calculate the areas of plane figures. In this chapter we will be calculating the surface areas and volumes
Finding Surface Areas and Volumes of Composite Solids
Finding Surface Areas and Volumes of Composite Solids Recall that the perimeter of a two-dimensional composite figure is the sum of the perimeters of the shapes that make up the figure, minus the lengths
UNIT 12. Volume and Surface Area CCM6+ Name: Math Teacher: Projected Test Date: Vocabulary 2. Basics of 3-D Figures 3 8
UNIT 12 Volume and Surface Area 2016 2017 CCM6+ Name: Math Teacher: Projected Test Date: Main Concept(s) Page(s) Vocabulary 2 Basics of 3-D Figures 3 8 Volume of Rectangular Prisms and Finding Missing
Solid Figures. Name. 22 Topic 18. Reteaching Polyhedrons Prisms
Solid Figures Polyhedrons Prisms Pyramids Reteaching 8- Properties of polyhedrons include vertices, edges, and faces, and base(s). Square Pyramid K Reteaching 8- Not Polyhedrons Cylinder Cone Sphere H
The 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
6th Grade. Slide 1 / 219. Slide 2 / 219. Slide 3 / 219. Geometry. Table of Contents
Slide 1 / 219 Slide 2 / 219 6th Grade Geometry 2015-12-01 www.njctl.org Table of Contents Area of Rectangles Click on a topic to Area of Parallelograms go to that section Area of Right Triangles Area of
Lesson 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
The School District of Palm Beach County Fifth Grade Mathematics Scope rd Trimester
Unit & Go Math! & lessons from each Measurement and Data MA.5.G.5.3 MD.1.1 Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within
11.6 Start Thinking Warm Up Cumulative Review Warm Up
11.6 Start Thinking The diagrams show a cube and a pyramid. Each has a square base with an area of 25 square inches and a height of 5 inches. How do the volumes of the two figures compare? Eplain your
Volume of Triangular Prisms and Pyramids. ESSENTIAL QUESTION How do you find the volume of a triangular prism or a triangular pyramid?
? LESSON 10.2 ESSENTIAL QUESTION How do you find the volume of a triangular prism or a triangular pyramid? Finding the Volume of a Triangular Prism The volume V of a prism is the area of its base B times
Volume of Rectangular Prisms. How can you find the volume of a rectangular prism?
? Name 12.3 Essential Question Volume of Rectangular Prisms How can you find the volume of a rectangular prism? Geometry and Measurement 5.6. lso 5.4.G MTHEMTIL PROESSES 5.1.F, 5.1.G onnect The base of
Chapter 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
Volume of Prisms and Cylinders
Volume of Prisms and Cylinders Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit
422 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
3. 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
Rectangular prism. The two bases of a prism. bases
Page 1 of 8 9.1 Solid Figures Goal Identify and name solid figures. Key Words solid polyhedron base face edge The three-dimensional shapes on this page are examples of solid figures, or solids. When a
Additional 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
Objective: Use multiplication to calculate volume.
Lesson 4 Objective: Use multiplication to calculate volume. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (12 minutes) (5 minutes) (33 minutes)
MATH-G P- Geometry Formulas Exam not valid for Paper Pencil Test Sessions
MATH-G P- Geometry Formulas Exam not valid for Paper Pencil Test Sessions [Exam ID:2M8EKV 1 A soda can has a diameter of 6 centimeters and a height of 13 centimeters. Which is closest to the surface area
Georgia Department of Education FIFTH GRADE MATHEMATICS UNIT 6 STANDARDS
Dear Parents, FIFTH GRADE MATHEMATICS UNIT 6 STANDARDS We want to make sure that you have an understanding of the mathematics your child will be learning this year. Below you will find the standards we
Measurement 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.
PART ONE: Learn About Area of a Parallelogram
13 Lesson AREA PART ONE: Learn About Area of a Parallelogram? How can you use a rectangle to find the area of a parallelogram? Area (A) tells how much surface a two-dimensional figure covers. You can use
Problem Sets. GRADE 5 MODULE 5 Addition and Multiplication with Volume and Area
GRADE 5 MODULE 5 Addition and Multiplication with Volume and Area Problem Sets Video tutorials: http://bit.ly/eurekapusd Info for parents: http://bit.ly/pusdmath 5 GRADE Mathematics Curriculum GRADE 5
Review: Geometry. Area Composite Figures Surface Area Volume Fractional Edge Length 3-D Figures and Nets Coordinate Graphing
Review: Geometry Area Composite Figures Surface Area Volume Fractional Edge Length 3-D Figures and Nets Coordinate Graphing Perimeter: the distance around a polygon. Area: the number of square units needed
TEACHER GUIDE INCLUDES. Tier 1 Tier 2 Tier 3 Correlations. Diagnostic Interviews for Every Common Core Cluster
TEACHER GUIDE FOR THE COMMON CORE STATE STANDARDS FOR MATHEMATICS 3 INCLUDES Tier Tier Tier 3 Correlations Diagnostic Interviews for Every Common Core Cluster Tier Lessons, Tier Prerequisite Skills, and
Surface Area and Volume
8 Surface Area and Volume 8. Three-Dimensional Figures 8. Surface Areas of Prisms 8. Surface Areas of Pyramids 8. Volumes of Rectangular Prisms I petitioned my owner for a doghouse with greater volume.
Math 202: Homework 6 Solutions
Math 202: Homework 6 Solutions 1. ( 11.3 #6) (a) 10 in 4 in 4 in 4 in Notice that each of the bases is a square, so each of the four lateral sides are congruent. Hence, S = 2(4 2 ) + 4(4 10) = 32 + 160
The radius for a regular polygon is the same as the radius of the circumscribed circle.
Perimeter and Area The perimeter and area of geometric shapes are basic properties that we need to know. The more complex a shape is, the more complex the process can be in finding its perimeter and area.
Surface 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.)
Lesson PROBLEM SOLVING
Name Problem Solving Compare Volumes Essential Question: How can you use the strategy make a table to compare different rectangular prisms with the same volume? Unlock the Problem PROBLEM SOLVING Lesson
Draw, construct, and describe geometrical figures and describe the relationships between them.
Focus Standards Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.A.2 7.G.A.3 Draw (freehand, with ruler and protractor, and with technology) geometric
8th Grade. Slide 1 / 97. Slide 2 / 97. Slide 3 / 97. 3D Geometry. Table of Contents. 3-Dimensional Solids. Volume. Glossary & Standards
Slide 1 / 97 Slide 2 / 97 8th Grade 3D Geometry 2015-11-20 www.njctl.org Table of Contents Slide 3 / 97 3-Dimensional Solids Click on the topic to go to that section Volume Prisms and Cylinders Pyramids,
6th Grade. Geometry.
1 6th Grade Geometry 2015 12 01 www.njctl.org 2 Table of Contents Area of Rectangles Area of Parallelograms Area of Right Triangles Area of Acute and Obtuse Triangles Area of Trapezoids Mixed Review Area
Polygon Practice. E90 Grade 5. Name
Lesson 11.1 Polygon Practice Write the number of sides and the number of angles that each polygon has. Then match each description to one of the polygons drawn below. Label the polygon with the exercise
6th Grade Math. Parent Handbook
6th Grade Math Benchmark 3 Parent Handbook This handbook will help your child review material learned this quarter, and will help them prepare for their third Benchmark Test. Please allow your child to
SOLIDS.
SOLIDS Prisms Among the numerous objects we see around us, some have a regular shape while many others do not have a regular shape. Take, for example, a brick and a stone. A brick has a regular shape while
Grade 6 Area and Volume
Name: lass: _ ate: _ I: Grade 6 rea and Volume Multiple hoice Identify the choice that best completes the statement or answers the question. 1. drama teacher is creating a scale model of the school s performing
Lesson 3: Definition and Properties of Volume for Prisms and Cylinders
: Definition and Properties of Volume for Prisms and Cylinders Learning Targets I can describe the properties of volume. I can find the volume of any prism and cylinder using the formula Area of Base Height.
Number/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
21.2 Volume of Pyramids
Name lass ate 21.2 Volume of Pyramids Essential Question: How do you find the volume of a pyramid? Explore eveloping a Volume Formula Resource Locker s shown at the left below, _ has length b, and is any
Three-Dimensional Figures and Nets
Lesson 11.1 Reteach Three-Dimensional Figures and Nets Solid figures have three dimensions length, width, and height. They can be named by the shapes of their bases, the number of bases, and the shapes
Geometry: Notes
Geometry: 11.5-11.8 Notes NAME 11.5 Volumes of Prisms and Cylinders Date: Define Vocabulary: volume Cavalieri s Principle density similar solids Examples: Finding Volumes of Prisms 1 Examples: Finding
Investigate Understand Volume
LESSON 11.6 Progress to Algebra Investigate Understand Volume FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards 5.MD.C.3b Recognize volume as an attribute of solid figures
Measurement 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
Find The Volume Of A Right Rectangular Prism - Step-by-Step Lesson
Find The Volume Of A Right Rectangular Prism - Step-by-Step Lesson Lesson 1 Rectangular Prism Problem A swimming pool is 10m long, 8m wide and 4m deep. Allen wants to know the volume of the swimming pool
1. Using snap cubes, build a rectangular prism with the following dimensions: a. Length 6 units b. Width 2 units c. Height 3 units
Study Guide Fifth Grade Day 151 Standard(s): 5.MD.3, 5.MD.4, 5.MD.5 5.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1
Houston 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
PYRAMIDS AND CONES WHAT YOU LL LEARN. Ø Finding the surface areas and volume of pyramids Ø Finding the surface areas and volume of cones
PYRAMIDS AND CONES A pyramid is a solid with a polygonal base and triangular lateral faces that meet at a vertex. In this lesson, you will work with regular pyramids. The base of a regular pyramid is a
Skills Practice Skills Practice for Lesson 2.1
Skills Practice Skills Practice for Lesson.1 Name Date Backyard Barbecue Introduction to Volume and Surface Area Vocabulary Write the term from the box that best completes each statement. surface area
STAAR Category 3 Grade 7 Mathematics TEKS 7.8A/7.9A. Student Activity 1. Problem 1: The height of a prism is the distance between the two.
Student Activity 1 Work with your partner to answer the following questions. Problem 1: The height of a prism is the distance between the two. The height of a pyramid is the distance from the vertex the
Surface Area of Triangular Prisms - Nets
U2B L6: Students will determine the surface area of a triangular prism Surface Area of Triangular Prisms - Nets Surface area - the area of all the faces of the prism Triangular prism - made up of three
Area. Domain 4 Lesson 25. Getting the Idea
Domain 4 Lesson 5 Area Common Core Standard: 7.G.6 Getting the Idea The area of a figure is the number of square units inside the figure. Below are some formulas that can be used to find the areas of common
CHAPTER. Daniel Nickerson Salisbury, NC. Three-Dimensional Figures 217
CHAPTER 9 Three-Dimensional Figures Daniel Nickerson Salisbury, NC Three-Dimensional Figures 7 9. Three-Dimensional Figures Objective: to classify three-dimensional figures A solid is a three-dimensional
STRAND 1 NUMBER and OPERATIONS
STRAND 1 NUMBER and OPERATIONS Understand division of whole numbers N.MR.05.01 Understand the meaning of division of whole numbers with and without remainders; relate division to fractions and to repeated
Surface Area and Volume
Name: Chapter Date: Surface Area and Volume Practice 1 Building Solids Using Unit Cubes Find the number of unit cubes used to build each solid. Some of the cubes may be hidden. 1. 2. unit cubes 3. 4. unit
Measurement 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
ACCELERATED 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
Mathematical Reasoning. Lesson 47: Prisms and Cylinders. LESSON 47: Prisms and Cylinders. D. Legault, Minnesota Literacy Council,
LESSON 47: Prisms and Cylinders Weekly Focus: prisms, cylinders Weekly Skill: calculate area and volume Lesson Summary: For the warm up, students will solve a problem about the earth and the moon. In Activity
Page 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)